Guillaume Desagulier

A lesson from associative learning: asymmetry and productivity in multiple-slot constructions

Keywords: asymmetry, association measures, ∆P (delta P ), collostructional analysis, construction grammar, adjectives, intensification, productivity

Non-redundant taxonomic models of construction grammar posit that only fully productive patterns qualify as constructions because they license an infinity of expressions. Redundant models claim that, despite subregularities and exceptions, partially productive patterns also count as constructions, providing the overall meanings of such patterns are not the strict sums of their parts. Because productivity is a major bone of contention between redundant and non-redundant construction grammar taxonomies, I examine the productivity of A as NP which, according to Kay (2013), is not a "construction" but merely a "pattern of coining" due to its limited type productivity. Expanding on Gries (2013), this paper explores how a combination of symmetric and asymmetric association measures can contribute to the study of the "Productivity Complex" described in Zeldes (2012). Although the productivity of A as NP is admittedly limited at its most schematic level, some partially-filled subschemas such as white/black as NP or A as hell/death are arguably productive.

Introduction

In Paul Kay's view of Berkeley Construction Grammar, only general and productive schemas such as let alone [START_REF] Fillmore | Regularity and idiomaticity in grammatical constructions: The case of let alone[END_REF]), what's X doing Y [START_REF] Kay | Grammatical constructions and linguistic generalizations: The What's X doing Y? construction[END_REF], or all -clefts [START_REF] Kay | The limits of (Construction) Grammar[END_REF]) qualify as constructions. Patterns such as A as NP do not contain what is necessary and sufficient to interpret and generate other linguistic expressions. They are therefore at the periphery of grammar [START_REF] Kay | The limits of (Construction) Grammar[END_REF]:

(1) stiff as a board

(2) cool as a cucumber

(3) flat as a pancake Admittedly, knowing the meaning of cool and the meaning of cucumber fails to predict the meaning of their combination in (2). Furthermore, this schema cannot be extended freely to similar A-NP pairs (e.g. ?? nervous as a zucchini). Kay concludes that A as NP is not a "construction" but a "pattern of coining".

By comparison, Cognitive Construction Grammar [START_REF] Goldberg | Constructions: A construction grammar approach to argument structure[END_REF][START_REF] Goldberg | Constructions at work: The nature of generalization in language[END_REF][START_REF] Goldberg | The nature of generalization in language[END_REF] is redundant: any pattern that is sufficiently entrenched and whose overall meaning is not the sum of the meaning of its parts counts as a construction. Based on these premises, even A as NP, counts as a construction.

Since the constructional status of A as NP differs depending on the theoretical perspective that one adopts, my aim is to test the boundary between what counts as a construction and what does not. To do this, I assess the productivity of A as NP in the 100-million-word British National Corpus (XML Edition).

In both Construction Grammar approaches, the productivity of a complex expression is generally indexed on type frequency (Croft & Cruse 2004, 309). As regards A as NP, this is problematic because the productivity of the pattern is more complex than it seems. Even though semantic constraints block some A-NP pairings (e.g. ?? safe as buildings) and make A as NP less productive than alledgedly full-fledged "constructions" such as let alone, what's X doing Y, or all -clefts, the pattern generates subschemas whose productivity is non-negligible, e.g. white as NP (white as snow/a sheet/a whiteboard/etc.), pale as NP (pale as a ghost/death/parchment/etc.), A as hell (mad/hot/angry/etc. as hell ), or (as) A as a cat ((as) jumpy/smug/tense/etc. as a cat).

The productivity of A as NP is therefore more complex than Kay suggests, and the difference between a "construction" and a "pattern of coining" needs deeper empirical foundations. Because A as NP has two lexically unspecified slots, a complete assessment of its productivity should not be restrained to the schematic level. It should also involve a complementary inspection of productivity at subschematic levels, where the construction is partially or fully specified. These levels concern: (a) the first slot, (b) the second slot, and (c) their combinations.

Hapax-based productivity measures have been implemented in morphology [START_REF] Baayen | A corpus-based approach to morphological productivity[END_REF][START_REF] Baayen | Productivity and English derivation: A corpus-based study[END_REF][START_REF] Baayen | Quantitative aspects of morphological productivity[END_REF][START_REF] Baayen | On frequency, transparency and productivity[END_REF] and applied with success in the syntactic domain, especially in the context of multiple-slot constructions [START_REF] Zeldes | Productivity in argument selection: From morphology to syntax[END_REF]. Such measures imply that productive linguistic units produce a large number of rare tokens. I will use these measures to show to what extent A as NP is productive and deserves a constructional status according to BCG (a position that I adopt for methodological purposes, without theoretical endorsement).

Zeldes (2012) also demonstrates that lexical choice is often mutually constrained in multiple-slot constructions. More precisely, observing one slot influences the expected realization of the other slot. This is in keeping with a key principle from associative learning: speakers tend to infer a linguistic outcome from cues available in their linguistic environment in an asymmetric fashion [START_REF] Ellis | Language acquisition as rational contingency learning[END_REF][START_REF] Gries | 50-something years of work on collocations: What is or should be next[END_REF]. To develop this point further, I will apply a directional association measure, ∆P [START_REF] Allan | A note on measurement of contingency between two binary variables in judgment tasks[END_REF], to the study of A as NP. Given a specific instance of A as NP, if ∆P reveals that the adjective is a better cue of the NP than vice versa, it is because the NP co-occurs with more adjectives. Conversely, if ∆P reveals that the NP is a better cue of the adjective than vice versa, it is because the adjective co-occurs with more NPs. ∆P alone cannot be used as a measure of productivity because it is based on token frequencies, not type frequencies. For a subschema indexed on an adjective to be considered productive, it must attract a significant number of distinct NP types. Likewise, for a subschema indexed on a NP to be considered productive, it must attract a significant number of distinct A types. However, once combined with the abovementioned productivity measures, ∆P can contribute to a better understanding of the productivity of multiple-slot constructions. Indeed, if it is confirmed that the choice of a slot influences the realization of the other slot, ∆P can specify the direction of this association.

In parallel, I will also examine attraction patterns between A and NP using a symmetric measure, namely log-likelihood ratio [START_REF] Dunning | Accurate methods for the statistics of surprise and coincidence[END_REF]. My assumption will be that the most strongly associated A-NP pairs are also the most conventional, the most autonomous, and the least productive. Again, this measure will be evaluated against hapax-based productivity measures and ∆P .

This paper is organized as follows. Section 2 reviews competing accounts of what counts as a construction and suggests ways in which opposing views can be reconciled thanks to an empirical assessment of productivity in construction grammar. Section 3 compares the assets of symmetric and asymmetric association measures and discusses to what extent these measures have a bearing in the productivity assessment of a two-slot construction. Section 4 combines hapax-based measures and association measures to assess the productivity of A as NP and maps the results with principal component analysis. Section 5 discusses the results and argues that by augmenting productivity measures with a combination of symmetric and asymmetric association measures, one can estimate the productivity of a pattern in more details than if one were to rely only on traditional productivity measures.

2 Theoretical issues 2.1 What counts as a construction: plain as day or clear as mud?

Construction grammar is a generic term for a family of approaches that focus on the grammatical status of syntax-semantics pairings: Berkeley Construction Grammar [START_REF] Fillmore | Construction grammar lecture notes[END_REF][START_REF] Fillmore | Regularity and idiomaticity in grammatical constructions: The case of let alone[END_REF][START_REF] Kay | Grammatical constructions and linguistic generalizations: The What's X doing Y? construction[END_REF], Cognitive Construction Grammar [START_REF] Goldberg | Constructions: A construction grammar approach to argument structure[END_REF][START_REF] Goldberg | Constructions: A new theoretical approach to language[END_REF][START_REF] Goldberg | Constructions at work: The nature of generalization in language[END_REF][START_REF] Goldberg | The nature of generalization in language[END_REF], Cognitive Grammar [START_REF] Langacker | An introduction to cognitive grammar[END_REF][START_REF] Langacker | Foundations of cognitive grammar[END_REF][START_REF] Langacker | Cognitive grammar: A basic introduction[END_REF][START_REF] Langacker | Investigations in cognitive grammar[END_REF], Radical Construction Grammar [START_REF] Croft | Radical Construction Grammar: Syntactic theory in typological perspective[END_REF], Fluid Construction Grammar [START_REF] Steels | Design patterns in Fluid Construction Grammar[END_REF][START_REF] Steels | Computational issues in Fluid Construction Grammar[END_REF], and Embodied Construction Grammar [START_REF] Bergen | Embodied Construction Grammar in simulation-based language understanding[END_REF]. All construction grammar approaches offer a non-derivational representation of grammatical knowledge and posit that grammar consists of a large inventory of constructions, varying in size and complexity, and ranging from morphemes to fully abstract phrasal patterns. Yet, not all theories agree as to how grammatical information is stored in the construction taxonomy, among other criteria. According to Croft & Cruse (2004, 257-290), there exist four taxonomic models. In the full-entry model, information is stored redundantly at various levels of the taxonomy. In the usage-based model, grammatical knowledge is acquired inductively, speakers generalizing over recurring experiences of use. In the normal-inheritance model, constructions with related forms and meanings are part of the same network. In the complete inheritance model, grammatical knowledge is stored only once at the most superordinate level of the taxonomy. The first three models are not mutually exclusive, each targeting a specific problem (e.g. the full-entry model resolves multiple inheritance conflicts). The last model is the odd one out because it leaves no room for redundancy.

Berkeley Construction Grammar (henceforth BCG) is a complete-inheritance model. It is nonredundant and it maintains a sharp distinction between "grammar" and the "meta-grammar". 1 "Grammar" is understood as "the strictly linguistic information required to produce and understand all possible utterances of a language, and no more" (Kay 2013, 30), whereas the "meta-grammar" consists of "patterns [that] are neither necessary nor sufficient to produce or interpret any set of expressions of the language (. . . )" (Kay 2013, 33). Given the above, only patterns that are general and fully productive qualify as constructions. Such is the case of all -cleft constructions:

(4) All I want is to stand and look at you, dear boy! (BNC-FPU)

Along with other cleft structures such as wh-clefts, all -clefts inherit their syntax from an abstract construction. What makes an all -cleft unique, and justifies its place as a construction in the grammar, is the scalar function, which Kay names the " 'below-expectation' reading". This reading is distinct from the default universal quantification reading illustrated in (5).

(5) All that I command is yours now. (BNC-FR0)

All -clefts such as (4) are fully productive because they are only constrained at the lexical level "with respect to the filler constituent of the subject phrase" (Kay 2013, 37), and because they offer a way to rule in the good cases and rule out the bad cases without listing them.

In contrast, patterns that are partially or imperfectly productive are relegated to the meta-grammar. Such is the case of A as NP, as exemplified in (1)-(3) above, and (6) below:

(6) a. dark as night b. black as pitch c. thin as a rail d. cold as hell Despite the pairing of an identifiable syntax (A as NP ) and a specific reading ("very A"), Kay considers A as NP "non-constructional" and "non-productive" because (a) knowing the pairing is not enough to license and interpret existing tokens (especially when there is no obvious semantic link between the adjective and the NP, as in easy as pie), and (b) speakers cannot use the pattern freely to coin new expressions. Kay concedes that the pattern has "many members" but each addition appears via "analogical creation" (Kay 2013, 38). Two idiosyncrasies further block A as NP from qualifying as a construction (Kay 2013, 39). First, some expressions are motivated by a literal association between the adjective and the NP (tall as a tree, white as snow ), 2 whereas others hinge on figurative associations between A and NP, including possible puns (safe as houses) 3 , and yet others are the sign that the NP has grammaticalized to intensifying functions (jealous as hell, sure as death). Second, some expressions are compatible with a than-comparative (flat as a pancake > flatter than a pancake) whereas others are not (happy as a lark > ?? happier than a lark ). Such idiosyncrasies provide BCG with further evidence that expressions of the A as NP kind are not generated by a rule (i.e. a "construction") but must be learned individually.

A pattern of coining may grow into a construction diachronically, thus augmenting the existing grammar via the creation of a new linguistic type. But in BCG, diachronic productivity is of little help because it fails to explain how new utterance tokens are created in accordance with the existing grammar (Kay 2013, 44). In other words, BCG's sole focus is on synchronic productivity.

Because it is a "severe view of grammar" (Kay 2013, 33), BCG treats as non-constructional patterns that would count as full-fledged constructions in normal-entry models of construction grammar such as Cognitive Construction Grammar (henceforth CCG). CCG considers that grammatical knowledge is acquired inductively. Therefore, the inventory of constructions is internally redundant and allows for subregularities and exceptions (Goldberg 1995, 73-74). Consequently, a CCG account of grammar contradicts each of the tenets of BCG outlined in the previous paragraphs. First, according to (a) above, all expressions based on a construction are interpretable regardless of previous exposure. Because A as NP is not a construction in BCG, the meaning of easy as pie and easy as duck soup is supposedly inaccessible to "a young, foreign, or sheltered speaker of English" even if the speaker knows the meanings of easy, pie, duck and soup (Kay 2013, 38). However, putting aside the (hopefully) rare case of a sheltered language learner, we could reasonably posit that when there is no semantic motivation from the NP, such motivation can arise from the adjective. Indeed, we may reasonably expect that through exposure to tokens of A as NP, a learner will infer that expressions such as easy as spit, easy as wink, or easy as apple pie mean "very easy" in contexts where no spit, wink, or apple pie is readily available.

Second, according to (b) above, only a construction allows the speaker to coin new expressions freely. Accordingly, Kay distinguishes cases of full creativity (a construction can generate an infinite number of expressions) from "analogical creations" (typical of patterns of coining and more limited in terms of the number of generated expressions). Admittedly, A as NP cannot be applied freely to build new expressions on the model of some highly conventional expressions. Even though its NP has nothing to do with vegetables, the idiomatic expression in (7c) is a far more likely antonym of (7a) than (7b):

(7) a. cool as a cucumber b. ?? nervous as a tomato/potato/zucchini/etc. c. as nervous as a long-tailed cat in a room full of rocking chairs Yet, there is evidence that, contrary to what Kay (2013, 38) claims, not all novel A as NP expressions "die aborning", and not all of them are the product of "self-conscious, literary usage". Some patterns, such as easy as pie, are sufficiently established to serve as templates for the creation of syntacticallyand semantically-related expressions:

(8) a. What I'm sayin', Benedict can take you out as easy as cake. More generally, even when some expressions are lexically filled, speakers are not necessarily blocked from creating new expressions when the adjective and the NP are semantically compatible. For example, since a hot-air balloon is big and can fly high, it is a good candidate for the intensification of big and high, including when these adjectives are used figuratively:

(12) a. (. . . ) he had a head as big as a hot air balloon.

(The Adventures of Jack Lime, James Leck) b. My denial bubble was about as big as a hot air balloon.

(Close to Mummy's Heart, Mary Cromwell-Hillenburg)

(13) a. Taking agritourism as high as a hot-air balloon. (smallfarms.cornell.edu) b. I was just high as a hot-air balloon. I didn't hear a word he said.

(Paradise Park, Allegra Goodman)

Whether some uses are considered as self-conscious or literary depends largely on the corpus that one adopts, and even nonce expressions are the sign that not yet attested expressions should not be ruled out as ungrammatical in the absence of empirical evidence. 4 Examples ( 10) and (11) above, and example ( 14) below make it clear that A as NP patterns are available for the creation of new tokens, or for the modification of existing tokens, even when the A-NP pairing appears to be fixed: ( 14) "Quicker Than a Wink:" Photographs by Harold Edgerton. (www.amherst.edu)

Excluding these examples from a BCG inventory of constructions is consistent with the tenets of a non-redundant view of grammar, but somewhat at odds with usage. I will argue below that it takes more than a cursory corpus search to assess the productivity of a pattern and decide whether it has the status of a construction, regardless of the theoretical premisses. At this point, productivity cannot be discussed further without a clear understanding of how the concept is used and how it can be operationalized in construction grammar approaches.

Productivity in construction grammar

According to [START_REF] Bybee | Morphology: A study of the relation between meaning and form[END_REF][START_REF] Bybee | Phonology and language use[END_REF][START_REF] Bybee | Language, usage, and cognition[END_REF], the account of morphological productivity outlined above also applies to morphosyntactic constructions in an exemplar framework. 5 As an exemplar of a construction reaches a certain token-frequency threshold, it is likely to be stored as a unit in the minds of speakers. As high-frequency tokens and formulaic expressions lose in terms of analyzability, compositionality, and productivity, they gain in terms of autonomy. In other words, autonomous units do not reinforce a schema if the schema can be generalized. Although productive with respect to type, WXDY and all -clefts generate instances that are not themselves so productive given the lexical openness and contextual specificity of their respective schemas.

Theoretical approaches

In other words, tokens modelled on WXDY or all -clefts rarely occur more than once, and this is precisely what keeps the mental representation of the constructions active in the minds of speakers. Such schemas are therefore productive at a the highest level of schematicity. In contrast, even though A as NP is somewhat restrained as to the number of A-NP pairs that it sanctions, among the many instances that are built on this schema, some have a relatively high token frequency (in the BNC, such is the case of good as gold, cold as ice, large as life, bold as brass, safe as houses, etc.). Some pairs are fixed (cool as a cucumber ), but many others are not. Among the latter, some instances are modelled on productive subschemas, e.g. A as hell/death, white/black/old as NP, etc. As will appear below, deciding on the productivity of A as NP requires inspecting more than the highest level of schematicity.

Three issues may be raised with respect to productivity in Kay's view of BCG. Firstly, as pointed out in [START_REF] Barðdal | Productivity: Evidence from case and argument structure in Icelandic[END_REF], BCG does not provide a unified definition of productivity, especially with regards to whether it is graded. Kay and Fillmore (1999, 31) seem to recognize several levels of productivity, ranging from partially productive (idiomatic, lexically filled) to fully productive (schematic) patterns: (. . . ) a construction-based approach appears to provide promise of accounting both for the relatively idiomatic and for the abstract and more fully productive aspects of a language.

However, in more recent works, Kay and Fillmore do not express similar views anymore. On the one hand, [START_REF] Kay | The limits of (Construction) Grammar[END_REF] understands productivity in an all-or-none fashion: patterns that are completely and fully schematic are productive whereas other patterns are not. On the other hand, [START_REF] Fillmore | Idiomaticity[END_REF] recognizes that "productivity is a notion of degree". Fillmore does distinguish productivity (i.e. applying a general rule without listing exceptions) from coining (exploiting unproductive patterns in the creation of new expressions). However, he does not relegate coining to the periphery of the "grammar proper" on account of partial or lacking productivity:

There is a view of grammar according to which the grammar proper will identify only the productive processes. Since the ability to create new words, using non-productive processes, is clearly a linguistic ability, it is my opinion that a grammar of a language needs to identify constructions that exist for "coining" purposes as well.

Fillmore admits that constructions are assumed to exist at all levels of schematicity (i.e. productive and less productive), a tenet shared by CCG. Elaborating on the terminology proposed by Barðdal (2008, 37), we can summarize the difference between Kay and Fillmore as follows: the former posits a regularity vs. extensibility distinction (productivity being indexed on regularity alone) whereas the latter posits a regularity vs. extensibility continuum (productivity being indexed on both). There being no general consensus on positing a radical view such as Kay's, one can choose either to disregard it on the grounds that it is a matter of theoretical preference (Barðdal 2008, 36-37) or to test it empirically. In the sections that follow, I choose the second option.

Secondly, the correlation between schematicity and productivity assumed by Kay is problematic. Bybee (2010, 94-95) observes that, in the construction V someone A (e.g. she drove me crazy) 6 , the adjective slot is very productive because it is quite open. In comparison, the verb slot is more schematic yet less productive, because open to a limited number of types, such as drive, send, or make. Just because a pattern is schematic does not mean that it is productive. Furthermore, as Croft and Clausner note, there are various levels of schematicity: "The instanciation of one schema may function as an intermediate schema for other more specific instantiations" (Croft & Clausner 1997, 251). Just because a pattern is not productive at the highest schematic level does not mean that it is unproductive at subschematic levels.

Finally, if we accept the view that morphosyntactic productivity corresponds to the likelihood that a construction will apply to a new item, we may still question that the productivity of a construction should be entirely determined by its type frequency. Other factors have been recognized to play a role, such as semantic similarity between tokens [START_REF] Croft | Productivity and schematicity in metaphors[END_REF] or semantic coherence [START_REF] Barðdal | Productivity: Evidence from case and argument structure in Icelandic[END_REF]. Moreover, cognitive-functional approaches to frequency effects on productivity posit a clear-cut distinction between high and low frequencies (whether type or token) [START_REF] Langacker | Foundations of cognitive grammar[END_REF][START_REF] Bybee | Morphology: A study of the relation between meaning and form[END_REF][START_REF] Bybee | Phonology and language use[END_REF][START_REF] Croft | Productivity and schematicity in metaphors[END_REF]. Once we try to operationalize this theoretical threshold, we realize that the boundary between what is frequent and infrequent in a corpus is relative. [START_REF] Bybee | Language, usage, and cognition[END_REF] illustrates her claims on frequency effects with several case studies (e.g. the English auxiliary sequence, the difference between no and not negation, etc.), but most of them are broad enough to return contrasted frequency scores. We should not be blinded to the fact that many patterns occur at intermediate frequency levels, where the difference between what is highly frequent and what is not is intuitively fuzzy.

Quantitative approaches

Productivity has received sustained attention in morphology. Broadly defined, morphological productivity is the property of an affix or a word-formation rule to generate new formations in a systematic way [START_REF] Plag | Word-formation in English[END_REF]. The more an affix is available for the creation of new words, the more productive it is. Less general processes generate new words in a local, ad-hoc fashion. For example, speakers may use existing affixes to derive new words analogically, e.g. beigeness and beigity [START_REF] Bauer | Morphological productivity[END_REF]. At a qualitative level, given the existence of rare but actual coinages, it is difficult to draw the line between productive and less productive processes.

In response, quantitative approaches have developed measures to capture the productivity of morphological processes in corpora. The first measure is V (C, N ), i.e. the type count V of the members of a morphological category C in a corpus of N tokens. It captures what [START_REF] Baayen | Corpus linguistics in morphology: Morphological productivity[END_REF] calls "realized productivity". One problem with indexing a measure on type is that it does not discriminate between established forms and new forms. Indeed, types are not distributed uniformly in a corpus, and the larger the corpus, the harder it is to find innovations. To keep track of vocabulary development across a given corpus, one can plot the number of types against the number of tokens at multiple intervals. One obtains a vocabulary growth curve (henceforth VGC) [START_REF] Baayen | On frequency, transparency and productivity[END_REF]. At first, the curve is expected to rise steeply as most tokens define a new type. Then, as more text is scanned, more and more tokens are included in already defined types, and the curve flattens out gradually. VGCs are a handy way of visualizing productivity: the steeper the curve, the more productive the linguistic unit/process under study.

A second set of measures, based on [START_REF] Baayen | A corpus-based approach to morphological productivity[END_REF] and further described in Baayen and[START_REF] Baayen | Productivity and English derivation: A corpus-based study[END_REF][START_REF] Baayen | On frequency, transparency and productivity[END_REF] inter alia, draws on the idea that the number of hapax legomena of a given morphological category correlates with the number of neologisms in that category, which in turn correlates with the productivity of the rule at work. Baayen estimates "expanding productivity" (also known as P*, the "hapax-conditioned degree of morphological productivity") as the number of hapax legomena in the category divided by the number of hapax legomena in the corpus:

P * = V (1, C, N ) V (1, N ) (i)
P* does not account for whether a morphological process, although productive, is saturated, unlike P, which measures "potential productivity". P is the ratio of the number of hapax legomena with a given affix and the sum of all tokens that contain the affix:

P = V (1, C, N ) N (C) (ii)
P corresponds to the probability of encountering new types. The larger the number of hapax legomena, the larger P and the productivity of the affix. Conversely, the larger the sum of all tokens, the smaller P and the productivity of the affix. One mathematical property of P is that it is the slope of the tangent to a VGC at its endpoint. It indicates the rate at which vocabulary increases at the end of a vocabulary growth curve. Like VGCs, P values must be compared at equal sample sizes. [START_REF] Baayen | On frequency, transparency and productivity[END_REF] explores further the correlation between productivity and frequency and observes that P captures only the probability of possible types to the detriment of observed types. He advocates for a measure of global productivity (P * ) which evaluates P in terms of type frequency (i.e. actual use):

P * = V P (iii)
Underlying Baayen's hapax-based measures is the following principle: productivity is a factor of both a large number of low-frequency words and a low number of high-frequency words. This combination contributes to parsing effects which maintain the affix activated in the minds of speakers. 7 Zipf (1949) showed that even the largest collection of text in a given language does not contain instances of all types in that language. Therefore, type count and distribution in a corpus cannot reliably estimate type count and distribution in a language. To circumvent this issue and predict the vocabulary size in a larger corpus or a whole language based on a much smaller corpus, [START_REF] Baayen | Word frequency distributions[END_REF] uses LNRE models (the acronym stands for "large number of rare events"). First, one converts the data into a frequency spectrum (i.e. a table of frequencies of frequencies). Next, one fits a model to the spectrum object, choosing from a range of LNRE models available in the zipfR package [START_REF] Evert | The zipfR library: Words and other rare events in R. Presentation at useR! 2006[END_REF], 2007) for R (R Core Team 2014), namely the Zipf-Mandelbrot model (ZM), the finite Zipf-Mandelbrot model (fZM), or the Generalized Inverse Gauss-Poisson model (GIGP). Once a satisfactory LNRE model has been fitted to the frequency spectrum, one obtains expected values for the vocabulary size and the spectrum elements within the range of the corpus/sample size (interpolation) and beyond (extrapolation). One can then plot the results on an enhanced VGC. LNRE models make it possible to compute S, the limit of V when N approaches infinity (Baayen 2001, Section 2.4):

S = lim N →∞ E[V (N )] (iv)
S is recognized to be an estimate of the total possible number of types for a given process. 8 [START_REF] Zeldes | Productivity in argument selection: From morphology to syntax[END_REF] shows that Baayen's family of hapax-based measures and LNRE models apply equally well to morphosyntactic constructions, providing one is willing to adapt the definitions of type and type count to the structural configuration of the construction under study. In the context of a construction with an invariable part and one slot to be filled, productivity is measured at the level of that single open slot. 9 In the context of a two-slot construction, 10 Zeldes (2012, 127) presents two options to compute hapax-based measures, plot growth curves, and fit LNRE models. The first option consists in concatenating the two slots to produce a single fused type -e.g. good_gold -which is then tested for productivity. If a given exact concatenation has not been observed before in the corpus, it is treated as a hapax legomenon. If it is observed again, it leaves the hapax list. However this first option makes little sense in the context of A as NP, where we can reasonably expect the A slot and the NP slot to be interdependent both semantically (A is intensified with reference to NP) and structurally (both A and NP are required by the form of the construction). The second option consists in treating as new types innovations in at least one slot. In this case, "novel combinations of lexemes already observed in their respective slots are considered repetitions" (Zeldes 2012, 128). Both options will be compared in Section 4.1.

The next sections will address the question of how we can determine the multilayered productivity of A as NP at various levels of schematicity. Qualitatively speaking, I will assume that productivity is a gradient that involves autonomy and analyzability, in the wake of [START_REF] Bybee | Morphology: A study of the relation between meaning and form[END_REF][START_REF] Bybee | Phonology and language use[END_REF][START_REF] Bybee | Language, usage, and cognition[END_REF], [START_REF] Croft | Radical Construction Grammar: Syntactic theory in typological perspective[END_REF][START_REF] Croft | Productivity and schematicity in metaphors[END_REF][START_REF] Barðdal | Productivity: Evidence from case and argument structure in Icelandic[END_REF]. Quantitatively speaking, I will follow Zeldes (2012, 135), who substantiates the idea that syntactic productivity is multidimensional: different measures will sometimes yield different productivity rankings, even at equal sample sizes. To capture what Zeldes calls the "Productivity Complex", I will examine frequency data not only in the light of the traditional productivity measures outlined above, but also in the light of symmetric and asymmetric association measures. I am aware that the question of whether association measures can even begin speak to the issue of productivity may raise serious doubts among linguists. Yet it is my intuition that valuable insights can be also drawn from such measures regarding the inner workings of productivity in multiple-slot constructions. I justify this intuition below.

Methods

Symmetric association measures

Because A as NP has two lexical slots, an obvious starting point would be to measure the collocativity between A and NP, choosing from a vast inventory of popular association measures many of which are reviewed in [START_REF] Church | Using statistics in lexical analysis[END_REF], [START_REF] Evert | The statistics of word cooccurrences: Word pairs and collocations[END_REF][START_REF] Evert | Corpora and collocations[END_REF], and [START_REF] Pecina | Lexical association measures and collocation extraction[END_REF]. 11 Most of these measures compare the observed occurrences of two forms in a contingency table with their expected frequencies to determine which collocations are statistically significant. Hypothesis tests such as t-score, z-score, Dunning's log-likelihood ratio [START_REF] Dunning | Accurate methods for the statistics of surprise and coincidence[END_REF]) or Pearson's χ 2 select a statistical test so that its distribution converges to a well-known distribution when the null hypothesis is true. These tests are powerful and easy to compute, but they suppose that the data is similar to one of these known distributions. Since co-occurrence data does not always satisfy these distributional assumptions, exact tests such as the binomial, Poisson, and Fisher's exact tests may be more appropriate. Exact tests compute the p-value of all possible outcomes that are similar to or greater than the observed frequencies of a contingency table.

Neither hypothesis tests nor exact tests are without problems. The χ 2 test presupposes that the linguistic phenomenon under scrutiny is distributed randomly across a corpus, but it is a well-know fact that "language is never, ever, ever, random" [START_REF] Kilgarriff | Language is never, ever, ever, random[END_REF]). Fisher's exact test [START_REF] Yates | Tests of significance for 2 x 2 contigency tables[END_REF] is considered more appropriate than parametric, asymptotic tests in the identification of dependent word pairs because it is not affected by the skewed and sparse nature of data samples typical of natural language corpora [START_REF] Pedersen | Fishing for exactness[END_REF]. In contrast to the above tests, pointwise mutual information [START_REF] Church | Word association norms, mutual information, and lexicography[END_REF] does not depend on distributional assumptions and can be computed at minimal computational cost. A product of information theory, pointwise MI determines to what extent the occurrences of a word w 1 influence the occurrences of another word w 2 . Because it is intuitively and methodologically simple, British lexicographers have made pointwise MI a standard association measure. Yet, pointwise MI is sensitive to data sparseness and invalid for low-frequency word pairs [START_REF] Evert | Corpora and collocations[END_REF][START_REF] Kilgarriff | Comparing corpora[END_REF][START_REF] Manning | Foundations of statistical natural language processing[END_REF]. Consequently, pointwise MI favors low-frequency collocates (Church et al. 1991, 133). All things considered, no association measure is fully satisfactory, and the choice of one over another depends on what aspects of collocativity one wishes to reveal [START_REF] Evert | The statistics of word cooccurrences: Word pairs and collocations[END_REF][START_REF] Wiechmann | On the computation of collostruction strength: Testing measures of association as expressions of lexical bias[END_REF]). For all the above, one should should always interpret ranked lists with caution.

In the Construction Grammar framework, Stefanowitsch and Gries have developed a family of methods known as collostructional analysis. Collexeme analysis measures the mutual attraction of lexemes and constructions [START_REF] Stefanowitsch | Collostructions: Investigating the interaction of words and constructions[END_REF], distinctive collexeme analysis contrasts alternating constructions in their respective collocational preferences [START_REF] Gries | Extending collostructional analysis: A corpus-based perspective on 'alternations[END_REF]. To measure the association between the two lexical slots of A as NP, we can use a third method known as covarying-collexeme analysis (Gries & Stefanowitsch 2004a;[START_REF] Stefanowitsch | Covarying collexemes[END_REF], using Dunning's log-likelihood ratio (G 2 ) as an association metric. To evaluate if such a method has any bearing in productivity assessment, let us anticipate briefly Section 4. We might be tempted to use the metric to determine those A-NP pairs which are highly conventionalized (due to verbatim recurrence), and therefore unproductive in Baayen's sense. Such would be the case for instance of the top elements ranked by collostructional strength in Table 1. That good and gold are the most strongly associated covarying collexemes in this construction should come as no surprise for distributional reasons. The method determines for each potential A occurring in the first slot which potential NPs in the second slot co-occur with it more often than expected. Table 2 shows that good and gold co-occur almost exclusively with each other in the sample (gold is used only once with another adjective). The differ-ence between observed and expected frequencies is therefore large, which reflects on the collostruction strength. By comparison, Table 3 indicates that queer and folk co-occur exclusively with each other, with no exception. This does not reflect so much on the collostruction strength because of the relatively low type count and the smaller difference between observed and expected frequencies. Finally, Table 4 shows that while sure and hell co-occur with each other significantly more than expected, which explains their relatively high ranking as a pair, each lexeme also co-occurs with other lexemes. This is especially true of hell, which appears with 44 adjective types in 98 tokens of (as) A as hell. Sure appears with only 11 NP types in 50 tokens of sure as NP. Good as gold seems to have reached a very high level of conventionalization, 12 autonomy, and lack of analyzability. Therefore, we could tentatively use collostruction strength as an inverse measure of productivity: the higher the association strength, the higher the level of autonomy, the lesser the productivity. However, this should be done with caution as ranked lists based on most association measures have caveats [START_REF] Schmid | Collostructional analysis and other ways of measuring lexicogrammatical attraction: Theoretical premises, practical problems and cognitive underpinnings[END_REF]. Being part of an informal saying (there's nowt as/so queer as folk ), as/so queer as folk is hardly less conventionalized and autonomous than good as gold, despite what its lower collostruction strength suggests. As a lexically-filled schema, sure as hell is fairly conventional, autonomous, and hardly analyzable. Yet, we also learn a lot about the distributional behavior of the partially-filled schemas A as hell and sure as NP from inspecting the details of Table 4.

An asymmetric association measure: ∆P

In a recent paper, Gries ( 2013) identifies yet another issue with traditional association measures. Such measures commonly assume a bidirectional dependency between two word pairs. Therefore, given the pair word 1 -word 2 , word 1 attracts word 2 as much as word 2 attracts word 1 . Yet, given ipso, the probability of obtaining facto is high, but given facto, the probability of obtaining ipso is not as high because of other words compete for the same slot (e.g. de or post). In other words, the collocation between ipso and facto is directional because one word is a better cue of the other than vice versa.

The idea that collocations are directional is inspired by studies on language acquisition (in particular [START_REF] Ellis | Language acquisition as rational contingency learning[END_REF][START_REF] Ellis | Constructions and their acquisition: Islands and the distinctiveness of their occupancy[END_REF] which draw from a rejection of classical conditioning in the field of associative learning. In classical conditioning, learning occurs when a conditioned stimulus (CS, or "cue") is temporally paired with an unconditioned stimulus (US, or "outcome"). Typically, in Pavlov's experiments [START_REF] Pavlov | Conditioned reflexes: An investigation of the physiological activity of the cerebral cortex[END_REF]), a CS (e.g. ringing a bell) was presented to a dog just before the US (delivering food). After several identical experiments, the dog emitted the conditional reflex (CR) of salivating upon being presented with the CS alone. Pavlov concluded that the US reinforced the CR of salivating to the CS. According to classical conditioning, it is the temporal pairing of the US and the CS that associates the two and therefore strengthens the CR. However, [START_REF] Rescorla | Probability of shock in the presence and absence of CS in fear conditioning[END_REF] showed that rats did not emit a CR when trials involving the US alone were added to trials where the temporal pairing between US and CS was preserved. He concluded that it is in fact contingency, not temporal pairing, that generates the conditioned response. According to [START_REF] Ellis | Language acquisition as rational contingency learning[END_REF] and Baayen (2011), Rescorla's revision of Pavlovian conditioning is at the root of contemporary inferential methods in animal and human learning. In line with Bayesian reasoning, the Rescorla-Wagner equations state that learners predict an outcome from cues available in their environment if such cues have a value in terms of outcome prediction, information gain, and statistical association [START_REF] Wagner | A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement[END_REF]. Drawing a parallel with optimal word processors, whose algorithms take into account recency of prior usage, frequency of prior usage, and context of usage to perform automatic completion, the association between a cue and an outcome is directional. When an event comprises a cue and an outcome, there are four possible configurations, summarized in Table 5 (where a, b, c, and d are frequencies): To measure the asymmetric dependency between C and O, Ellis relies on ∆P , a one-way-dependency statistic developed by [START_REF] Allan | A note on measurement of contingency between two binary variables in judgment tasks[END_REF]:

∆P = p(O|C) -p(O|¬C) = a a + b - c c + d (v)
The closer ∆P is to 1, the more C increases the likelihood of O. Conversely, the closer ∆P is to -1, the more C decreases the likelihood of O. If ∆P = 0, there is no covariation between C and O. [START_REF] Gries | 50-something years of work on collocations: What is or should be next[END_REF] transposes the above to the study of bigrams. Given a bigram involving word 1 and word 2 , four configurations are also possible (Table 6). This time, two ∆P values must be computed, depending on whether the cue is word 1 and the outcome is word 2 or whether the cue is word 2 or and the outcome is word 1 :

∆P (word 2 |word 1 ) = p(word 2 |word 1 ) -p(word 2 |¬word 1 ) = a a + b - c c + d (vi) ∆P (word 1 |word 2 ) = p(word 1 |word 2 ) -p(word 1 |¬word 2 ) = a a + c - b b + d (vii)
If ∆P (word 2 |word 1 ) -∆P (word 1 |word 2 ) is positive, then word 1 is a better predictor of word 2 than vice versa. Conversely, if ∆P (word 2 |word 1 ) -∆P (word 1 |word 2 ) is negative, then word 2 is a better predictor of word 1 than vice versa. If ∆P (word 2 |word 1 ) -∆P (word 1 |word 2 ) is null, then no word is a good predictor of the other. Table 2 and formulas (vi) and (vii) can be easily transposed to the study of A as NP.

Arbitrarily, the adjective is the cue and the NP is the outcome in Table 7 :

∆P (N P |A) = p(N P |A) -p(N P |¬A) = a a + b - c c + d (viii) ∆P (A|N P ) = p(A|N P ) -p(A|¬N P ) = a a + c - b b + d (ix)
Similarly, if ∆P (N P |A) -∆P (A|N P ) is positive, then the adjective is a better predictor of the NP than vice versa. Conversely, if ∆P (N P |A) -∆P (A|N P ) is negative, then the NP is a better predictor of the adjective than vice versa. If ∆P (N P |A) -∆P (A|N P ) is null, then neither the adjective nor the NP is a good predictor. For the sake of illustration, let us now apply Table 7 and formulas (viii) and (ix) to one concrete example of A as NP : mad as a March hare. We obtain Table 8 andformulas (x) and(xi

∆P (M arch hare|mad) = p(M arch hare|mad) -p(M arch hare|¬mad) = 2 2 + 7 - 0 0 + 98363774 ≈ 0.22 (x) ∆P (mad|M arch hare) = p(mad|M arch hare) -p(mad|¬M arch hare) = 2 2 + 0 - 7 7 + 98363774 ≈ 1 (xi) ∆P (M arch hare|mad) -∆P (mad|M arch hare) ≈ -0.78 (xii)
Unsurprisingly, March hare is a much better predictor of mad than vice versa. This is because mad co-occurs with other NPs such as hatter (another reference to Alice in Wonderland ) or hell. On the other hand, March hare co-occurs exclusively with mad in the BNC. In other words, because mad is far more productive than March hare in A as NP, the former is much less of a good predictor than the other in the corpus.

The above suggests that we could use the asymmetric dependency between the adjective and the NP to locate the subschematic productivity of each type of A as NP. More precisely, instead of deciding whether A as NP is productive as a the most schematic level, we could use ∆P to spot productive subschemas. Thus, given an adjective A i , the subschema built on A i would be productive if it attracted several types of NPs. Given a noun phrase NP j , the subschema built on NP j would be productive if it attracted several types of adjectives. Yet, ∆P computes asymmetries from token frequencies and yields results that are valid at the token level. To avoid this pitfall, one must show how token frequencies may reflect tendencies observable at the type level. I address this issue in Section 4.

Data

The data comes from the British National Corpus (XML Edition), which consists of 98363783 words of spoken and written British English divided among over 4049 texts [START_REF] Burnard | Reference guide for the British National Corpus (World Edition)[END_REF]. Its size and its relatively balanced sampling scheme contribute to the reliability and validity of observations. 8 text types are represented in either written or spoken English: "academic writing", "non-academic writing", "published fiction", "news and journalism", "other published writing", "unpublished writing", "conversation" and "other spoken". Only instances of A as NP where the adjective is intensified were kept. Typically, such instances display non-literal comparisons. Examples involving a literal comparison and no intensification were discarded.

The idea that literal comparisons can be filtered out may seem intriguing to anyone used to handling natural language corpus data. For example, he had a head as big as a hot air balloon is clearly figurative in ( 12a). Yet, one can easily find a literal equivalent. In (17), the monster described by the child is literally as tall as a 50-floor building. Its head is therefore literally as big as a hot air ballon:

(17) My monster has a huge head, as big as a hot air balloon. The monster is huge, as big as a 50 story building. (My Monster by Sean, http://www.woodlandroad-p.schoolwebsites.com.au)

Sometimes, writers deliberately blur the lines between literal and figurative meanings, as in ( 18):

(18) Is mastering food idiom a piece of cake, as easy as a pancake, or a roll with butter? (The Guardian, 17 October 2012)

Once retrieved, the examples were therefore filtered manually with special attention paid to the context. Because the immediate context was not always decisive, it was sometimes necessary to resort to the extended context. By way of illustration, ( 19) is an excerpt from an ad for a company selling Afghan and Persian carpets. The text being meant for a British audience, it is very likely that the Northern Line refers to a London underground line. Because delays have made this line infamous, the author considers "a delay on the Northern Line" a paragon of commonness:

(19) Over the years, Liberty have maintained their reputation for Afghan and Persian carpets despite tough competition. On the Afghan border with Soviet Uzbekistan lies Mazar-e-Sharif. Not a city for the lily-livered or faint-hearted. Here a Kalashnikov in the back is as common as a delay on the Northern Line. (BNC-CFS)

Insofar as as common as a delay on the Northern Line can be paraphrased as "very common", the NP is assumed to intensify the adjective and this token of A as NP was kept. The remaining difficulty concerns the delimitation of the construction tokens. For the purpose of this study, NP determiners and modifiers were ignored except in cases where some degree of collocation between the NP and its modifier(s) was assumed to exist:

(20) The answers were clear as ash in a smouldering grate. (BNC-K5M)

(21) You were as mad as a March hare. (BNC-ACK)

In cases like these, the NP, its determiner, and its modifier(s) were amalgamated into one complex NP.

Taking the above difficulties into account, 1819 tokens of A as NP were extracted. Admittedly, these tokens attest a small vocabulary size for a study on productivity. 13 This could be a problem insofar as most construction samples are located in the "LNRE zone" (Baayen 2001, 55). Given the large number of rare constructions, asymptotic properties will not emerge easily (or even not at all) if the distribution is based on too small a sample size N (C). A solution suggested by [START_REF] Zeldes | Productivity in argument selection: From morphology to syntax[END_REF] is to obtain samples from very large corpora such as those compiled from the web by [START_REF] Baroni | The WaCky Wide Web: A collection of very large linguistically processed web-crawled corpora[END_REF]. Admittedly, the BNC is much smaller than, say, the 2.25-billiontoken ukWaC corpus of English [START_REF] Ferraresi | Building a very large corpus of english obtained by web crawling: UkWaC[END_REF]. However, to extract a large volume of error-free matches so as to minimize manual inspection, one must formulate a high-accuracy corpus query that will filter away unwanted data. As regards A as NP, this is easier said than done as both the BNC and ukWaC have a high proportion of patterns which search engines mistake for intensifying components (ex. happy as a child, available as an alternation/an option/a remedy, likely as a result, etc.) despite careful effort to run a highly accurate query. One could of course implement a heuristic such as a stoplist of unwanted patterns. One could also turn to some form of supervised learning, but then one would still have to tease apart those matching patterns that potentially have an intensifying function, like (22a), and those that clearly do not, like (22b):

(22) a. (. . . ) Haig, who was an unemotional man with a character as hard as granite (. . . ).

(ukWaC) b. But this basalt is as hard as granite (. .

. ). (ukWaC)

To the best of my knowledge, available techniques are far from reaching the accuracy of manual inspection. Therefore, I believe the BNC is a viable alternative for the task at hand, as long as the statistical models presented in Section 2.2.2 show a satisfactory goodness of fit.

Results

Type and vocabulary growth

The number of types depends on how we parse the construction. If we consider exact matches, which include variation as to the choice of the comparative structure (as. . . as vs. as), the NP determiner (indefinite, definite, and zero), number (snug as a bug vs. snug as bugs), an optional NP postmodifier (sure as eggs vs. sure as eggs is/are/was eggs), and the two lexical slots (A and NP), V = 1316. If we concatenate the two lexical slots (A-NP), the type count is 1206. There are 402 A types, and 876 NP types.

We might expect exact matches to be more productive than A-NP concatenations because the former have more loci of innovation than the latter. This is confirmed in the left part of Table 9.

Table 9: Left part: productivity measures for exact matches, concatenated slots, A, and NP; right part: corresponding LNRE models and goodness-of-fit (multivariate chi-squared test) Exact matches are more productive than concatenated slots in terms of V , V 1, and P. As expected, the elements of structural variation present in exact matches have a positive impact on the productivity of the construction. Once deprived of those elements, A as NP displays a higher degree of conventionalization due to the restrictions in the range of its A-NP combinations in the sample. As expected, again, A and NP slots are less productive when they are considered individually than when they are combined. This is due to the verbatim recurrence of most adjectives and, to a lower extent, most NPs.

N (C) V V 1 P S LNRE
The high S scores in Table 9 mean that there are many types yet to be discovered if one went on browsing more data of the BNC kind. S is especially high for the NP slot, which is hardly surprising given the structural variation inherent to NPs (i.e. determiners + number agreement + the potential presence of postmodifiers). In theory, combining these elements yields a high number of yet unseen possible types.

The right part of Table 9 shows which LNRE model provides the most adequate fit for each distribution. The goodness of fit of the LNRE model to the empirical distribution of each configuration is evaluated with a multivariate chi-squared test (Baayen 2001, Section 3.3.). According to Baayen (2008, 233), "[f]or a good fit, the χ 2 -value should be low, and the corresponding p-value large and preferably well above 0.05". The models are globally satisfactory and can therefore provide reliable interpolated and extrapolated expected values for the vocabulary size and the spectrum elements. These values are plotted on VGCs in Figure 1.

V(N)/E[V(N)]/V 1 (N)/E[V 1 (N)] N(C)=1819 V V 1 V V 1 V V 1 V V 1 exact matches (int) exact matches (ext) exact matches (empirical) A_NP (int) A_NP (ext) A_NP (empirical) NP slot (int) NP slot (ext) NP slot (empirical) A slot (int) A slot (ext) A slot (empirical)
Figure 1: Vocabulary growth curves for exact A as NP matches, concatenated slots (A_NP), the A slot, and the NP slot with LNRE interpolations (int) and extrapolations (ext) to four times the sample size Due to the limited size of N (C), all configurations are located in the early LNRE zone, where V and V 1 are all increasing, and asymptotic limits are far outside the boundaries of the plot (see S scores in Table 9). However, inspecting the VGCs reveals that the differences observed in Table 9 are likely to hold whatever the sample size (except for the NP slot judging from its large S score).

As seen at the bottom of section 2.2.2, a productivity measurement of the two slots is all the more relevant as we have good reasons to assume that the A slot and the NP slot are interdependent. Following Zeldes (2012, 130), we can show this interdendence by computing the probability of a A as NP hapax legomenon. For N tokens, this probability should be 1 minus the product of the complementaries to P in each slot:

P (HL A slot ∪ HL N P slot ) ≈ 1 -(1 -P A slot )(1 -P N P slot ) (xiii)
The prediction in equation (xiii) is not good for A as NP, where 1 -(1 -P A slot )(1 -P N P slot ) = 0.44 (vs. P A-N P = 0.56). We observe a 20.6% deviation from the expected probability of hapax legomena. This means that lexical choice is mutually constrained in the two slots of the construction. It also means that if we see a given slot (A or NP), we have a reasonably strong expectation about the other slot. What is left to explore is the direction of this expectation. This is what we now turn to.

Symmetry & asymmetry

To measure the asymmetric dependencies at work in A as NP, ∆P N P |A and ∆P A|N P were computed for each A-NP type found in the BNC. Figure 2 displays the sorted pairwise differences ∆P N P |A -∆P A|N P for each A as NP subschema based on A-NP types. It reveals that most of them are asymmetric. Among the 1206 A-NP pairs in the sample, 686 display a large difference (-0.5 ≥ ∆P ≥ 0.5) and 153 are characterized by an absence of covariation (∆P = 0). About 80% of those that show asymmetry are observed when the difference ∆P N P |A -∆P A|N P is negative, i.e. when the presence of the NP increases the likelihood of the adjective. To appreciate the detail of those asymmetries, let us follow [START_REF] Gries | 50-something years of work on collocations: What is or should be next[END_REF] and observe the distribution of A-NP pairs with regard to both the sorted pairwise differences of ∆P values and a bidirectional association measure (Dunning's log-likelihood ratio score). Initially, Gries's idea is to show how symmetric measures often return high association scores regardless of collocation asymmetries. At first sight, the shape of the cloud of data points in Figure 3 confirms that the degree of symmetric association and the lack of covariation between A and NP are not correlated. A line of data points stretches vertically where ∆P (N P |A) -∆P (A|N P ) is close to 0. Admittedly, the most strongly associated A-NP pairs at the top of this line are among the least asymmetric tokens: good_gold, quick_flash, right_rain, etc. Yet, such is also the case of some the least strongly associated A-NP pairs: black_hell, strong_death, soft_silk, etc. More interestingly, a denser line of data points follows a concave curve whose extremities converge to a value of log 10 G 2 that approximates 1 where ∆P (N P |A) -∆P (A|N P ) has extreme values (i.e. close to -1 and 1). 14 Table 10 zooms in on the hardly legible margins of Figure 3 and compares them to the top and bottom margins (i.e. collostruction strength).

Table 10a displays the A-NP pairs with the highest collostruction strengths, whereas Table 10b displays the A-NP pairs with the weakest association score. As seen above, all pairs with extreme G 2 values (whether high or low) are characterized by little or no covariation. All the most strongly associated A-NP pairs are highly conventional and used as popular idioms. For each A-NP pair in Table 10c, the NP is a much better predictor of the adjective than vice versa. Conversely, Table 10c displays pairs for which the adjective is a much better predictor of the NP than vice versa. We find 4 instances of hell in Table 10b, where the collostruction strength is the weakest. Interestingly, the same NP is found in all the A-NP combinations in Table 10d, where the positive ∆P values reach their highest. This suggests that there is local correlation in the data between a low collostruction score and a high ∆P score. This tendency is confirmed if we compare Tables 10b and10c, where the negative ∆P values reach their lowest. All the adjectives in Table 10b also appear in pairs with extreme negative ∆P values (i.e. ∆P ≤ -0.9). If we were to extend Table 10c to the top 300 values, we would find only 37 adjective types, all of which denoting basic properties such as colors and shades (white, black, red, pale, clear ), texture and constitution (big, stiff, hard, heavy, solid, strong, smooth, soft, sharp, thick, dry), age (old ), speed (quick ), mental/physical states (happy, sick, dead ), temperature (hot, cold ), and epistemic judgment (sure). The semantic similarity between groups of tokens being a productivity criterion according to [START_REF] Croft | Productivity and schematicity in metaphors[END_REF], we could hypothesize that productive adjectives and NPs are found where asymmetry is attested. To interpret the above results at the type level, the mean scores of ∆P (N P |A) -∆P (A|N P ) and G 2 were calculated for each A and each NP. Collostruction strength and ∆P can now be compared to two productivity measures described in Section 2.2.2, namely P * , and P, notwithstanding caveats regarding the difficulties inherent to comparing the latter values at different sample sizes.

∆P , collostruction strength, and hapax-based productivity measures

As originally designed in morphology, P is calculated by dividing the number of hapax legomena with a given affix by the total number of tokens of that affix in the corpus (see Section 2.2.2). Although P works well in the productivity assessment of a single affix, difficulties emerge when comparing the productivity scores of several affixes with different sample sizes. As pointed out by [START_REF] Gaeta | Productivity in Italian word formation: A variable-corpus approach[END_REF], [START_REF] Baayen | Productivity and English derivation: A corpus-based study[END_REF] obtain counterintuitive results when they compare deverbal suffixes with different token frequencies on the basis of the size of the whole corpus. According to Gaeta and Ricca, computing P values using the whole corpus size as an independent reference point amounts to comparing these values at the endpoints of as many curves as there are different suffixes, each endpoint corresponding to a distinct value of N . Given that P is a decreasing function of N , this can lead to overestimating P for the less frequent items, especially when token frequencies differ greatly in the sample. For this reason, [START_REF] Gaeta | Productivity in Italian word formation: A variable-corpus approach[END_REF] insist on computing P for equal values of N. 15 This is no minor constraint as, at the current state of the art, hapax-based productivity measures best apply to macro-scale studies based on preferably very large corpora and case studies (such as affixes) with token frequencies that are a priori high enough to return a critical mass of hapax legomena.

Using texts from continuous issues of the Italian daily newspaper La Stampa over a period of 36 months, Gaeta and Ricca (2006, Section 2) adopt a variable-corpus approach to evaluate the productivity of Italian affixes. The corpus is split into subcorpora. For each subcorpus, a token-frequency spectrum of word forms is created, on the basis of which type, token, and hapax legomena are calculated for each affix. The procedure advocated by [START_REF] Gaeta | Productivity in Italian word formation: A variable-corpus approach[END_REF] allows for a direct comparison of affix productivity scores because it is assumed that the distribution of a given affix in any subcorpus is proportional to its distribution in the whole corpus. For this to work, however, the subcorpora must be homogeneous with respect to their textual typology. Although the variable-corpus approach is feasible and relevant in the case of a study of affixes in the La Stampa corpus (36 months can easily be divided into 36 similar subcorpora, each subcorpus displaying a critical mass of tokens), respecting the distribution of text types found in the BNC in the study of A as NP is far more challenging and beyond the scope of this article.

In the context of A as NP, one canonical procedure could involve breaking down N (C) into as many sample sizes as there are slot types, i.e. 402 adjective slot types + 876 NP slot types = 1278 sample sizes. In order to compare P values over the whole data set, one would need to set N to the smallest common sample size, which would make little sense given the presence of many rare types in the overall sample. Many of these rare types consist of a single hapax legomenon, in which case P=1 for whichever slot is considered the variable. Such an extreme score may be poorly indicative of productivity (these rare types may just be archaisms or nonce innovations). As inspired by Zeldes (2012, Table 15), one could instead compare the potential productivity of only the most frequent A slots and NP slots, which would guarantee a maximal common sample size. However, that would be at the cost of losing potentially interesting items from the viewpoint of other measures, notably ∆P and G 2 .

In the remainder of the paper, I adopt a workaround that deviates from the canonical procedure outlined in [START_REF] Gaeta | Productivity in Italian word formation: A variable-corpus approach[END_REF] and [START_REF] Zeldes | Productivity in argument selection: From morphology to syntax[END_REF]. The above caveats notwithstanding, I consider that slot types are extracted from the same sample of A as NP slot types and therefore N (C)=1278. This has the advantages of avoiding extreme productivity scores and paving the way for a complex scale of productivity. It may only be the second-or third-best workaround (and it is certainly not the only workaround available), but at least it is a procedure whose main shortcoming we are aware of, thanks to [START_REF] Gaeta | Productivity in Italian word formation: A variable-corpus approach[END_REF], namely overestimating the productivity of low-frequency items when doing fixed-corpus calculations. The ensuing P and P * measurements must therefore be considered with caution even though, fortunately, no such overestimations were found after cross-checking with the original frequency data. If the productivity of A as NP were assessed with hapax-based measures only, the smallest-common-sample-size issue might be insuperable. Yet, in this paper, P and P * are but two among several factors in the multidimensional productivity assessment of A as NP. In Section 4.4, it is the role of Principal Component Analysis to weight hapax-based measure against other metrics and include illustrative frequency variables to help identify potentially counterintuitive data points.

Given formula (iii), P * can be plotted with V on the y-axis and P on the x -axis, as in Figure 4. Each point corresponds to either an adjective type or a NP type. We should expect the most globally productive lexemes to appear in the upper-right part of the plot. In this respect, the NP hell stands out in the sense that A as hell is far from having exhausted its combinations with other A types. Next we find a cluster of adjectives that belong to highly asymmetric pairs. These adjectives denote the following properties: colors and shades (white, black, bright, clear, pale), texture and constitution (big, sharp, thick, strong, stiff ), and temperature (cold ).

To see how ∆P performs comparatively, the absolute value of ∆P N P |A -∆P A|N P is plotted instead of V in Figure 5. The same items as in Figure 4 stand out as indices of the most productive subschemas in the upper-right corner of the plot. The most potentially productive lexemes are also among the most asymmetric. However, despite being part of highly asymmetric pairs, the data points in the upper-left corner of Figure 5 are poorly productive. These items do not readily form nonce A-NP combinations.

Finally, to see if collostruction strength provides a reasonable estimation of the lack of productivity (see Section 4.2), the mean G 2 score for each A and NP is plotted against P in Figure 6. We observe an inverse correlation for extreme values. Indeed, the most productive items according to P have among the lowest G 2 scores: hell, big, sharp, bright, cold, black, strong, pale, thick, white, and stiff. Conversely, the items with the highest collostruction strengths are among the least potentially productive: gold, bold, right, rain, queer, and folk. Two A-NP pairs match highly conventional constructions: right-rain (as in right as rain) and queer -folk (as in queer as folk ). Because these constructions combine a high degree of (exclusive) association and a low productivity score, they rank among the most autonomous units in our sample. The added value of collostruction strength is important for extreme values as well: items that occur in the most strongly associated pairs are far less productive than the other items.

Although insightful, two-dimensional plots such as the above make it difficult to weight the relative contributions of the horizontal and vertical dimensions. As Baayen (1992, 124) concedes, one cannot rely on plots such as Figure 4 to derive meaningful P * rankings when both extent of use (V ) and degree of productivity (P) are different for non-competing items. For example, gold and sure have large P * scores (P * gold ≈ 54570 and P * sure ≈ 22738), but such scores are not reflected in the plot. Criticisms can also be made against the other plots. In Figure 5, even though ∆P _diff and the probability of encountering new types are correlated locally, we are left to wonder how to account for the data points in the top-left corner. In Figure 6, even though an inverse correlation is observed for data points with extreme values, those in the bottom-left corner of the plot are not accounted for.

Summary

Ideally, we would want to summarize the contributions of all the above measures to the "Productivity Complex" of A as NP in the BNC. To this aim, the mean ∆P and collostructional strength scores for each adjective and NP appearing in A as NP were collected together with V , V 1, P, and P * . The figures were summarized in a data frame which was submitted to principal component analysis, henceforth PCA [START_REF] Baayen | Analyzing linguistic data. A practical introduction to statistics using R. Cambridge[END_REF][START_REF] Husson | Exploratory multivariate analysis by example using R[END_REF] is to explore multidimensional data tables where rows are considered as individuals and columns as variables. The individuals consist of all adjective and NP types of A as NP tokens. Each of the 1278 individuals (402 adjective types and 876 NP types) was examined in light of four active variables: the mean collostructional strength, the mean difference ∆P N P |A -∆P A|N P (henceforth ∆P _diff), P, and P * . Three supplementary quantitative variables were also projected to verify that no counterintuitive results were obtained with respect to the non-canonical computation of hapax-based measures (see Section 4.3): V , V 1, and construction frequency (henceforth const_freq). 17 The variables were centered and standardized. Inspection of Figure 7 reveals that the first component (i.e. the horizontal axis), which accounts for one third of the variance, is largely correlated with collostruction strength (r ≈ 0.79) and P * (r ≈ 0.75). A positive correlation exists with ∆P _diff but it is much smaller than that of the other variables (r ≈ 0.42). This is because ∆P _diff contributes more to the third component (see below). The second component (i.e. the vertical axis) accounts for 15.39% of the variance. It is mostly correlated with P and V 1 (r P = r V 1 ≈ 0.95), 18 V (r ≈ 0.8), and to a much lesser extent P * (r ≈ 0.33). In other words, the further up along the vertical axis, the more potentially productive the individuals.

Figure 8 charts the two-dimensional space spanned by the first two principal components. So as not to clutter the graph, only the individuals that contribute the most to each dimension were projected. Other individuals appear as dots without a label. Three clusters stand out: individuals that are productive according to P cluster along the vertical axis in the upper part of the plane, globally productive elements cluster in the upper-right corner of the plane along the horizontal axis, and individuals that occur in A-NP pairs with a high collostruction strength cluster along the same axis, but in the lower-right corner.

As seen in Figure 6, the most productive individuals according to P belong to weakly associated pairs. Some marginal tendencies observed in Figure 3 and Table 10 of Section 4.2 are confirmed. The subschemas indexed on productive adjectives denote basic properties such as: anthracite, coal, midnight, thunder, etc. white as marble, paper, etc. red as blood, a tomato, holly, etc. clear as crystal, mud, 19 (a) spring, etc. bright as stars, a button, day, copper, etc. pale as ice, a nun, cream, ivory, etc. texture and constitution big as a giant, a bus, an elephant, a house, etc. sharp as a knife, a razor, a blade, daggers, etc. strong as a horse, a tree, a viking, a bull, etc. thick as thieves, mud, a book, etc. stiff as a board, a rod, a fence post, etc. light as a feather, a harebell, thistledown, etc. temperature cold as ice, slate, debt, stone etc.

On the one hand, a rather straightforward semantic correspondence can be found between the adjective and the NP even when the subschema is used figuratively: granite is hard, crystal is clear, ice is cold, thieves are thick in the sense that they are close, etc. On the other hand, regarding the most productive subschema A as hell, the NP seems to have lost its literal meaning to the benefit of an exclusively intensifying function: angry as hell, guilty as hell, hot as hell, jealous as hell, rich as hell, rusty as hell, shy as hell, uncomfortable as hell, etc. Yet, while conventional, A as hell is flexible enough to accommodate new adjectives.

Conversely, individuals that belong to highly associated pairs are among the least potentially productive. The positive correlation between P * and G 2 along the horizontal axis suggests that the individuals characterized by these variables are used more than once. For G 2 , this is evidenced by its proximity to the construction frequency variable (r coll.strength ≈ r const_f req ≈ 0.8). For P * , this is evidenced by its position in the upper part of the plane under the influence of V (see formula (iii)).

Individuals with extreme values for the first component are mostly nouns. Most nouns with the highest P * values denote paragons whose semantic relation with the adjective can be easily accessed or reconstructed despite its conventional nature: day is bright or clear; night is black, dark, or dull; snow and sheets are white; a grave is easily conceived as cold, quiet, or silent, and a dodo as dead. Most nouns with the highest G 2 values denote paragons whose semantic relation with the adjective is more remote. Because these lexemes belong to highly conventionalized expressions, it takes more than common sense to guess the semantic relation that holds between the adjective and the noun in some expressions, e.g. bold as brass, safe as houses, and old as the hills. Often, it is the phonetic affinity between two lexemes that conditions their pairing, as in good as gold (both lexemes share /g/), thick as thieves (/T/), bold as brass (/b/), high as a kite (/ai/), and pretty as a picture (/p/ + /t/).

The difference between P * (upper part) and G 2 (lower part) can be explained as follows: globally productive individuals are more likely to be used in new formations than individuals belonging to strongly associated pairs. Despite being used often as an expression, right as rain is therefore not as fixed as Figure 6 suggests because right and rain are each likely to be used in other A-NP combinations. With respect to good as gold, only gold is more likely to be used in other combinations with other adjectives. 20 As far as bold as brass is concerned, neither bold nor brass are likely to be used in other A-NP pairs. In other words, as we move down from the upper-left to the bottom-right part of the plot, productivity declines and conventionalization and autonomy increase.

Figure 8 further confirms the relevance of a two-slot productivity assessment. The individual behavior of lexemes does not necessarily match the behavior of the same lexemes once they are paired. Two dimensions of productivity may underlie the same subschema. In cold as a grave and black as night, the adjective is potentially productive whereas the NP is globally productive. In thick as thieves, thick is potentially productive but thieves is not. In sure as hell, sure is globally productive whereas hell is potentially productive. In old as the hills, pretty as a picture, and high as a kite, the adjective is globally productive, whereas the NP is not.

Figure 9 shows that the contribution of ∆P _diff is manifest in the third component (r ≈ 0.9) along with P and V 1 (r P ≈ r V 1 ≈ 0.11). This component is negatively correlated with coll.strength (r ≈ -0.21), global productivity (r ≈ -0.28), and construction frequency (r ≈ -0.3). In the fourth and last component, coll.strength displays the maximum positive correlation (r ≈ 0.52), followed by const_freq (r ≈ 0.43), P, V 1 (r P ≈ r V 1 ≈ 0.3), and V (r ≈ 0.23). P * displays the maximum negative correlation (r ≈ -0.49), followed by ∆P _diff (r ≈ -0.07). Individuals stretching towards the upperright part of the plot belong to potentially productive asymmetric pairs. Individuals stretching towards the lower-right part of the plot belong to globally productive asymmetric pairs.

Figure 10 charts the two-dimensional space spanned by the third and fourth principal components, zooming in on the selected individuals with the highest P and P * values. If the individuals belonging to asymmetric pairs were characterized by a high ∆P score only, they would stretch far along the right end of the horizontal axis. Such is not the case. The fact many data points stretch from the lower-right corner of the plot to the upper-right and lower left-corners suggests that most asymmetric subschemas are also potentially or globally productive.

Given the above, even if asymmetry alone is not sufficient to measure productivity, it nevertheless helps spot loci of productivity for a multiple-slot construction at subschematic levels. The precise nature of productivity (or the lack thereof) depends on how these subschemas are characterized by type frequency, the number of hapax legomena, or their ratio.

Discussion

It might be objected that ∆P applies too conviently to our case study because of the presence of two lexical slots which nicely fit in a co-occurrence table such as Table 6. Yet, this method applies equally well to constructions that are patterned differently. Gries (2013, 154-155) suggests one way in which ∆P can be extended to the study of multi-word units with more than two lexical items. Through an iterative process, collocations characterized by high ∆P values can be amalgamated into larger multiword patterns until all amalgamation possibilities have been exhausted. As regards constructions with only one lexical slot (typically, such constructions are amenable to collexeme analysis), 21 one straightforward option -already implemented in Coll.analysis 3.2a [START_REF] Gries | Coll.analysis 3.2. a program for r for windows 2[END_REF]) -is to consider, for instance, the construction schema as outcome and the collexeme as cue and modify Table 6 accordingly. We obtain Table 11. If ∆P (collexeme|construction) -∆P (construction|collexeme) is positive, then the construction schema is a better predictor of the collexeme than vice versa. Conversely, if the difference is negative, then the collexeme is a better predictor of the construction schema than vice versa. If the difference is negative, there is no covariation between the construction schema and the collexeme.

It could also be objected that some constructions are not equally productive despite identical ∆P scores. 22 Such would be the case of the NPN construction, where both NPs are identical, as exemplified by construction after construction or door to door [START_REF] Jackendoff | Construction after construction and its theoretical challenges[END_REF]. Jackendoff (2008, 13) observes that "[i]n general, N by N seems more productive than N to N." Vocabulary measures could easily confirm this intuitive productivity assessment. If one computed attractions based on ∆P for NPN, as one would for any two-slot construction where the two slots are distinct, one would inevitably find no asymmetry. Yet, because the NPs are identical, it would make little sense to look for asymmetry between the two slots. One should instead adopt the methodology outlined in the above paragraph regarding one-slot constructions. More challenging would be the case of the Xer the Yer, which has lower productivity for X and Y than the Xer NP VP, the Yer NP VP (Zeldes 2012), although both adjectives can be novel in both constructions. Here, a combination of symmetric and asymmetric association measures would certainly not replace the productivity measures used in the previous section, but they would certainly be helpful to (a) compare the degrees of conventionalization and autonomy of the two forms of comparative correlatives both at schematic and subschematic levels, and (b) determine the direction of expectation between the two mutually constrained slots in each construction. [START_REF] Gries | 50-something years of work on collocations: What is or should be next[END_REF] provides two validations of ∆P , the first involving bigrams with a high mutual association, the second based on a study of randomly chosen bigrams. In line with the first validation, future research will have to show that our results differ significantly from those that one would obtain with syntactically similar but functionally unrelated patterns, such as those where as is not an adverb but a preposition, and where no intensification is expressed, as in ( 23), ( 24), and ( 25

. ). (BNC-JJV)

In line with the second validation, future research will have to show that my results differ significantly from those that one would obtain with random A-NP pairs, regardless of how they pattern.

Pending validation, I believe my findings have important implications for the study of constructions. If productivity is key in determining whether an expression is a construction, then we obtain a more detailed picture when we examine different levels of schematicity than by considering exclusively the most schematic level. We gain a lot by examining frequencies in a corpus rather than intuitively. In the context of multiword expressions, these frequencies make sense when inspected in light of both productivity and association measures.

The methodology presented here could be extended to the study of what BCG considers as fully productive patterns such as all -clefts, what's X doing Y, or let alone. It may well appear that syntactic, semantic, and contextual constraints influence the joint distribution of each of these constructions' constituents, thus putting their full productivity into perspective.

Conclusion

Some linguists might argue that whether construction grammar should be "severe" or less so is, after all, a matter of theoretical preference. Judging from the inherent bond established between productivity and constructional status in BCG, I believe otherwise. Firstly, arbitrary sets of bigrams may well be very productive according to any of the above measures, but this does not mean that they constitute a construction (Baayen 2001, 221). Secondly, even the most schematic construction will not generate an infinity of instances. Thirdly, intermediate productivity levels must be recognized. A as NP may not be fully productive at the schematic level, but it generates subschemas whose productivity is doubtless.

For a construction not to be fully schematic does not necessarily involve that it should not be granted constructional status or that it is unproductive. In fact, construction grammar approaches assume even fully specified schemas as constructions. For this reason, the productivity assessment carried out in this paper was not primarily meant to determine what is a construction and what is not (although I showed that A as NP is more productive than Kay suggests), but to recognize the existence of productive subschemas underlying A as NP and compare them.

All in all, the evidence from this study suggests that (a) there is more to the productivity of a multiple-slot construction than high-schematic-level type frequency, (b) the borderline between "constructions" and "patterns of coining" cannot be set introspectively, and (c) multiple-slot schemas, as statistically significant sequences of constituents, are amenable to principles of associative learning, especially the fact that some constituents are cues for the outcome of others.

This paper does not aim to replace existing measures of (constructional) productivity. The methodology I have proposed is but another way of exploring the multitiered productivity of complex, multipleslot expressions. I believe that analyses based on traditional productivity measures can only gain from a combination with symmetric and asymmetric methods. Quantitative assessments of this kind may arguably find their place in the inventory of existing productivity measures in the capture of what Zeldes (2012) calls "the multidimensional productivity complex". More generally, any measure that reflects human language processing is an undeniable asset in corpus linguistics.

Notes

1 The idea that grammar has a center and a periphery echoes one of the main tenets of generative linguistics, which BCG is close to alongside other sign-based theories such as HPSG.

2 For some expressions, even though the correspondence between A and NP is literal, their combination in A as NP becomes figurative. Such is the case of cold as ice. Ice is cold, but cold as ice has little to do with low temperatures: e.g. His mind went cold as ice. (BNC-ARK)

3 Although the origin of safe as houses is unclear, folk etymology may relate it to hiding places known as "safe houses". 4 Kay (2013, 37) concedes: "corpora can never present direct evidence of ungrammaticality". 5 The main difference with morphological constructions is that morphosyntactic constructions are all schematic to some degree, with the exception of fully substantive idioms.

6 After [START_REF] Boas | A constructional approach to resultatives[END_REF]. 7 This idea finds empirical support in [START_REF] Hay | Lexical frequency in morphology: Is everything relative?[END_REF] and [START_REF] Hay | Lexical frequency in morphology: Is everything relative?[END_REF]Baayen (2002, 2003). It also finds theoretical support in usage-based accounts of mental storage, frequency, and productivity.

8 See Aronoff (1976, 76), Baayen and Lieber (1991, 817), and Zeldes (2012, Section 3.6) for discussion. 9 E.g. wegen constructions in German (Zeldes 2012, Section 4.3) 10 E.g. comparative correlatives (Zeldes 2012, Section 4.5).

11 See also Stefan Evert's comprehensive inventory of existing association measures: http://www.collocations.de/AM/ (last accessed November 21, 2012).

12 This is visible at the usage level: good as gold is used exclusively with a non-compositional, figurative meaning in the BNC. 13 As pointed out by one anonymous reviewer.

14 The log-transformation of G 2 is meant to stretch the plot vertically to make the top and bottom margins more legible. Without this log-transformation, all the data points whose G 2 score is below 50 would cluster at the bottom of the y axis all along the x axis.

15 According to Gaeta and Ricca (2006, footnote 4), Baayen (1989, 117) disregards this possibility on the grounds that "what is being studied by comparing affixes for identical sample size is [...] pragmatic usefulness, a concept that, to our mind, is a component of the pretheoretical notion of morphological productivity".

16 I used the package FactoMineR for R [START_REF] Husson | FactoMineR, an R package dedicated for multivariate analysis[END_REF] 17 As opposed to active elements, supplementary elements, do not contribute to the construction of the principal components. The sole function of supplementary elements is to illustrate the principal components (Husson et al. 2011, 20). 18 The near perfect correlation between P and V 1 should come as no surprise since P is largely based on V 1. 19 Clear as mud is one of the very few examples in the data where A as NP means "not A", along with as compatible as salt and strawberries and as compatible as oil and water. 20 In fact, we know from Table 2 that gold occurs only once with another adjective. In cases like this one, P * should be used with caution.

21 See [START_REF] Stefanowitsch | Collostructions: Investigating the interaction of words and constructions[END_REF].

22 I wish to thank one of the anonymous reviewers for pointing this out.

  ):

Figure 2 :

 2 Figure 2: Sorted pairwise differences between ∆P values for 1206 A-NP pairs in the BNC

Figure 3 :

 3 Figure 3: Distribution of A-NP pairs according to ∆P differences (x -axis) and log-likelihood ratio (y-axis, logged)

Figure 6 :

 6 Figure 6: Distribution of A-NP pairs according to P (x -axis) and mean collostruction strength (y-axis)

Figure 7 :Figure 8 :

 78 Figure 7: PCA -4 active variables (plain arrows) and 3 supplementary variables (dashed arrows) in dimensions 1 & 2

Figure 9 :Figure 10 :

 910 Figure 9: PCA -4 active variables (plain arrows) and 3 supplementary variables (dashed arrows) in dimensions 3 & 4

  ∆P values should be computed, depending on whether the cue is the construction schema and the outcome is the collexeme or vice versa:∆P (collexeme|construction) = p(collexeme|construction) -p(collexeme|¬construction)

  ): (23) I was never happy as a child. (BNC-FPK) (24) Have your policy or claim number ready as a reference. (BNC-HB5) (25) It is not admissible as evidence, (. .

  From a BCG perspective, full productivity is blocked when there is no straight semantic correspondence between the adjective and the NP. Nevertheless, A as NP is flexible enough to accommodate antonymic pairings:(10) I'm as heavy as a feather. Hallelujah. (from the song Hello, Dear Wind by Page France) (11) Ladies' golf shafts are about as stiff as rubber bands. (forums.quattroworld.com)

(Last Action Hero) b. Buying Wireless: Easy As Candy? (connection.ebscohost.com/) c. Her father groans and leans for his glass. "Simple as pie." (The Significance of Birds, Lynn Hanson) (9) a. Easy as a wink, so I'm told. (www.wattpad.com) b. (. . . ) you'll find managing your parameters as easy as a blink. (www.soundonsound.com)

  Turning now to what Kay considers full-fledged constructions, What's X doing Y (WXDY ) and allclefts have a high type frequency because they generate a potentially infinite number of instances:

	(15) a. What is this fly doing in my soup?
	b. What is my best friend doing under the bed?
	c. What is it doing raining?
	d. . . .

(16) a. All I want is get out of here. b. All she does is sing. c. All he reads is pulp fiction. d. . . .

Table 1 :

 1 Top covarying collexemes in A as NP in the BNC

	rank A	NP	coll.strength (G 2 )
	1	good	gold	288.8138
	2	quick flash	189.2885
	3	right rain	175.9832
	4	large life	164.5468
	5	safe	houses	148.3236
	6	sure	hell	141.9763
	. . .	. . .	. . .	. . .
	25	queer folk	56.9492

Table 2 :

 2 Distribution table for a covarying collexeme analysis involving good and gold

		gold other NPs
	good	29	0
	other As	1	3638

Table 3 :

 3 Distribution table for a covarying collexeme analysis involving queer and folk

		folk other NPs
	queer	4	0
	other As	0	3638

Table 4 :

 4 Distribution table for a covarying collexeme analysis involving sure and hell

		hell other NPs
	sure	33	17
	other As 65	3638

Table 5 :

 5 Co-occurrence table involving a cue (C) and an outcome (O)

		O ¬O
	C	a	b
	¬C c	d

Table 6 :

 6 Co-occurrence table involving a cue (word 1 ) and an outcome (here, word 2 )

		word 2 : present word 2 : absent
	word 1 : present	a	b
	word 1 : absent	c	d

Table 7 :

 7 Co-occurrence table involving a cue (here, A) and an outcome (here, NP)

		NP: present NP: absent
	A: present	a	b
	A: absent	c	d

Table 8 :

 8 Co-occurrence table for mad and March hare in mad as a March hare in the BNC

		March hare: present March hare: absent
	mad : present	2	7
	mad : absent	0	98363774

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bright bright clear big big big big bald white silent quick smooth high cold black safe sweet cold sick dark quiet strong strong strong dead pale pale innocent dry quiet warm light hard bitter safe white bright bright clear large miserable gentle big pale pale old old light strong thick thick transparent quiet flat common cold cold sweet sweet gentle dark clear dumb fierce grim lonely mean painful randy selfish sexy skinny stiff sharp white heavy cold cold bright pretty quiet sharp clear cold sweet big big black light soft clear warm thick boring clever light dead hard bright bright white silent sharp big pale daft funny sure white quick cold dark heavy safe sure heavy flash rain life houses hell hills picture brass rock ice snowthieves sheet kite chalk_and_cheese parrot clockwork mustard button fiddle rake bird folk grave feather dust dodo church_mouse pie doornail lead sin whistle church_mice hatter toast brush tack bell blood bat schoolgirl nails pikestaff ox mutton silk bowstring punch time cucumber board berry day_is_long dog iron daisy air night coal nut bone pitch thunder kitten horse glass night grave poker day day pie crystal gall eel bug house lord reed razor nose die lamb butter football pancake sin eggs_is_eggs water coot birds chalk_from_cheese love march_hare wool history arrow ramrod mule angel daisies sandboy paper silk velvet mud holly cream ivory thistledown heaven cat lamb church glass plague hamburgers hamster barbs boil_in_the_wrong_place ferret squirrel barley squid phosphor_dot bacon_sandwich dales laburnum_pods funeral piece_of_old_limestone chemist bout_of_flu headhunters couple_of_kids doll_ bed squash_ball birdcage practices stars_of_heaven cappuccino christmas_turkeys lace_pants poison trees set_of_skittles droughts toilet_tissues vacuum_cleaners fairy_bells wallpaper closing_of_a_coffin_lid pole_star souk foundations reed_in_the_fable storm climbing_Mount_Everest salmon parakeets evangelists dad silver_spoon aubergine word grass words spiders hurricane stone_elephants rachmaninoff_concerto pinafore cat_in_hot_weather fistful_of_sand lion_apologizing_to_a_gazelle flipper sleep schoolboy mescal trout foe ninepence wildcat daylight sign_on_a_streetcar politician fields colander moth_in_spring lump_of_granite dog_chasing_its_tail porcupine prune mankind shoot_from_a_bulb_in_spring star_trekk_tribble cotton_bud tiger_to_her_cub shelves_of_the_local_bookshop damsons pinballs sack_of_rocks husband_who_suspects_infidelity scree pint_of_guinness drunk_on_a_unicycle steel_engraving cancer boy cypress_tree chrysanthemums vases slap_in_the_face fabric_itself leper sight plaster_saint traffic_bollard pair_of_shire_horses sparrow bikini pictures breath players spider patriot_missile_strike sermon_in_church fishermen cougar secretary gypsy_whores railing game_show_host bitch_on_heat mince_pies grave_postmod hypnotist fox_guarding_a_ckicken_coop wire_rope rabbit belief_in_fairies marionette bricks branch_drifting_in_the_water flood_water gallows barnacle_on_a_boat dollar hangers_in_a_wardrobe_of_aeolian_harps kick_in_the_teeth lizards fen serpents chairs_they_sit_on piece_of_dirt putty shite child syrup world bull book kitten pig_in_shit blade bus fist potato tennis_court pig honey butter nails anthracite eggs eggs_are_eggs night_follows_day dolphin greeks womanhood donkey copper seasons cows oil_and_water salt_and_strawberries fox foxes babies sea boot_polish farmer gypsy labrador lovers fusitron quicksand anaconda_postmod hedgehog_for_a_flea gargoyle bridge pillows gargoyle visit_to_the_supermarket hawk cat_outside_a_birdcage hunter weather_outside snowflakes dick_in_the_refrigerator anemone cowslips swan play pin soldiers cats_on_hot_bricks flea_in_air sword bishop fart chastity adolescent smell_of_roasting_meat dream staff sea ball sprite caviar toffee watchstrap week falling_of_a_leaf seal snail chickens jacks_on_playing cat_that_has_licked_the_cream judges philology honey_on_a_wound set_of_worry_beads ship_heaving_landward swans children attack_of_flu plate_of_polenta mummy dream parachute_in_a_spaceshift powder_puff_to_a_man_with_chronic_heart_disease gull mice granite stone clown monkey muck potatoes ants hens_on_hot_griddles sun_behind_the_Dawns circus_monkeys arrows blade_of_a_knife torture cats cattle coffins sewer smoke_postmod snowflake bar_of_soap wormwood butterfly christmas_sherry buttercups cultivation corpse lizard pair_of_mannequins infant sweeper queen scot bird_song prophet hens osprey pencil sting wand shoe_box speedfreak beachballs clouds_of_electrons soul lamb rue bricks_in_a_wall door_behind_her stone_worn_by_aeons_of_tides_postmod lake mill_pond pond surface ditch_water puddle obituary_office toothache butterfly_wings shadows trail_of_smoke rasp sack shag_on_the_floor_of_a_sandpaper_factory bugs mummies clam clasp_on_his_wallet drum sculpture skin_of_a_baby house needle ghost frost sky_outside wind_postmod winter_ice mole owl_in_daylight_without_glasses brother_and_sister flesh_on_his_body limpet lover sheet_to_a_blanket lords skunk vicar apple_pie flax garden_of_eden line sandpaper whisker clouds morning_ashes mountain_rock_pool school_sweater shingle curry school_boy wine_press bunk plastic_bag christmas money soupkitchen_to_the_indigent stick_of_shit_in_the_tub swarm_of_greenfly_at_the_chelsea_flower_show glass shit sun honey_spiked_with_arsenic idea sliver_of_the_moon spike tiger_at_bay whirlpools barn_door stains_on_butcher bananas cheese sulphur terror lion spit egg donkey eels mist lapis_lazuli megrim periwinkle sailor summer_sky top_of_a_ballpoint_pen ironing lakes pancakes lambs couple_of_puppies fuck kittens teenager_going_on_her_first_date guard_of_honour piece_of_sculpture shelf sonnet gazelle razorwing shadow armour dinosaur teak walnut dribble_from_a_baby mouse butcher flea day_was_born doves cable flesh_of_an_olive lute_string sail violin_strings pug_dog truth barns canal continent football_pool height motorway nuns plain_of_the_world glacier jet midnight raven fate bladder_of_lard drumsticks fledgeling vulture breeze cathedral stroll_in_the_Black_Forest champion moon_is_high palm_tree steeple tower monkey flowers sunrise dirt people babies pearl swan wind dandelion_seeds sky glacier hen refrigerator surgeon toothpaste cold delay_on_the_Northern_Line sararimen_in_bowler_hats stones_through_the_windscreen street_hustlers taxes telephone_boxes day_and_night vinegar_from_wine beggar clock pulse_beat tides maypole rest snake chip doll eye_of_a_hurricane miser ruler stick_insect strands_of_spider vice summer_wind_across_white_sands ghost angels autumn_sunset lily miracle morning_itself queen_of_Egypt rainbow_trout rose space berries dew fish maids_in_may maids_in_May paint primrose tin birds_in_spring dog_with_two_dicks kings larks man_with_a_toothache pig_in_poop robin_postmod sparrows teen_heart_throbs turkey_in_january pitch hen dandelion_seeds badger moon eels soap skin flowers rawhide salt_mine scones straw_in_a_barn metal oak sheet_of_lead sumo_wrestler sisters trace bite creosote heather heather_in_the_dell honeycomb sea_breeze violet wine fate devil apples_postmod autumn_apple carrots embers flames_of_hell mahogany morning_sun_in_winter mulberry_walls porter radish rubies tomato weather horse weather spit mouse milk girl leaf men baby ducks feathers filigree floss harebell moth puff summer_breeze bobbin catacomb cinema gathering_twilight pansies treacle varnish velvet_bag clouds_of_heaven condor fetlock bayonets beanpole bristles crow dummies fence_post habit_of_a_nun ironing_board ramrods rod rods log perfume pillow brick_wall castle_puddings echo lorry rock_of_gibraltar wall ivory ivory steel alchemy dodos gold_standard herring phlogiston salmon_into_a_fishmonger diamondwood ground_outside rocks ashes baker ghosts lard nun parchment parchment_walls_around_her perivale_ghost plover seashell_in_the_moonlight winter_daybreak_postmod porcelain tomb dawn cricket punch boards sheep people pig rake blow eagle hares lamb morse pirouettes vorderman dogs duck fondant gossamer kid mop billiard_ball rainbows_in_oil sea_washed_pebbles silk_mix velvet_scabbard babe children mustard child stone wind schoolgirl milk pig_in_shit needle mouse porcelain civilisation humankind lillies_of_the_field trade day cart desire nd_on_her_shoulder_postmod harse horses lioness ploughox pull_of_their_own_lives railway_porter rope stag stone_wall carpet chair_leg daisies_on_a_lawn hairs leather mince oaks phlegm plate_of_home railway_sleepers roof_beams sausages vodka yoke chalk marble cat arrowhead carving_knife crack_of_a_pistol dagger_points daggers flint ice_hanging_from_rock jackal knife knives lemons needles row_of_daggers scar splinters stiletto teeth tinker baby devil badger chicken egg giant tree carrot unk_of_Wensleydale_cheese copper_warming_pan doubloons easter icon magnesium_fireworks magnesium_flares mandarins meringues parrots swords tattoos terrier tinder violets sh_in_a_smouldering_grate bronze daylight_in_the_sky of_a_mother_of_pearl_lined_shell uctions_on_a_packet_of_seeds oincloth_on_the_Crucifixion map_of_a_well moonstone spring_water allotments armchair bible empire_state_building eye fanlights forceball_pitch frying_pan giants goat hangar lilypond lorry_wheels nome pigeon pullet railway_station room settee world_trade_center soap spring viking virgin staff sin schoolgirl steel sky pig dirt lightning clockwork chicken ice abin_in_the_frozen_woods charity clay coin debt dip glass_of_lager _forming_on_the_windscreen joint_of_beef sea_bed snowball stone_she_sat_on stones sword_in_winter witch ace_of_spades ing_of_the_Camden_Falcon crows devil_would_wish ebony jeweller liquorice midnight_ink moonshine nightfall panther root soot storm_cloud tea_taken_without_milk voids eggs_isn eggs_was_eggs rooster stone stone butter child lead virgin cream shit shit sword girl ash candlewax desert fire flour jellyfish office_paper quicklime snow_on_the_ground towel_around_her_head wall_behind_him wedding dirt muck mice cricket dawn glass glass road water sun winter rain snail board shit gypsy life life boards road death slate bird bird mustard pie moon death death rock elephant mist snowflakes night tomb summer water babe skin wind tree viking summer hell bone steel steel child chalk midnight raven sky stars ramrod mountain blow eagle hell cat diamonds porcelain copper sunrise spring giant gull hares sheep pig bone ghost lightning honey moon slate boot_polish milk birds death pig death tomb elephant lion winter history chalk marble sin paper death house birds death death air pearl diamonds stars stars mountain hell snow elephant cream milk cricket man air man man mud ice baby glass water granite winter bell child rain thunder dawn hell hell hell hell hell hell hell hell hell hell bone lightning sin marble tomb crystal water cat paper mountain weather bird mountain ox velvet silk shit ice life child bird butter child milk death cat sheet death ivory bird steel rock gold shit glass death hell hell house stone stone hell hell iron	hot hell	steady handsome brilliant intelligent straigth unfeeling beauteous fragrant gay kind mysterious young fluid modest tender unavoidable immovable obtrusive poised sensitive vast dated loud wrinkled sound empty guilty angry edgy jealous rusty scared uncomfortable true lithe relaxed stupid tense colourless ordinary runny splashy translucent grave tactile sacrosanct single fruitful brittle chill urgent frozen monumental slick sparkling awkward bleary conservative depressed difficult frustrated gloomy lonesome nosy nutty raw ruthless wet rock hell hell death diamonds devil mule arrow jet dawn summer cricket summer moon man weather mouse velvet weather hell hell hell hell hell mountain church_mouse baby baby mountain dodo thunder pig bell steel cat cat shit cat water water water water water stone stone grave bird day glass glass life ice death ice ice hell hell hell hell hell hell hell hell hell hell hell hell hell hell
		0			quiet hard pale cold soft black white old strong death silk death hell sharp rock grave death stone rock ice	ugly hell
		-1
					hard hell
					black hell
			-1.0	-0.5	0.0	0.5	1.0
					P NP|A	P A|NP

Table 10 :

 10 A comparison of the top, bottom, left and right margins of Figure3

	a. Top 10 covarying collexemes (top margin)	c. Top 10 negative ∆P values (left margin)
	A	NP	G 2	∆P N P |A -∆P A|N P	A	NP	G 2	∆P N P |A -∆P A|N P
	good	gold	288.8138	0.033333323	white	ash	6.6782	-0.984614734
	quick	flash	189.2885	-0.259259188	white	candlewax	6.6782	-0.984614734
	right	rain	175.9832	0	white	desert	6.6782	-0.984614734
	large	life	164.5468	0.134920604	white	fire	6.6782	-0.984614734
	safe	houses 148.3236	-0.176470558	white	flour	6.6782	-0.984614734
	sure	hell	141.9763	0.323264818	white	jellyfish	6.6782	-0.984614734
	old	hills	130.8729	-0.51612887	white	office paper	6.6782	-0.984614734
	pretty picture 126.4332	-0.249999959	white	quicklime	6.6782	-0.984614734
	bold	brass	113.2006	-0.166666646	white	snow + postmod. 6.6782	-0.984614734
	solid	rock	110.9541	0.104895064	white	towel + postmod. 6.6782	-0.984614734
	b. Bottom 10 covarying collexemes (bottom margin)	d. Top 10 positive ∆P values (right margin)
	A	NP	G 2	∆P N P |A -∆P A|N P	A	NP	G 2	∆P N P |A -∆P A|N P
	black	hell	0.0366	0.029387267	awkward	hell	5.8518	0.989794932
	hard	hell	0.0527	0.033273417	bleary	hell	5.8518	0.989794932
	strong death	0.5004	-0.007211477	conservative hell	5.8518	0.989794932
	old	death	0.5367	-0.006203423	depressed	hell	5.8518	0.989794932
	white	silk	0.585	-0.067948179	difficult	hell	5.8518	0.989794932
	sharp hell	0.5895	0.017573066	frustrated	hell	5.8518	0.989794932
	ugly	hell	0.5927	0.114795003	gloomy	hell	5.8518	0.989794932
	soft	death	0.7054	-0.001424491	lonesome	hell	5.8518	0.989794932
	cold	grave	0.7417	-0.051020052	nosy	hell	5.8518	0.989794932
	black	stone	0.8146	-0.056922701	nutty	hell	5.8518	0.989794932

  ).16 PCA is a multifactorial method whose purpose Global productivity for As and NPs in A as NP in the BNC

	150
		gold.np
	100					hell
	75
	100
					white
	50 G 2 V		sure		black	cold.adj
		bold	right rain	clear		bright	big
		queer folk				sharp
	absolute ace_of_spades adolescent agile air alchemy allotments american anaconda_postmod ancient anemone angel angels angry anthracite ants anxious apple_pie apples_postmod armchair armour arrow arrowhead arrows ash _in_a_smouldering_grate ashes attack_of_flu aubergine autumn_apple autumn_sunset awkward babe babies baby bacon_sandwich bad badger baker ball bananas bar_of_soap barbs barley barn_door barnacle_on_a_boat barns bat bayonets beachballs beanpole bearable beauteous bed beggar belief_in_fairies bell belligerent berries berry bible bikini billiard_ball bird_song birdcage birds birds_in_spring bishop bitch_on_heat bite bitter bladder_of_lard blade blade_of_a_knife blank bleak bird bleary blind blinkered blithe blonde blood blow blue bald board boards bobbin il_in_the_wrong_place bold bone boneless bookboot_polish boring bossy bout_of_flu bowstring boy ch_drifting_in_the_water brass breath breeze brick_wall bricks bricks_in_a_wall bridge brief brilliant bristles british brittle broad bronze brother_and_sister brown brush bug bugs bull bumpy bunk buoyant bus busy butcher butter buttercups butterfly butterfly_wings button n_in_the_frozen_woods cable calloused calm canal cancer candlewax cappuccino careful carpet carrot carrots cart carving_knife castle_puddings cat cat_in_hot_weather at_outside_a_birdcage at_has_licked_the_cream catacomb cathedral cats cats_on_hot_bricks cattle caviar g_of_the_Camden_Falcon certain chair_leg chairs_they_sit_on chalk alk_and_cheese lk_from_cheese champion changeable charity charming chastity cheap cheese chemist chicken chickens child children chill chip christian christmas christmas_sherry christmas_turkeys chrysanthemums chuffed _of_Wensleydale_cheese church church_mice church_mouse cinema circus_monkeys civilisation clam clasp_on_his_wallet claustrophobic clay clean clever mbing_Mount_Everest clock clockwork close osing_of_a_coffin_lid clouds clouds_of_electrons clouds_of_heaven clown coal coarse coffins coin colander cold.np colourless comfortable compact compatible condor confining conservative continent cool coot copper copper_warming_pan corpse corrupt cotton_bud cougar countless couple_of_kids couple_of_puppies cows cowslips crack_of_a_pistol cream creamy creosote crestfallen cricket crow crows cruel crystal cucumber cultivation cunning curious curry cute cypress_tree dad daft dagger_points daggers daisies daisies_on_a_lawn daisy dales damsons dandelion_seeds dangerous dank dated dawn day day_and_night day_is_long day_was_born daylight daylight_in_the_sky dead deadly deaf dear death beautiful common dark debt deep y_on_the_Northern_Line delicate depressed desert desire devil devil_would_wish dew diamonds diamondwood ck_in_the_refrigerator die different difficult digestible dinosaur dip dirt disorganised dispiriting disposable ditch_water dodo dodos dog dog_chasing_its_tail dog_with_two_dicks dogs doll doll_ dollar dolphin donkey door_behind_her doornail doubloons doves dream dreary dribble_from_a_baby droughts drum drumsticks drunk drunk_on_a_unicycle dry duck ducks dull dumb dummies dust eagle easter easy ebony echo edgy eel eels egg eggs ggs_are_eggs eggs_is_eggs eggs_isn eggs_was_eggs elephant embers mpire_state_building empty evangelists evil excited expressionless eye eye_of_a_hurricane fabric_itself faint fair fairy_bells faithful falling_of_a_leaf familiar fanlights farmer fart fast fat fate feather feathers featureless fen fence_post ferret fetlock fiddle fields fierce filigree final fine fire firm fish fishermen fist fistful_of_sand fit fixed flames_of_hell flash flat flavoursome flawed flax flea flea_in_air fledgeling flesh_of_an_olive flesh_on_his_body flexible flint flipper flood_water floss flour flowers fluid foe folk fondant football football_pool forceball_pitch forceful formidable foundations fox uarding_a_ckicken_coop foxes fragile fragrant frail free fresh friendly frightened frightening frost frozen fruitful frustrated frying_pan fuck full funeral funny fusitron futile gall gallows game_show_host garden_of_eden gargoyle gathering_twilight gauche gaudy gay gazelle gentle ghastly ghost ghosts giant giants gifted girl glacier glad glamorous glass glass_of_lager gloomy glorious glossy goat gold_standard gold.adj gold.np golden good gossamer granite grass grave_postmod grave.adj grave.np greeks green grey grim ground_outside guard_of_honour guilty gull gypsy gypsy_whores habit_of_a_nun hairs hamburgers hamster on_her_shoulder_postmod handsome hangar _a_wardrobe_of_aeolian_harps happy hard harebell hares harmless harse harsh hateful hatter hawk headhunters heather heather_in_the_dell heaven heavy hedgehog_for_a_flea height helpless hen hens ens_on_hot_griddles herring high hills history holly honest honey honey_on_a_wound ey_spiked_with_arsenic honeycomb horse horses hot house houses humankind hungry hunter hurricane nd_who_suspects_infidelity hypnotist ice rming_on_the_windscreen e_hanging_from_rock icon icy idea ignorant immobile immovable important infant innocent a_mother_of_pearl_lined_shell ons_on_a_packet_of_seeds insubstantial intelligent intense iron ironing ironing_board ivory jackal jacks_on_playing jealous jellyfish jet jeweller joint_of_beef judges jumpy keen kempt kick_in_the_teeth kid kind kings kite kitten kittens knife knives labrador laburnum_pods lace_pants lake lakes lamb lambs lapis_lazuli lard large larks lazy lead leaf leaky leather lemons leper life lifeless light lightning likely lillies_of_the_field lily lilypond limp limpet line lion apologizing_to_a_gazelle lioness liquid liquorice lithe lizard lizards log cloth_on_the_Crucifixion lonely lonesome lord lords lorry lorry_wheels loud love lovely lover lovers lump_of_granite lustrous lute_string mad magnesium_fireworks magnesium_flares mahogany maids_in_may man an_with_a_toothache mandarins mankind map_of_a_well marble march_hare marionette maypole mean meek megrim men meringues merry mescal metal mexican mice midnight midnight_ink mild milk mill_pond mince mince_pies mindless miracle miser miserable mist modest mole money monkey monumental moon moon_is_high moonshine moonstone mop morning_ashes morning_itself orning_sun_in_winter morse moth moth_in_spring motionless motorway mountain mountain_rock_pool mouse muck mud mulberry_walls mule mummies mummy mustard mutton mysterious nails natty natural neat needle needles nervous nervy nice night ht_follows_day nightfall nimble ninepence nome normal nose nosy nun nuns nut nutty oak oaks obituary_office obtrusive obvious office_paper oil_and_water oily old open ordinary osprey _daylight_without_glasses ox painful paint pair_of_mannequins pair_of_shire_horses palm_tree pancake pancakes pansies panther paper achute_in_a_spaceshift parakeets parchment hment_walls_around_her parrot parrots patriot_missile_strike pearl pencil people perfume perivale_ghost periwinkle permeable philology phlegm phlogiston phosphor_dot picture pictures pie piece_of_dirt ece_of_old_limestone piece_of_sculpture piercing pig pig_in_poop pig_in_shit pigeon pikestaff pillow pillows pin pinafore pinballs pink pint_of_guinness pirouettes pissed pitch pitiful plague plain plain_of_the_world plaster_saint plastic_bag plate_of_home plate_of_polenta play players pleased pliable ploughox plover pointless poised poison poker pole_star politician pond poor porcelain porcupine porter potato potatoes _a_man_with_chronic_heart_disease practices precious pretty prickly prim primal primrose pristine prolific prophet prosaic protective proud prune public puddle puff pug_dog ull_of_their_own_lives pullet pulse_beat punch pure purple putty queen queen_of_Egypt queer quicklime quicksand quiet rabbit achmaninoff_concerto radish railing railway_porter railway_sleepers railway_station rain rainbow_trout rainbows_in_oil rake ramrod ramrods random randy rare rasp raven raw rawhide razor razorwing real reed reed_in_the_fable refrigerator regular relaxed responsive rest restless rich ridiculous rife rigid road robin_postmod rock_of_gibraltar rocks rod rods romantic roof_beams room rooster root rope rose rotten rough round row_of_daggers rubies rue ruler runny rusty ruthless sack sack_of_rocks sacrosanct safe sail sailor salmon mon_into_a_fishmonger alt_and_strawberries salt_mine sandboy sandpaper arimen_in_bowler_hats satisfying sausages scar scared school_boy school_sweater schoolboy schoolgirl scones scot scree sculpture sea sea_bed sea_breeze ea_washed_pebbles seal ashell_in_the_moonlight seasons secretary secure selfish sensitive serene serious sermon_in_church serpents set_of_skittles set_of_worry_beads settee sewer sexless sexy shadow shadows shadowy e_floor_of_a_sandpaper_factory shaggy shapely sheep sheet sheet_of_lead sheet_to_a_blanket shelf es_of_the_local_bookshop shingle shiny hip_heaving_landward shit shite shocking shoe_box t_from_a_bulb_in_spring short shy sick sight sign_on_a_streetcar silent silk silk_mix silky silver_spoon simple sin single sisters skin skin_of_a_baby skinny skunk sky sky_outside slap_in_the_face slate sleek sleep slender slick slighted slim slippery sliver_of_the_moon slow small smart mell_of_roasting_meat smoke_postmod smug snail snake snow now_on_the_ground snowball snowflake snowflakes snug soap sober soldiers solitary sonnet soot soothing souk soul soulless sound pkitchen_to_the_indigent space sparkling sparrow sparrows speedfreak spider spiders spike spiritual spit splashy splinters sportive spring spring_water sprite spry squash_ball squid squirrel staff stag stains_on_butcher star_trekk_tribble stars stars_of_heaven startling stately statuesque steady steel steel_engraving steeple stick_insect ck_of_shit_in_the_tub stiletto sting stone stone_elephants stone_she_sat_on stone_wall n_by_aeons_of_tides_postmod stones s_through_the_windscreen storm storm_cloud straight straigth strands_of_spider straw_in_a_barn street_hustlers oll_in_the_Black_Forest stubborn stuffy stupid subdued subject substantial sudden sulphur summer summer_breeze summer_sky r_wind_across_white_sands sumo_wrestler sun n_behind_the_Dawns sunrise superfluous superstitious supple surface surgeon swan swans enfly_at_the_chelsea_flower_show sweeper sweet swift sword sword_in_winter swords syrup tack tactful tactile tall tattered tattoos taut taxes a_taken_without_milk teak tedious teen_heart_throbs er_going_on_her_first_date teeth telephone_boxes tender tennis_court tense terrier terror thieves thin thistledown threatening thrilling thunder tides tiger_at_bay tiger_to_her_cub tight time tin tinder tinker toast toffee toilet_tissues tomato tomb toothache toothpaste p_of_a_ballpoint_pen torture touchy tough wel_around_her_head tower trace trade traditional traffic_bollard trail_of_smoke tranquil translucent transparent trapped treacle tree trees trout true trustworthy truth turkey_in_january twisted twitchy ugly unavoidable ncomfortable unfeeling unfounded ungainly uniform unreadable unreal unremarkable unstoppable uplifting uptight urgent useful useless vacuum_cleaners vague valid varnish vases vast velvet velvet_bag velvet_scabbard vengeful vicar vice viking vinegar_from_wine violet violets violin_strings virgin it_to_the_supermarket vodka voids vorderman vulture wall wall_behind_him wallpaper walnut wand warm wary watchstrap water weak weather weather_outside wedding week weightless welcome wet whirlpools whisker whistle whole wide wild wildcat wind wind_postmod wine wine_press winter ter_daybreak_postmod winter_ice wire_rope wise witch womanhood wooden wool word words world world_trade_center wormwood worthless wrinkled yellow yoke young 0.000 0.005 red happy wide fresh dangerous taut close fine grey welcome beautiful thin blue solid calm drunk different dead light mad cruel motionless slender weightless snug blind bleak plain old common sweet sure yellow clear stiff soft bald insubstantial rough tight clean dry regular tall high smooth flat blank quick tough fit cool swift dark nervous free ancient compatible cunning faithful friendly full hungry lovely neat nimble pissed shiny short smart sober soothing stately thrilling useful busy delicate rare rigid slim heavy curious straight hard dank important proud quiet small whole harmless warm pink ugly innocent pure bitter slippery silent stubborn dull pleased easy funny certain glamorous sleek unreadable weak frail gentle clever agile icy rich round transparent changeable coarse golden fat lifeless fair simple smug hot boring firm miserable natural precious real dumb fierce randy sexy absolute american anxious bad bearable belligerent blithe blonde boneless brief british broad bumpy buoyant calloused careful charming christian chuffed claustrophobic comfortable compact confining corrupt countless creamy crestfallen cute deadly dear disorganised dispiriting disposable expressionless faint familiar final fixed flavoursome flawed flexible forceful formidable futile gaudy gifted glad glorious glossy gold.adj green harsh hateful helpless immobile intense kempt lazy leaky likely limp liquid merry mexican mild mindless natty nervy normal obvious oily open permeable pitiful pliable pointless prickly prim primal pristine prolific prosaic protective public purple random responsive restless rotten satisfying secure serene serious sexless shadowy shaggy shapely shocking silky slighted solitary soulless spiritual sportive spry startling statuesque stuffy subdued substantial sudden superfluous superstitious supple tactful tattered tedious threatening touchy traditional tranquil trapped trustworthy twisted twitchy unfounded ungainly uniform unremarkable unstoppable uplifting uptight useless vague valid wary wild wise wooden worthless aubergine bacon_sandwich barbs barley arnacle_on_a_boat bed belief_in_fairies bikini birdcage bitch_on_heat _in_the_wrong_place bout_of_flu boy h_drifting_in_the_water breath bricks cancer cappuccino at_in_hot_weather chairs_they_sit_on chemist christmas_turkeys chrysanthemums bing_Mount_Everest sing_of_a_coffin_lid colander cotton_bud cougar couple_of_kids cypress_tree dad dales damsons daylight og_chasing_its_tail doll_ dollar droughts unk_on_a_unicycle evangelists fabric_itself fairy_bells fen ferret fields fishermen fistful_of_sand flipper flood_water foe foundations arding_a_ckicken_coop funeral gallows game_show_host grass grave_postmod gypsy_whores hamburgers hamster a_wardrobe_of_aeolian_harps headhunters hurricane d_who_suspects_infidelity hypnotist kick_in_the_teeth laburnum_pods lace_pants leper pologizing_to_a_gazelle lizards lump_of_granite mankind marionette mescal mince_pies moth_in_spring ninepence air_of_shire_horses parakeets atriot_missile_strike phosphor_dot pictures piece_of_dirt ce_of_old_limestone pinafore pinballs pint_of_guinness plague plaster_saint players poison pole_star politician porcupine practices prune rabbit hmaninoff_concerto railing reed_in_the_fable sack_of_rocks salmon schoolboy scree secretary sermon_in_church serpents set_of_skittles _of_the_local_bookshop _from_a_bulb_in_spring sight gn_on_a_streetcar silver_spoon slap_in_the_face sleep souk sparrow spider spiders squash_ball squid squirrel star_trekk_tribble stars_of_heaven steel_engraving stone_elephants storm tiger_to_her_cub toilet_tissues traffic_bollard trees trout vacuum_cleaners vases wallpaper wildcat wire_rope word words boot_polish gull copper snowflakes jet diamonds man gypsy snail sword ivory velvet staff thunder children bell steel child lamb dawn cricket shit sin moon babies swan devil arrow mule bird death schoolgirl mountain pig mouse stone summer baby weather cat water glass donkey dream gargoyle sea ice day daft mustard grave.np pie poor sick pretty brown honest berry dodo rock church_mouse day_is_long rake red right solid stiff keen life safe quick rock smooth soft 50 0 25	strong 0.010 thick thick black strong white pale pale	sharp bright cold.adj	0.015 big	hell
	0			potential productivity
		0.000		0.005	0.010	0.015
				potential productivity
	strong black Figure 4: hell bright dead different drunk calm solid blue thin beautiful sharp thick stiff close fine grey welcome big taut dangerous fresh wide happy red 0.75 water dream gargoyle sea cat life weather ice glass dull stubborn silent slippery bitter pure innocent ugly keen pink warm harmless whole small quiet dank important proud hard straight curious heavy slim right rigid bold busy delicate rare ancient compatible cunning faithful friendly full hungry lovely neat nimble pissed shiny short smart sober soothing stately thrilling useful sick poor nervous swift quick smooth high tall regular dry clean insubstantial rough tight clear yellow sure sweet common old plain bleak blind snug cruel motionless slender light white weightless mad cold.adj soft bald pale blank flat fit tough cool dark pretty free 0.50 | P_diff|
	0.00 0.25	baby summer pleased easy certain funny pie donkey mouse church_mouse rock mountain stone schoolgirl mustard rain bird arrow mule devil babies swan moon dodo shit cricket dawn day lamb child steel children thunder staff velvet ivory sword gold.np snail gypsy man diamonds jet snowflakes copper gull boot_polish aubergine bacon_sandwich barbs barley arnacle_on_a_boat bed belief_in_fairies berry bikini birdcage bitch_on_heat _in_the_wrong_place bout_of_flu boy h_drifting_in_the_water breath bricks cancer cappuccino at_in_hot_weather hairs_they_sit_on chemist christmas_turkeys chrysanthemums bing_Mount_Everest sing_of_a_coffin_lid colander cotton_bud cougar couple_of_kids cypress_tree dad dales damsons day_is_long daylight og_chasing_its_tail doll_ dollar droughts unk_on_a_unicycle evangelists fabric_itself fairy_bells fen ferret fields fishermen fistful_of_sand flipper flood_water foe folk foundations arding_a_ckicken_coop funeral gallows game_show_host grass grave_postmod gypsy_whores hamburgers hamster a_wardrobe_of_aeolian_harps headhunters hurricane _who_suspects_infidelity hypnotist kick_in_the_teeth laburnum_pods lace_pants leper pologizing_to_a_gazelle lizards lump_of_granite mankind marionette mescal mince_pies moth_in_spring ninepence air_of_shire_horses parakeets atriot_missile_strike phosphor_dot pictures piece_of_dirt ce_of_old_limestone pinafore pinballs pint_of_guinness plague plaster_saint players poison pole_star politician porcupine practices prune rabbit hmaninoff_concerto railing rake eed_in_the_fable sack_of_rocks salmon schoolboy scree secretary sermon_in_church serpents set_of_skittles _of_the_local_bookshop _from_a_bulb_in_spring sight gn_on_a_streetcar silver_spoon slap_in_the_face sleep souk sparrow spider spiders squash_ball squid squirrel star_trekk_tribble stars_of_heaven steel_engraving stone_elephants storm tiger_to_her_cub toilet_tissues traffic_bollard trees trout vacuum_cleaners vases wallpaper wildcat wire_rope word words absolute american anxious bad bearable belligerent blithe blonde boneless brief british broad brown bumpy buoyant calloused careful charming christian chuffed claustrophobic comfortable compact confining corrupt countless creamy crestfallen cute deadly dear disorganised dispiriting disposable expressionless faint familiar final fixed flavoursome flawed flexible forceful formidable futile gaudy gifted glad glorious glossy gold.adj green harsh hateful helpless honest immobile intense kempt lazy leaky likely limp liquid merry mexican mild mindless natty nervy normal obvious oily open permeable pitiful pliable pointless prickly prim primal pristine prolific prosaic protective public purple queer random responsive restless rotten satisfying secure serene serious sexless shadowy shaggy shapely shocking silky slighted solitary soulless spiritual sportive spry startling statuesque stuffy subdued substantial sudden superfluous superstitious supple tactful tattered tedious threatening touchy traditional tranquil trapped trustworthy twisted twitchy unfounded ungainly uniform unremarkable unstoppable uplifting uptight useless vague valid wary wild wise wooden worthless daft dumb fierce randy sexy real natural precious miserable firm boring hot smug simple bell fair lifeless fat changeable coarse golden safe transparent round rich sin agile icy clever gentle frail weak grave.np pig glamorous sleek unreadable	death
		0.000		0.005	0.010	0.015
				potential productivity

Figure 5: Distribution of A-NP pairs according to P (x -axis) and the mean absolute value of ∆P differences (y-axis)

Table 11 :

 11 Co-occurrence table involving a cue (construction