Márta Abrusán
email: marta.abrusan@gmail.com

Semantic Anomaly, Pragmatic Infelicity and Ungrammaticality

Keywords: semantic anomaly, grammaticality, pragmatic infelicity, natural logic, polarity items, meaning shift

A major goal of modern syntax has been to find principles that rule out sentences that seem ungrammatical. To achieve this goal, it has been proposed that syntactically odd (or ungrammatical) sentences can be distinguished empirically and theoretically from semantically odd (or semantically anomalous) sentences. However, sometimes it is not clear why a sentence is "weird" and this has repercussions for our syntactic and semantic theories. According to a number of proposals semantic and pragmatic processes can lead to weirdness that empirically feels more like ungrammaticality than semantic oddness. But if this is so then the question arises: what explains the intuitive difference between sentences that feel ungrammatical and those that merely feel semantically (or pragmatically) anomalous? This article addresses this question by describing and comparing various semantic and pragmatic proposals for explaining different types of weirdness: ungrammaticality, semantic anomaly and pragmatic infelicity.

Introduction

Linguistics has learned a lot about language by studying when things go wrong, for example when an utterance is "weird". A major goal of modern syntax has been to find principles that rule out sentences that seem ungrammatical. To achieve this goal, it has been proposed that there are different types of "weirdness", in particular that syntactically odd (or ungrammatical) sentences can be distinguished empirically and theoretically from semantically odd (or semantically anomalous) sentences.1 (1a) *Read you a book about modern syntax? (1b) #Colorless green ideas sleep furiously. [START_REF] Chomsky | Syntactic Structures[END_REF] Initial psycholinguistic evidence seemed to confirm this sharp division. Kutas andHillyard (1980, 1984) discovered that reading a semantically anomalous word in a sentence (e.g. #John buttered his bread with socks) produces what came to be known as the N400 effect: a strong negative ERP 400ms after the presentation of the anomalous word.2 Simple grammatical errors, for example agreement violations did not produce the N400 effect (cf. [START_REF] Kutas | Event-related brain potentials to grammatical errors and semantic anomalies[END_REF]. In contrast, syntactic or morphological anomalies (e.g. *The cat will eating the food) were found to elicit a large positive wave peaking at 600ms after the presentation of the anomalous word (the P600 effect) as well as a left anterior negativity (LAN) (cf. [START_REF] Osterhout | Event-related brain potentials elicited by syntactic anomaly[END_REF][START_REF] Von Fintel | Exceptive constructions[END_REF][START_REF] Osterhout | Event-related brain potentials elicited by failure to agree[END_REF][START_REF] Osterhout | On the language specificity of the brain response to syntactic anomalies: Is the syntactic positive shift a member of the p300 family?[END_REF].

However, sometimes it is not clear why a sentence is "weird" and this has repercussions for our syntactic and semantic theories. In particular, it has been proposed that semantic and pragmatic processes can lead to "weirdness" that empirically feels more like ungrammaticality than semantic oddness. For example, the unacceptability of negative polarity items in unsuitable contexts as in example (2) has been argued to follow from semantic or pragmatic processes. But empirically the example feels ungrammatical rather than semantically anomalous.

(2) *Anyone stole John's sandwich yesterday.

As more and more cases of seemingly ungrammatical sentences started to receive semantic explanations, the dichotomy of syntactic vs. semantic oddness became blurred.

On closer scrutiny it has turned out that processing data do not support a oneto-one mapping between N400 and semantic processing vs. P600 and syntactic processing either (cf. e.g. [START_REF] Coulson | Expect the unexpected: Event-related brain response to morphosyntactic violations[END_REF][START_REF] Osterhout | The neurobiology of sentence comprehension[END_REF][START_REF] Kutas | Thirty years and counting: finding meaning in the n400 component of the event-related brain potential (erp)[END_REF]. Rather, it is currently thought that N400 is involved in lexical access (lookup) and can be influenced both by semantic and syntactic factors. P600 seems to be present when there is a deviation from some expected pattern or sequence. Neither effects are language specific: stimuli in the visual or musical domain can elicit N400/P600 as well.

If interpretive processes can lead to what feels like ungrammaticality, then the question arises: what explains the intuitive difference between sentences that feel ungrammatical and those that merely feel semantically anomalous or pragmatically infelicitous in a given context? This question is rarely raised in the literature 3 and even more rarely answered.

In this article I describe and compare various semantic and pragmatic proposals that were put forth in order to explain the reasons for the unacceptability of ungrammatical sentences. The first type of proposal assumes that ungrammaticality can follow from a failure to satisfy semantic conditions. The second type of proposal derives ungrammaticality from systematic pragmatic failure. The third type of proposal takes logical triviality to be responsible for various cases of ungrammaticality. I also discuss, where relevant, how these explanations differ (or not) from explanations for semantic anomaly and different types of pragmatic infelicity. I touch upon a number of different linguistic examples, but the running theme of this article will be polarity items: a number of competing semantic and pragmatic analyses were given to explain their distribution and so they can serve as test case for comparing different types of analyses. In the last section of this paper I outline a recent proposal that aims to explain what leads to the difference of intuitions between cases of semantic anomaly and ungrammaticality.

NB: In this paper I do not discuss processing studies of semantic or syntactic oddness any further, nor proposals that explain ungrammaticality via processing factors (e.g. [START_REF] Kluender | Subjacency as a processing phenomenon[END_REF] and much subsequent work) because the topic is so rich that it would deserve a paper on its own.

2 Semantic conditions for grammaticality

Lexical semantic conditions

Perhaps the best-known examples that argue that semantic conditions can underlie ungrammaticality judgments are polarity items. Let's take the example of the so-3 See some discussion in [START_REF] Giannakidou | Negative polarity and positive polarity: Licensing, variation, and compositionality[END_REF] in the context of analyses of polarity items. The comparison between syntactic violations and semantic anomaly played an important role in the early days of generative syntax [START_REF] Chomsky | Syntactic Structures[END_REF][START_REF] Chomsky | Aspects of the theory of syntax[END_REF] and of generative semantics, see [START_REF] Harris | The linguistics wars[END_REF] for an overview. (5a) Everyone who budged an inch was rewarded.

(5b) *Three students who budged an inch were rewarded.

NPI's such as anything, lift a finger or budge an inch have a restricted distribution: they are acceptable in certain types of sentences but not in others. In example (3a), the element that licenses the NPI is negation, in example (4a) it is the quantifier few and in example (5a) it is the restriction of the quantifier every. The most influential analysis of NPIs was given by [START_REF] Ladusaw | Polarity Sensitivity as Inherent Scope Relations[END_REF]), who (building on Fauconnier 1975) argued that the environments that allow NPI's to occur should be characterised in semantic terms: He proposed that NPIs are licensed in downward entailing (DE) contexts. This type of explanation was truly novel at the time as the first approaches to the problem were syntactic (cf. [START_REF] Klima | Negation in English[END_REF][START_REF] Baker | Double negatives[END_REF]. But now a purely semantic property was proposed to be the cause for an apparent syntactic infelicity.

Definition A context C[ ] is downward entailing iff for all α and β such that α ⊆ β , C[β ]→ C[α]
In other words, downward entailing contexts license inferences from supersets to subsets. As the examples below illustrate, the scope of negation, the scope of the quantifier few and the restrictor of the universal quantifier are downward entailing, but the scope of the quantifier some or the restriction of the numeral three people are not: (6a) zebra⊆ animal (6b) John did not see an animal→ John did not see a zebra.

(6c) John saw an animal John saw a zebra.

(6d) Few people saw an animal → Few people saw a zebra.

(6e) Some people saw an animal Some people saw a zebra.

(6f) Everyone who saw an animal was happy → Everyone who saw a zebra was happy.

(6g) Three people who saw an animal were happy Three people who saw a zebra were happy.

The property of downward entailingness does not delineate a particular syntactic environment (pace [START_REF] Klima | Negation in English[END_REF][START_REF] Linebarger | The grammar of negative polarity[END_REF][START_REF] Progovac | Negative and positive polarity: A binding approach[END_REF]; it is a potential semantic characteristic of the sentences in which NPIs occur. This is also shown by the fact that NPIs are acceptable in the complement of negativeimplying verbs, e.g. lack, as in He lacks any sense of humour. On Ladusaw's view, the requirement on NPIs that they should occur in DE environments is formulated as a special semantic licensing condition that must be met in order to use these expressions in a grammatical way. This means that syntax and semantics need to conspire in order to produce a grammatical output, grammaticality results from syntactic and semantic well-formedness (cf. also [START_REF] Ladusaw | Logical form and conditions on grammaticality[END_REF]. Thus, if a correct syntactic structure is not semantically well-formed, then such a structure can be filtered out by the semantics. The result of this semantic filtering, in the case of NPIs, is a sentence that feels ungrammatical, and not only semantically anomalous in the sense of example (1b).

A lot has been written on polarity items since the seminal work of Ladusaw, both the empirical generalisations and the accuracy of downward entailingness as a licensing condition have been challenged (See [START_REF] Linebarger | The grammar of negative polarity[END_REF][START_REF] Progovac | Negative and positive polarity: A binding approach[END_REF][START_REF] Zwarts | Three types of polarity[END_REF][START_REF] Kadmon | [END_REF][START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF][START_REF] Von Fintel | Npi licensing, strawson entailment, and context dependency[END_REF][START_REF] Giannakidou | Polarity sensitivity as (non) veridical dependency[END_REF][START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF] for some influential proposals). But much work on polarity items has preserved the idea of explaining their distribution in terms of a semantic licensing condition. Some examples beside downward entailingness include Strawson DE (von Fintel 1999), intensionality, non-veridicality [START_REF] Zwarts | Three types of polarity[END_REF][START_REF] Giannakidou | Polarity sensitivity as (non) veridical dependency[END_REF], and most recently scope-licensing [START_REF] Barker | Negative polarity as scope marking[END_REF]. The licensing condition might be expressed as a filtering condition on the whole structure in which PI's appear (e.g. [START_REF] Ladusaw | Polarity Sensitivity as Inherent Scope Relations[END_REF][START_REF] Barker | Negative polarity as scope marking[END_REF] or as a rule of lexical semantics (e.g. [START_REF] Zwarts | Three types of polarity[END_REF][START_REF] Von Fintel | Npi licensing, strawson entailment, and context dependency[END_REF][START_REF] Giannakidou | Polarity sensitivity as (non) veridical dependency[END_REF]. Either way of thinking entails that the unacceptability of examples (3b), (4b) and (5b) is the result of a lexical semantic condition gone wrong.

Failures of semantic composition

In the case of NPI licensing, one can identify a single lexical item (e.g., anyone) that requires its environment to meet special semantic conditions. When these conditions are not met, composition fails. In other cases there is no single culprit; a general failure of semantic composition can lead to ungrammaticality. An example is the analysis of so-called weak islands by [START_REF] Szabolcsi | Weak islands and an algebraic semantics for scope taking[END_REF]. Wh-movement was considered a classical example of a syntactic process, but it shows certain restrictions that appear to be semantic in nature. For example, negation and some other negative elements block the formation of degree-questions:

(7) *How fast didn't John swim? But negation is not an absolute block for wh-movement: for example, questions about individuals are not sensitive to negation: (8) Which painting did John not see?

According to [START_REF] Szabolcsi | Weak islands and an algebraic semantics for scope taking[END_REF] algebraic semantic analysis, example (7) is not acceptable because its logical form, represented schematically in (9), is not meaningful. The reason is that negation requires a domain for which complements are defined, but such a domain is not provided in the case of questions formed over degrees. More generally, weak islands arise whenever the operation associated with a scope-taking element needs to be performed on a domain for which it is not defined.

An analysis in a similar spirit for island effects in the framework of dynamic semantics was given by [START_REF] Honcoop | Dynamic Excursions on Weak Islands[END_REF]. [START_REF] Beck | Intervention effects follow from focus interpretation[END_REF] explains so-called intervention effects in Korean by appealing to uninterpretability: in this case composition cannot be successful because of the interplay of the interpretation of questions and focus leads to uninterpretable structures.

In these examples there is no lexical element that is responsible for the observed ungrammaticality. The closest we can get to finding a designated culprit is to say that ultimately uninterpretability in these cases follows from the interpretation of questions. [START_REF] Szabolcsi | Weak islands and an algebraic semantics for scope taking[END_REF] explicitly liken the deviance of weak-islands to cases such as the example below:

Comparison with semantic anomaly

(10) #six mists They argue that in this example, as in the case of (7), we observe failure of semantic composition. In example (10) we cannot apply a numeral to a mass noun: counting is not defined in the mass domain. However, there is something to explain about the difference of intuitions with respect the two examples. 4More generally, there is an open question why semantic failure such as that observed with polarity items or intervention gives rise to a different intuition than semantic failure that results from composing a predicate with an unsuitable argument.

(11) #My toothbrush is pregnant.

Intuitively, the reason why example (11) is unacceptable is because my toothbrush is not the sort of object to which the predicate pregnant can apply. In the linguistic and philosophical literature many competing ways to capture this intuition formally were proposed (see Magidor 2013 for a recent overview). The different types of proposals make different predictions about the unacceptability of ungrammatical vs. semantically anomalous sentences. Let's briefly review here three major types of proposals for semantic anomaly. 5According to one popular view, in examples such as (11) semantic composition fails because the argument is not in the domain of the function denoted by the predicate, and thus the result is uninterpretable (or 'meaningless') (cf. [START_REF] Russell | Mathematical logic as based on the theory of types[END_REF][START_REF] Strawson | Introduction to Logical Theory[END_REF][START_REF] Chomsky | Syntactic Structures[END_REF][START_REF] Drange | Type crossings[END_REF], Beall and Fraassen 2003, among others). This view does not predict a difference between cases of semantic anomaly and the ungrammatical examples discussed above.

According to another popular approach to semantic anomaly, such examples have meanings that speakers can intuitively grasp (hence are not 'meaningless'), but they cannot be used in a truthful way in any situation. Semantic composition can succeed, but the selectional restrictions of predicates (modelled as preconditions for having a truth value) are not met (cf. e.g. [START_REF] Halldén | The logic of nonsense[END_REF][START_REF] Goddard | Predicates, relations and categories[END_REF][START_REF] Thomason | A semantic theory of sortal incorrectness[END_REF][START_REF] Lappin | Sorts, ontology, and metaphor: the semantics of sortal structure[END_REF][START_REF] Asher | Lexical Meaning in Context[END_REF][START_REF] Shaw | Anomaly and quantification[END_REF]. Such selectional restrictions might be expressed as type-presuppositions that guide semantic composition cf. [START_REF] Asher | Lexical Meaning in Context[END_REF]. Technically, this approach does predict a difference between the ungrammatical sentences discussed above and semantic anomaly because in the latter case the semantic failure is at the level of presuppositions. However, precisely because the difference between semantic conditions and semantic presuppositions is merely technical (and semantic conditions are often formulated technically as semantic presuppositions), we are still in need of an explanation of the difference.

On a variant of the presuppositional view, selectional restrictions are modelled as purely pragmatic presuppositions; failure to meet them results neither in meaninglessness nor in a lack of truth value. Instead, the interpretive failure of sentences such as (11) only produces pragmatic infelicity [START_REF] Magidor | Category Mistakes[END_REF]. This view predicts a clear difference of intuitions between examples of semantic anomaly and the ungrammatical examples discussed above, at least when the latter are derived via semantic conditions. We are still left with the following question: What makes sortal restrictions of lexical predicates so fundamentally different from other types of semantic conditions?

The last section of this paper outlines a proposal that aims at explaining the difference between semantic anomaly on the one hand and ungrammaticality due to unmet semantic conditions/presuppositions on the other.

Systematic pragmatic infelicity

The pragmatic context, the norms of assertion, the assumptions of the conversational partners all influence and modulate what sentences are taken to mean in context. Traditionally, pragmatics was assigned the role of a conversational "post-processor"; but increasingly, pragmatic processes are thought to interact with other components of the language system (syntax, semantics, prosody and phonology) in a fundamental way. Most interesting for the purposes of this review is that systematic failure to observe general conversational principles can also lead to ungrammaticality.

Krifka's analysis of polarity items

An influential example is [START_REF] Krifka | Polarity phenomena and alternative semantics[END_REF][START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF] analysis of polarity sensitive items. Krifka's goal was to derive the distribution of polarity items from their semantic structure and independently motivated pragmatic principles. Here I illustrate the general idea with his analysis of the NPI any. The analysis has a semantic and a pragmatic component. As for the semantics, NPI's are assumed to introduce a property and a set of alternative properties. In order to capture this dependency on alternatives, the semantics of NPI's makes use of structured meanings that were originally developed for the semantic analysis of focus. According to this, the denotation of a sentence containing an NPI is a triple B,F,A , where B stands for background context, F for focus value, i.e. the relevant property introduced and A a set of alternative properties that are more restricted:

(12) a function from properties to propositions B , a property P F , the set of subsets of P A Thus the BFA-structure of the (unacceptable) sentence *Mary saw anything is the following:

(13) B: a function from properties Q to the proposition that Mary saw Q F: the property of being a thing A: a set of properties that are stronger than the most general property of being a thing

If we apply the background B to the focus F, we get B(F), the proposition that Mary saw a thing. If we apply the background B to some alternative F' in A, we get B(F'), for example, the proposition that Mary saw a spoon. Note that there is an ordering wrt. informativeness between B(F) and B(F'): in this case B(F') is more informative (stronger) than B(F). Now, to the pragmatic component: The kind of BFA-structure exemplified above triggers a special pragmatic rule called SCALAR.ASSERT. This rule takes a BFA-triple and adds a strengthened proposition to the common ground. This strengthened proposition consists of (i) the proposition expressed by B(F) (ii) the negation of the alternative propositions that are informationally at least as strong as B(F).

Definition SCALAR.ASSERT (BFA)(c)= (i) add B(F) to the common ground c (ii) add the negation of every alternative B(F') that is informationally at least as strong as B(F), to the common ground c.

Thus SCALAR.ASSERT hardwires Gricean scalar implicatures into a special assertion operator that applies whenever a relevant scalar structure is present. Applying Scalar.Assert in the case of ( 13) gives us, informally, ( 14) SCALAR.ASSERT (BFA-structure for Mary saw anything)(c)= (i) add to the common ground c that Mary saw a thing (ii) add to the common ground c that Mary did not see any specific thing (e.g. that Mary did not see a spade, that Mary did not see a spoon, and so on for any F' in A.)

But the two conditions are contradictory because whenever there is some thing that Mary saw, that thing must also have some more specific property P. Since the two conditions are contradictory, adding both of them to the common ground c reduces c to the empty set and communication fails. In contrast, in the case of a negative sentence Mary did not see anything the second condition of SCALAR.ASSERT is vacuous because for every P, such that P is a subset of things, the proposition that Mary did not see a P is weaker than the proposition that Mary did not see a thing.

A crucial aspect of the approach of [START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF] is that there is no licensing condition involved, the behaviour of NPIs follows from general conversational principles. Thus this approach goes one step further than approaches based on licensing conditions: it seeks to answer the question of why these contexts license NPIs.

The idea that uninformativity due to a systematic clash of implicatures can lead to ungrammaticality has been taken up by a number of researchers. In the domain of polarity sensitive items, [START_REF] Lee | Any as indefinite plus even[END_REF], [START_REF] Lahiri | Focus and negative polarity in hindi[END_REF] and [START_REF] Van Rooy | Negative polarity items in questions: Strength as relevance[END_REF] have proposed analyses in the spirit of [START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF]. The ungrammaticality of certain so-called syntactic islands has also been analysed as a result of implicature clash, see for example [START_REF] Kuno | Remarks on negative islands[END_REF] analysis of negative islands, [START_REF] Oshima | On factive islands: pragmatic anomaly vs. pragmatic infelicity[END_REF] analysis of factive islands or [START_REF] Simonenko | Semantics of dp islands: the case of questions[END_REF] proposal for explaining DP islands.

Another line of pragmatic approaches attributes the unacceptability of certain constructions to a clash of presuppositions. For example, [START_REF] Dayal | Any as inherently modal[END_REF] analysis of free choice any assumes that the reason why any cannot be used in episodic sentences is due to conflicting presuppositions. The peculiar distribution of certain focus particles (e.g. auch nur, even) has also been proposed to follow from incompatible presuppositions, which can be resolved in some semantnic environments (cf. [START_REF] Guerzoni | Why even ask?: on the pragmatics of questions and the semantics of answers[END_REF], Abrusán 2007b[START_REF] Crnic | Getting even[END_REF]. Likewise, Abrusán (2007a[START_REF] Abrusán | Weak Island Semantics[END_REF] proposed that certain island constraints can be derived from systematically unmet or outright contradictory presuppositions. In another domain, [START_REF] Portner | The (temporal) semantics and (modal) pragmatics of the perfect[END_REF] derives the incompatibility of the present perfect with temporal adverbials such as yesterday (e.g. *Mary has read Middlemarch yesterday.) by assuming that the presupposition of the latter contradicts the presupposition of the former. Another example is [START_REF] Zucchi | The ingredients of definiteness and the definiteness effect[END_REF] analysis of the definiteness effect observed in there-existential sentences.6

Systematic vs. occasional pragmatic infelicity

One question that is often raised about the idea that systematic pragmatic infelicity can lead to ungrammaticality is the following: What distinguishes the ungrammatical cases from better known and more innocent pragmatic violations such as implicature cancellation or presupposition failure? For example, uttering the sentence John stopped paying taxes in a context in which it is known that John has never paid taxes forces the hearer to accommodate a presupposition that clashes with what is known. Similarly, the ignorance implicature of the sentence John is at home or in the bar will clash with the context if it is known that John is in the bar. The result in such cases might be a communicative breakdown, or a cancellation of the relevant presupposition/implicature, or an adjustment of the context, but it does not seem to involve ungrammaticality. 7It is for this reason that I have emphasised the word systematic above. In simple cases of presupposition failure or violations of Gricean maxims it is not possible to accomplish a successful speech-act because what is presupposed/implicated clashes with the particular context in which they are uttered. Under different circumstances, the relevant sentences could have been felicitously uttered. These cases are similar to Grice's particularised conversational implicatures. In contrast, the pragmatic infelicity of the type proposed by Krifka and others does not depend on the particular context chosen, any context will lead to an infelicitous assertion. Thus these cases represent a special type of pragmatic infelicity, similar to Grice's generalised conversational implicatures. [START_REF] Oshima | On factive islands: pragmatic anomaly vs. pragmatic infelicity[END_REF] calls such cases 'pragmatic anomaly'.) 8 The same point holds for the analyses cited above where unacceptability was based on systematic presupposition failure that did not depend on the discourse context.

One might wonder what explains the difference of intuitions between the ungrammatical examples referred to in this section and semantic anomaly understood as a failure of pragmatic presuppositions. A possible answer is that examples of semantic anomaly, as it will be discussed in the last section, show a high degree of context sensitivity, unlike the cases above.

Recursive pragmatics

A thorny issue for the approaches based on pragmatic infelicity (or, 'pragmatic anomaly') is that (at least some of them) need to assume that the relevant pragmatic process can apply in embedded contexts, i.e., at the sub-sentential (subutterance) level. For example, making [START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF] approach work, in general, requires (as he points out) that the SCALAR.ASSERT operator apply to embedded constituents. One case is double licensing exemplified in (15b); here SCALAR.ASSERT needs to apply to the restrictor of the conditional: (15a) If he knows anything about logic, he will know Modus Ponens.

(15b) If he doesn't know anything about logic, he will (still) know Modus Ponens. [START_REF] Hoeksema | Monotonicity phenomena in natural language[END_REF] Krifka himself proposes to embrace this radical assumption. As he puts it (page 245), "we must develop a framework in which illocutionary operators are part of the semantic recursion", in other words, that embedded constituents can count as illocutionary acts. This might be done, for example, if we assume some form of dynamic semantics. Others took such facts to show that certain implicature-like processes should be encoded at the level of truth-conditional semantic interpretation. We turn to some such approaches in the next section.

4 Ungrammaticality from triviality: a case for natural logic?

Another line of research has proposed that triviality of meaning can also lead to ungrammaticality. A well-known case concerns the acceptability of quantifiers in there-existential sentences. [START_REF] Milsark | Toward an explanation of certain peculiarities of the existential construction in english[END_REF] observed that certain quantifiers, that he called strong quantifiers, such as every, both, neither, etc. are unacceptable in this construction, as shown in example (16a). In contrast, weak quantifiers such as some, few, three, etc. are acceptable.9

(16a) *There is every fly in my soup.

(16b) There are some flies in my soup.

There is no obvious syntactic difference between the two examples above, and indeed most explanations of this contrast reduce it to some difference in the semantic and pragmatic meaning of the quantifiers involved (cf. Milsark 1977, Barwise and[START_REF] Barwise | Generalized quantifiers and natural language[END_REF][START_REF] Zucchi | The ingredients of definiteness and the definiteness effect[END_REF][START_REF] Comorovski | On quantifier strength and partitive noun phrases[END_REF][START_REF] Keenan | The definiteness effect: Semantics or pragmatics? Natural Language Semantics[END_REF], McNally 1998, etc.) A prominent early explanation of the contrast by [START_REF] Barwise | Generalized quantifiers and natural language[END_REF] proposed that the reason for the unacceptability of strong quantifiers in the thereexistential construction is because the meaning of such sentences is trivial: they are true (or false) independently of the properties of the context. In contrast, a there-existential sentence with a weak quantifier has a meaning that is contingent on the properties of the context. This conclusion follows from the theory of generalised quantifiers and the crucial assumption that the expletive there denotes the domain of individuals D e . If we grant this assumption, then example (16a) can be paraphrased as 'The set of flies in my soup is a subset of D e ' which cannot be false since the empty set is also a subset of D e . In contrast, the meaning of (16b) can be paraphrased as 'the intersection of the set of flies in my soup and the domain D e is not empty', which can be false if there are no flies in my soup.

This proposal, although controversial, has also been quite influential in the literature. Similar explanations have been given to a number of phenomena, for example the partitive constraint [START_REF] Barwise | Generalized quantifiers and natural language[END_REF][START_REF] Ladusaw | Semantic constraints on the English partitive construction[END_REF], the butexceptive construction (von Fintel 1993), restrictions on comparatives (Gajewski 2008), polarity items [START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF], free-choice items (Menéndez-Benito 2005), various island constraints and intervention effects [START_REF] Fox | The Universal Density of Measurement[END_REF], Abrusán 2007a[START_REF] Abrusán | Weak Island Semantics[END_REF][START_REF] Mayr | Intervention effects and additivity[END_REF]. Most recently the idea has been used to explain restrictions on complement selection [START_REF] Uegaki | The anti-rogativity of non-veridical preferential predicates[END_REF]Sudo 2017, Theiler et al. 2017).

In the case of many of these proposals, there is a natural connection to pragmatic approaches. If one assumes, following [START_REF] Chierchia | The Grammatical View of Scalar Implicatures and the Relationship between Semantics and Pragmatics[END_REF], that Gricean conversational implicatures can (or should) be computed at the level of semantics via a silent operator that 'exhaustifies' alternatives (i.e. negates all stronger alternatives), then a Krifka-style pragmatic clash involving contradictory implicatures will appear at the level of truth-conditions. This is what is proposed by [START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF]. Similarly, analyses for syntactic island constraints that rely on the necessary exhaustification of answers could be, in principle, cast in pragmatic or semantic terms, depending on whether exhaustification of alternatives is assumed to happen in the pragmatic or in the semantic module. This is the case in [START_REF] Fox | The Universal Density of Measurement[END_REF], Abrusán 2007a[START_REF] Abrusán | Weak Island Semantics[END_REF].

Typical semantic anomalies of the type My toothbrush is pregnant are not predicted to be ungrammatical by this proposal since they are not logically trivial. But a question arises in connection with sentences that express meanings that are logically trivial, for example (17a) and ( 17b (17b) This table is red and not red.

Intuitively, these sentences need not be tautological if the predicates woman and red are understood differently in their occurrences. For example, woman may be understood in a biological sense in its first occurrence, and in a psychological sense in its second occurrence. Such apparent tautologies even are a common rhetorical figure, cf. War is war or Boys will be boys. It seems that in order for such sentences to be interpreted, the occurrences of the the expressions have to be interpreted differently. A version of this idea was developed in [START_REF] Gajewski | On Analyticity in Natural Language[END_REF], reviewed in the next subsection.

L-triviality

In an unpublished but widely cited paper, Gajewski proposed that there is a formally specifiable subset of trivial sentences, called 'L-trivial', whose members are systematically unacceptable (cf. Gajewski 2002). 11 On the standard, Tarskian conception, logical truth and consequence are defined in terms of variation of truth across all interpretations of the logical form. The logical form of sentences, as usually understood, is a level of semantic representation that preserves all semantically significant features of the sentence (e.g. its lexical content) but is free of imperfections such as ambiguity. L-triviality, in contrast, is calculated on modified logical forms in which all lexical material has been 'bleached', i.e. replaced non-uniformly by a fresh variable of the appropriate type. [START_REF] Gajewski | On Analyticity in Natural Language[END_REF] calls these impoverished logical forms 'logical skeletons' (LS): 12Definition Logical skeletons (LS) are obtained from the logical form (LF) α as follows:

(i) Identify the maximal constituents of α containing no logical items.

(ii) Replace each such constituent with a distinct variable of the same type.

Thus the logical form (LF) of the sentence It is raining or it is not raining is something akin to (18a) (where raining stands for the proposition that it is raining), but its logical skeleton (LS) is (18b), where p and q stand for propositional variables:

(18a) LF: raining ∨¬ raining (18b) LS: p ∨ ¬ q Given logical skeletons, L-triviality can be defined as follows:

Definition An LF constituent a of type t is L-trivial iff a's logical skeleton receives the denotation 1 (or 0) under all interpretations.

Notice that according to this definition, the sentence It is raining or it is not raining, even though it is a tautology, is not L-trivial. L-triviality and unacceptability are linked by the following hypothesis:

Hypothesis A sentence is ungrammatical if its LF contains an L-trivial constituent.

According to [START_REF] Gajewski | On Analyticity in Natural Language[END_REF], the triviality of (16a) can be derived even after destroying the identity of non-logical predicates, simply by looking at the logical skeleton. The determiner every as well as the particle there are elements of the logical vocabulary and are preserved in the logical skeleton. Lexical predicates such as every fly in my soup are replaced by a fresh variable of the appropriate type. Therefore the logical skeleton of (16a) looks as follows:

(19a) LS of (16a): there is every P. Whatever the interpretation of P is in the model, the meaning assigned to the logical skeleton in (19a) is tautologous.

In contrast, a sentence such as (17a) is not L-analytical: once we remove the identity of the non-logical expressions (in this case, woman) when constructing the logical skeleton, we cannot deduce the triviality any more.

(20a) LS of (17a): every P is Q

(20b) Interpretation: [[every]] (I(P)) (Q)
As a consequence, such sentences are not predicted to be ungrammatical by Gajewski's ( 2002) system.

Under the resulting picture, grammar itself is endowed with the capacity to calculate L-triviality. This means that the grammar of natural languages has to include (or at least interact with) a system of 'natural logic', or a 'natural deductive system' (see [START_REF] Fox | The Universal Density of Measurement[END_REF][START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF][START_REF] Del Pinal | The logicality of language: Triviality and logical form[END_REF]. By assumption, this deductive system is blind to conceptual information and cannot 'see' non-logical terms, it operates only on the basis of functional terms. This in turn presupposes that terms can be sorted into two non-overlapping classes, lexical terms and functional (or logical) terms.

In the remainder of this section I first discuss the application of L-triviality to Chierchia's analysis of polarity items. Second, I go on observing some problems that motivate us to look for an alternative explanation. Chierchia's (2005[START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF] analysis of polarity items is based on [START_REF] Krifka | Polarity phenomena and alternative semantics[END_REF][START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF] approach, but with some important differences. Chierchia adopts the idea that NPIs contribute a property whose alternatives are subproperties. He also adopts the idea that there is a communicative pressure to make the strongest claim possible with scalar items. However, instead of the SCALAR.ASSERT operator, this is achieved by a silent exhaustivity operator (O) whose meaning is roughly equivalent to only. Similarly to SCALAR.ASSERT, the presence of an exhaustivity operator is triggered by the presence of grammatically-encoded alternatives. In contrast to Krifka's approach, exhaustification happens at the level of semantics, and is not tied to making a speech act.

Application to Chierchia's analysis of polarity items

Thus Chierchia assumes that any associates with focus, causing it to trigger alternatives. Any also has a lexical requirement that its active alternatives must range over subdomains D' of the domain D that any associates with. Any furthermore requires that these alternatives be exhaustified by an exhaustive operator O: the operator O negates every alternative in the domain that is not entailed by the original sentence. In the case of a sentence such as Anything is blue its logical form, truth conditional import and focus alternatives are as follows:

(21a) LF of Anything is blue: O[any F,D thing is blue] (21b) the truth conditional import of (21a): ∃x∈D[thing(x)∧blue(x)] (21c) the alternatives of (21a): { ∃x∈D' [thing(x)∧blue(x)] | D'⊆ D } Just as we saw in the analysis of Krifka, each alternative in (21c) entails the assertion in (21b). As the alternatives in (21c) are not entailed by (21b), exhaustifying the assertion via the O operator will negate them. This leads to a contradiction because the resulting statement implies that there there is some thing that is blue (= the meaning of (21b)) but there is no particular thing such that is blue (=the negation of each alternative in (21c)).

The interpretation of the LF in ( 21a) is thus a contradiction, but is it also Ltrivial in Gajewski's sense? Only with a number of auxiliary assumptions. Firstly, any and the silent operator O need to be part of the logical vocabulary. This is a stipulation, but not problematic in itself. However, Chierchia's derivation is encoded by a set of lexical restrictions introduced by any. These restrictions, namely that any associates with focus, the requirement that its active alternatives must range over subdomains of the domain D that any associates with, the requirement that the alternatives have to be exhaustified by the operator O are presumably encoded as presuppositions of any. Accordingly, Gajewski's proposal needs to be modified in order to take presuppositions into account. Such a modification was offered in [START_REF] Gajewski | More on quantifiers in comparative clauses[END_REF]

(for slightly different reasons):

Definition A sentence S is L-trivial iff S's logical skeleton receives the truth value 1 (or 0) on all interpretations in which it is defined.

Another necessary auxiliary condition is that when constructing the logical skeleton, the variables that replace lexical predicates have to be given the same assignment in all the alternatives as in the LS of the original sentence. For example, in the case of (22c), the variables P and Q that replace the non-logical vocabulary have to be given the same assignment in each of the alternatives that they had in the LS of the original sentence; otherwise triviality does not follow. Similar auxiliary assumptions need to be used for many accounts that rely on L-triviality, e.g. [START_REF] Gajewski | More on quantifiers in comparative clauses[END_REF], [START_REF] Fox | The Universal Density of Measurement[END_REF] [START_REF] Abrusán | Weak Island Semantics[END_REF].

Some problems

Defining logical words [START_REF] Gajewski | On Analyticity in Natural Language[END_REF] proposal hinges on distinguishing two types of vocabulary, logical and non-logical vocabulary. Despite intuitions about the existence of the two classes of words, finding a precise semantic difference has proven difficult. The most frequently cited idea, borrowed from a tradition in logic aimed at defining logical constants, is that function words have meanings that are invariant across certain algebraic transformations of their domains. 13 Examples of transformations that have been proposed to diagnose logical constants include invariance under permutations [START_REF] Tarski | A formalization of set theory without variables[END_REF][START_REF] Van Benthem | Logical constants across varying types[END_REF][START_REF] Sher | The Bounds of Logic[END_REF], invariance under surjective functions [START_REF] Feferman | Logic, logics, and logicism[END_REF], invariance under potential isomorphisms [START_REF] Bonnay | Logicality and invariance[END_REF], etc. The underlying idea is that logical meanings are topic-independent: the validity of a logical inference should not depend on the particular properties of what we are talking about. The appropriateness of the above ideas for diagnosing logical constants is a subject of lively debate; but they are clearly unsuitable for diagnosing function (logical) words of natural language (see [START_REF] Gajewski | On Analyticity in Natural Language[END_REF][START_REF] Van Benthem | Invariance and definability: two faces of logical constants. essays in honor of sol feferman[END_REF]. This is because they predict certain lexical items to be logical (e.g. the predicates self-identical, exist), and they also predict that certain intuitively logical elements of natural language, e.g. the quantifier every or each are not logical since they have a lexical restriction that they need to quantify over countable objects, hence *Every/*Each milk is in the fridge.

It seems that there is no foolproof method that can distinguish logical words from non-logical ones that also makes the cut in a linguistically intuitive way. The difficulties mentioned above suggest that the logical/grammatical aspects and the conceptual aspects of meaning do not map neatly onto two different classes of words. Instead, both functional and lexical words have logical and conceptual aspects of meaning, packaged together (see also [START_REF] Abrusán | Content vs. function words: The view from distributional semantics[END_REF] An alternative possibility, one that Gajewski also considers, is to replace the logical/non-logical distinction with the functional-lexical distinction familiar from the linguistic literature (see for example [START_REF] Abney | The English Noun Phrase in Its Sentential Aspect[END_REF][START_REF] Von Fintel | The formal semantics of grammaticalization[END_REF]. This too suffers from difficulties, as some words, for example prepositions or the word there are not clear cases of either category. [START_REF] Gajewski | On Analyticity in Natural Language[END_REF] proposal has profound implications for how we should think about the language system and its interaction with other cognitive systems in general. If L-triviality can have implications for grammaticality, grammar needs to interact with a natural deductive system (cf. also Fox and Hackl 2007, Chierchia to appear). The idea that grammar might be related to some system of natural logic is not in itself new; it has been much discussed in the context of the semantics of quantifiers, monotonicity reasoning, polarity items etc. (see e.g. [START_REF] Van Benthem | Essays in logical semantics[END_REF], 2008[START_REF] Dowty | The role of negative polarity and concord marking in natural language reasoning[END_REF][START_REF] Moss | Natural logic[END_REF]. What is new is that L-triviality suggests a radical form of modularity of language: grammar is insulated not only from conceptual systems, general world knowledge, but also from most of the information encoded in lexical items. At the same time, grammar needs to have a privileged access to some aspects of the meaning of lexical items, namely their types and (other) presuppositions that they induce.

An exotic deductive system

As it was emphasised in Del Pinal (2017), a deductive system that operates on logical skeletons is a rather exotic system for which most classical formulas and rules of inference are invalid. It is conceivable that the properties of the natural deductive system, as used by grammar, could indeed be radically different from classical systems. However, Del Pinal (2017) argues that certain key accounts depending on logical skeletons, e.g. [START_REF] Chierchia | Logic in grammar: Polarity, free choice, and intervention[END_REF] account of polarity-sensitive items, cannot be maintained if the Law of Non-Contradiction is invalid at the level of representation where the deductive system determines grammaticality.

Del Pinal (2017) therefore proposes a modification of [START_REF] Gajewski | On Analyticity in Natural Language[END_REF] idea which allows triviality to be calculated on standard logical forms instead of skeletons. He defends a semantic version of contextualism according to which the interpretation of lexical predicates (or 'open class items') can be modulated by a polymorphic operator RESCALE. This covert operator allows for a more specific interpretation of lexical items and can be freely inserted at LF.

Definition RESCALE

For any open class term P, argument of suitable type x and context c, {x : RESCALE c (P)(x)} ⊆ {x : P(x)}

Crucially, the context sensitive parameter of RESCALE can be fixed differently at each position in a sentence and RESCALE cannot modulate the meaning of closed-class items. Given this, we can see that a sentence such as (17a) can have the LF in (23a), which might get a non-tautologous reading. Notice that the two RESCALE operators are independent of each other and we have a non-tautologous meaning if they select two different specific meanings of the predicate. On the other hand, RESCALE does not help with (16a) since it can only modulate lexical predicates, whose meaning is irrelevant for deriving the triviality of the sentence: (23a) Every RESCALE c (woman) is a RESCALE c' (woman).

(23b) There is every RESCALE c (fly in my soup). Del Pinal's (2017) solution has a number of advantages: It resolves the problems that arise with exotic deductive systems and allows us to stick to better known systems. Il also resolves certain empirical problems with L-triviality concerning bound variables and reflexives (see [START_REF] Gajewski | L-triviality and grammar[END_REF], Sauerland 2017, Chierchia to appear). However, it still crucially depends on a sharp division of lexical vs. logical vocabulary. Moreover, the proposal is slightly unintuitive in the case of examples such as (24a), in which semantic modulation of the meaning of the predicates raining in the antecedent would clash with the consequent: (24a) John believes that it is raining and it is not raining, therefore he has inconsistent beliefs.

(24b) possible LF of (24a): John believes that it is RESCALE c (raining) and it is not raining, therefore he has inconsistent beliefs.

According to Del Pinal (2017), the first clause of the above sentence is saved from being ungrammatical because its meaning can be made non-contradictory, in theory, by inserting a RESCALE operator that modulates at least one occurrence of the predicate raining. Grammar is sensitive to the presence of this operator, which allows for the possibility of interpreting the the two occurrences of the predicate raining differently and thus resolving the trivial meaning. However, the actual fixing of the context parameter of the RESCALE operator happens at the pragmatic level and it might, in theory, pick out a non-specific reading of the predicate raining. This is what explains why the second clause in (24a) does not seem to contradict the first clause. The insertion of the RESCALE operator is vacuous from the point of view of the actual interpretation of the sentence, but its presence is enough to make the antecedent potentially-non trivial and hence grammatical.

Future directions

Where do we stand now? We have seen a number of different types of semantic and pragmatic analyses of ungrammatical sentences. We have seen how systematic pragmatic infelicity ('pragmatic anomaly') differs from occasional pragmatic infelicity. However, no clear answer emerged as to what distinguishes sentences that are felt merely as semantically anomalous from other cases of semantically or pragmatically deviant sentences that are felt ungrammatical.

In what follows I outline a recent proposal by [START_REF] Abrusán | Grammaticality and meaning shift[END_REF] that argues that the underlying cause for both semantic anomaly (e.g. #My toothbrush is pregnant) and ungrammaticality is failure to observe semantic compositional rules (including semantic-presuppositions). 14 According to this proposal the difference comes about because cases of semantic anomaly, in contrast to ungrammatical examples, could be repaired by meaning shift, however far-fetched a scenario that would require. 15 This approach, in a sense, asks the reverse of the question we have been asking so far: Why don't the examples of semantic anomaly feel ungrammatical? In the case of (1b), semantic composition fails because the meaning and the selectional restrictions of the predicates give us a meaning that is nonsensical. But in contrast to many ungrammatical examples, we know exactly where the locus of inconsistency lies and we also have the ability to shift the meaning of the predicates in an interpretive context in order to try to resolve this inconsistency. (See the results of a Stanford competition in 1985 to find contexts in which (1b) could be meaningfully uttered. 16 ) Contextual shifting of the meaning of words has been a major topic in the philosophy of language. 17 Some of the most extreme cases of meaning shift are demonstrated by metaphors (25a) and metonymy (25b) (e.g. coercion, i.e. a reinterpretation process triggered by a mismatch between the selectional restrictions of a function and its argument):

(25a) Language is the breath of God, the dew on a fresh apple, it's the soft rain of dust that falls into a shaft of morning sun when you pull from an old bookshelf a half-forgotten volume of erotic memoirs. (26a) heavy box (26b) heavy traffic expressed in a framework in which presuppositions are thought of as pragmatic. The usefulness of a formal system using rich types comes, in part, from the fact that it is easier to integrate it with a computational semantic framework. 15 Logically trivial sentences such as It is raining an not raining do not show a compositionality problem and are not semantically anomalous. I return to this below. 16 An example entry from the competition, from C.M. Street, is: "It can only be the thought of verdure to come, which prompts us in the autumn to buy these dormant white lumps of vegetable matter covered by a brown papery skin, and lovingly to plant them and care for them. It is a marvel to me that under this cover they are labouring unseen at such a rate within to give us the sudden awesome beauty of spring flowering bulbs. While winter reigns the earth reposes but these colourless green ideas sleep furiously". 17 A growing body of work assumes that the meaning of lexical words can be shifted or modulated in one way or another: either within the semantics (cf. e.g. [START_REF] Martí | Unarticulated constituents revisited[END_REF][START_REF] Stanley | Language in context: Selected essays[END_REF][START_REF] Alxatib | Acceptable contradictions: Pragmatics or semantics?[END_REF] or within the pragmatics (e.g. [START_REF] Kamp | Prototype theory and compositionality[END_REF][START_REF] Recanati | Truth-conditional pragmatics[END_REF][START_REF] Lasersohn | Contextualism and compositionality[END_REF] 18 see https://www.youtube.com/watch?v=0gjWUiVtldk (26c) heavy bleeding (26d) heavy drinker

Meaning shifts can happen with more or less of an ease. It has been observed that semantic anomaly is a graded phenomenon (cf. [START_REF] Drange | Type crossings[END_REF][START_REF] Magidor | Category Mistakes[END_REF][START_REF] Lappin | Sorts, ontology, and metaphor: the semantics of sortal structure[END_REF]. For example, it is increasingly more difficult to interpret the examples below: One way to think about this gradience is in terms of distance within a semantic space. Intuitively, tigers and humans are fairly close in meaning in that they share a number of features, e.g. they are both animate. In contrast, tigers and Zermelo-Fraenkel sets do not have much in common. Let's assume that selectional restrictions of predicates and other lexical conditions are modelled formally as type-presuppositions in a richly-typed system as in Type-Composition Logic, TCL (cf. [START_REF] Asher | Lexical Meaning in Context[END_REF]. Types are organised into a type hierarchy that represents the conceptual organisation of semantic categories and allows for a calculation of semantic distances. Applying meaning shift to the examples in (27a-c) means that we can try to relax the type presuppositions in question. Depending on the semantic distance between the actual and the target types, type shift allows us to make sense of examples of semantic anomaly to a greater or smaller degree. The higher the type that is involved in the type clash, the more difficult is it to shift the meaning of predicates to resolve type conflict. Nevertheless, even with examples such as (27c), we can glean what could have been said. The contradiction between type presuppositions in these examples is somehow localized. And by relaxing those type presuppositions, for instance by supposing that the predicate in example (27c) simply is seeking an entity of general type E, the composition could actually have succeeded.

The problems of composition in ungrammatical sentences are worse in that no shifting of the type presuppositions seems possible. These types are somehow constitutive of the construction in a way that simpler type presuppositions of open class expressions, nouns, verbs and adjectives, are not. Abrusán et al.'s (2019) hypothesis is that the type presuppositions that are violated in ungrammatical sentences are constitutive of the type of denotation at the highest level of the type hierarchy. For instance, it is something about the nature of existential predication that leads to the uninterpretability of there is every girl; it is something about the semantic type of questions that leads to the uninterpretability of weak island sentences, and so on. (I came back to these ideas below.) Another property that might underlie the difference between semantic anomaly and certain ungrammatical examples is the locality of the type-conflict. In the case of classic examples of semantic anomaly, type conflict (presupposition failure) arises at the level of predicate-argument composition. If shifting were to occur, it would also happen at this level, where the nature of the type-conflict is clear and lowest common types are easy to calculate. In the case of many ungrammatical examples the type conflict arises at a more global level with more linguistic elements (and types, as a consequence) that are involved. Calculating lowest common types is harder, and it is more likely there are simply none.

Meaning shifts in Distributional Semantics [START_REF] Abrusán | Grammaticality and meaning shift[END_REF] assume that meaning shift can be diagnosed and calculated precisely with the help of a computational method called distributional semantics (DS). A simple-minded way to think about word meaning in this framework is to assume that it is a vector in space V whose dimensions are contextual features. 19 This computational method can find low-level types and calculate distances in semantic space as well as meaning shift involved in semantic composition (cf. [START_REF] Asher | Integrating type theory and distributional semantics: A case study on adjective-noun compositions[END_REF]. It predicts, e.g. shifts that occur with the various occurrences of heavy in (26a-d) or meaning shifts enforced by the context, e.g. the shift from Julie enjoyed the monologue to Julie enjoyed listening to the monologue. It does not, however, predict shifts with highlevel types (e.g. the types for questions or quantifiers) for at least two reasons. Firstly, these types denote context-invariant logical meaning that is simply invisible for distributional methods. Second, the conflicting type-clash is attached to a type so high in the type hierarchy that the type has no neighbours that share the same syntactic/semantic dependencies and so there is nowhere in the space for its meaning to shift. Thus types that are at a maximally general level, for example questions, whose type is a family or set of propositions, propositions themselves, the general type E of entities, the general type of determiner phrases DP, quantifiers or second order properties etc. don't have any neighbours in a vector space, in the way that say a common noun like tiger or idea does. This is because other expressions that are not of say DP type will belong to a different syntactic category with different syntactic/semantic dependencies; they will be in a different space (though they may share the same latent dimensions as particular DPs). As a result, there is nowhere in the space for such a type to shift and preserve its corresponding syntactic category. DS methods can't shift those types, in the way that they can shift the meaning of lexical words in context. Furthermore, because these types don't have neighbours in the vector space if indeed they inhabit a vector space at all, these semantic principles will not show up in particular latent dimensions of the vector space. DS methods, at least of the sort [START_REF] Asher | Integrating type theory and distributional semantics: A case study on adjective-noun compositions[END_REF] and [START_REF] Abrusán | Grammaticality and meaning shift[END_REF] have employed, will not be able to see these principles. For expressions that have type presuppositions at this level, it follows that they cannot be shiftable. 20 On the other hand, one can imagine another kind of shift -one that rescues some sort of content from a predication in which there is an irresolvable type clash between a predicate and its argument. ( 1b) or ( 27a-c) are examples of this. If we simply move to the supertype of the type presuppositions, we can see that the author of (1b) or (27a-c) was predicating a property of some object; she was just confused about or wilfully misusing the meaning of the property or the object expression. The distance between the type presuppositions of the predicate and arguments may be great, but it is still defined, as tiger and say ordinal are both in the same vector space DS defines for common nouns. And thus DS and TCL together provide us with a means to distinguish (1b) and (27a-c) from ungrammatical examples. 21 Examples This approach allows for an integration of various perspectives mentioned above, in particular, approaches based on a violation of a semantic condition and presupposition clash. For example, in the case of polarity items such as any we might assume, in accordance with various authors cited in Section 2, that its distribution is governed by a lexical semantic condition. (Possibly, [START_REF] Krifka | The semantics and pragmatics of polarity items[END_REF] account might be viewed as providing a functional motivation for this semantic condition.) As for existential sentences, we might adopt [START_REF] Mcnally | Existential sentences without existential quantification[END_REF] proposal according to which the existential predicate has a sortal restriction on its postverbal argument, requiring it to be a nonparticular (formalised as properties). An argument in favour of this view comes from examples such as (28b), which shows that the restriction is not simply on the type of quantification: (28a) *There was every doctor at the convention. 20 An interesting question raised by an anonymous reviewer is what happens in the case of number words. These have logical meanings, but they also have neighbours in vector space. Possibly we might observe shifting in the granularity standard associated with numerical expressions, e.g. as in 5.3 grams of radioactive material vs. 50 thousand protesters on the street. But one would need to perform experiments to be able to tell. 21 Abrusán et al.'s (2019) proposal is explicitly about semantic anomaly and ungrammatical sentences for which semantic/pragmatic analyses have been proposed. It remains to be seen whether this approach can be generalised to all cases of ungrammaticality. The idea that ungrammaticality is a compositionality problem at the syntactic level, is a rather classical one. If one assumes a categorial syntax accompanied by type-driven composition, e.g. [START_REF] Klein | Type-driven translation[END_REF], than syntactic compositionality problems ultimately boil down to a type-clash of some very basic types. Such compositionality problems are very similar to the type clash of unshiftable high-types observed in TCL and thus a unified analysis seems promising.

(28b) There was every kind of doctor at the convention. This view also allows for integrating pragmatic accounts, e.g. those based on systematic presupposition failure such as [START_REF] Abrusán | Weak Island Semantics[END_REF] analysis of weak islands, as these can be expressed as type conflicts. See [START_REF] Abrusán | Grammaticality and meaning shift[END_REF] for more details.

Meaning shift vs. triviality Triviality of meaning, on the other hand, does not play any role in this explanation: trivial sentences do not show a compositionality problem and are thus predicted to be acceptable. (Meaning shift might still apply to them in order to increase their informativity, as in the case of (17a).) Nor is there any reason to assume a sharp conceptual division between lexical and logical vocabulary. The conceptual content of lexical as well as logical words might have both logical aspects (their model theoretic meaning) and lexical ('worldly') aspects. For example, the conceptual content of a universal quantifier such as every might be composed from its logical content (i.e. universal quantification) and a more lexical content, e.g. it's lexical restriction to countable predicates. We cannot neatly separate grammar and conceptual knowledge because they are packaged together within lexical entries. However, we can distinguish conceptual content that is contextually invariant from shiftable conceptual content (cf. [START_REF] Abrusán | Content vs. function words: The view from distributional semantics[END_REF]. Conceptual content that supports logically valid inferences for first order definable quantifiers (whose conceptual content in the form of proof rules can determine all logical consequences of such quantifiers) should always be contextually invariant, since a particular context should not render logically valid inferences incorrect. We would never expect meaning components that lead to logically valid inferences to shift in context. Other types of conceptual content of logical words, however, can be shiftable; that is, context might affect the conceptual content and the extension of a predicate or its argument as well.

Conclusion

We find out how things work when they are broken. In linguistics, it has often been assumed to be intuitively clear to which domain the source of the problem of an unacceptable sentence can be attributed: phonology, syntax, semantics, processing, etc. However, the history of the field shows that problems that appear at first sight to be belong to one domain (e.g. syntax) are sometimes later shown to have a semantic, pragmatic (or processing) motivation. One example, discussed in this paper, is the case of NPIs.

Once we accept that different types of "weirdness" can have similar interpretive sources, a new question arises: what leads to a difference in intuitions if the source of the problem is the same? In particular, what distinguishes ungrammatical examples from cases of semantic anomaly or pragmatic infelicity? This paper has reviewed various proposals that address this question and also outlined a possible new direction.

  called negative polarity items (NPI's), shown in italics in the sentences below: (3a) John didn't see anything.

(

  3b) *John saw anything. (4a) Few people lifted a finger to help. (4b) *Someone lifted a finger to help.

( 9 )

 9 WH degreeX [...NEG(...x...)]

  ) below: If logical triviality leads to ungrammaticality, then what distinguishes the ungrammatical examples from the examples in (17a) and (17b), which are syntactically acceptable or at worst semantically anomalous? 10 (17a) Every woman is a woman.

(

  19b) Interpretation: [[every]] (I(P)) (D e )

(

  22a) LS of Anything is blue: O[any F,D P is Q ] (22b) the truth-conditional import of (22a): ∃x∈D [P(x)∧Q(x)] (22c) the alternatives of (22a): { ∃x∈D' [P(x)∧Q(x)] | D' ⊆ D }

  (Stephen Fry 18 ) (25b) Hugh enjoyed the monologue. (e.g. 'listening to the monologue') More mundane meaning shifts happen with most examples of predication, e.g. in adjective-noun composition. As shown by the examples below, the meaning of the adjective heavy is modulated depending on the noun that it modifies:

(

  27a) #Tigers are human. (27b) #Tigers are buildings. (27c) #Tigers are Zermelo-Fraenkel sets.

I use the terms ungrammatical and semantically anomalous purely descriptively to capture the intuition of speakers. I use the terms weird and unacceptable in a neutral way to refer to any of the previous. The symbol '*' is used to mark ungrammaticality, and '#' to mark semantic anomaly (or category mistakes, as they are called in the philosophical literature). See[START_REF] Graffi | The asterisk from historical to descriptive and theoretical linguistics: An historical note[END_REF] for the history of the asterisk.

Event related potentials (ERPs) are patterned voltage changes that can be measured on the scalp by electroencephalograms (EEG) in response to specific processing events.

[START_REF] Szabolcsi | Weak islands and an algebraic semantics for scope taking[END_REF] mark both examples of weak islands and (10) with '*', but this does not quite render justice to the intuitions of my informants.

This summary approximately follows[START_REF] Magidor | Category Mistakes[END_REF] classification.

One might ask whether the presuppositions assumed in these accounts are necessarily pragmatic or whether they should or could be thought of as semantic presuppositions. The answer, it seems to me, has more to with one's general world-view and favourite theory of presuppositions than with the empirical facts.

 7 A theory for various cases of oddness (e.g. A father of the victim arrived) resulting from computing obligatory implicatures that conflict with common knowledge was offered in[START_REF] Magri | A theory of individual-level predicates based on blind mandatory scalar implicatures[END_REF].

One problem that is sometimes raised against Krifka's analysis is that trivial sentences, e.g. tautologies are also uninformative but are acceptable. However, trivial sentences can be used informatively in a given context, e.g. mathematical proofs; further we have a natural drive to shift the interpretation of the predicates in trivial sentences to make them more informative, cf.[START_REF] Kamp | Prototype theory and compositionality[END_REF]. This argument has more force when raised against the approach discussed in Section 4, see discussion there.

A similar contrast holds for definites vs. indefinites, hence the puzzle is also sometimes called the definiteness effect.

See for example[START_REF] Kamp | Prototype theory and compositionality[END_REF],[START_REF] Alxatib | Acceptable contradictions: Pragmatics or semantics?[END_REF].

[START_REF] Gajewski | On Analyticity in Natural Language[END_REF] original condition is called 'L-analyticity', but this might be slightly misleading, hence we use L-triviality, similarly to some other authors, e.g. Del Pinal (2017).

12[START_REF] Gajewski | On Analyticity in Natural Language[END_REF] works with the notion of logical form that arises from generative grammar, cf.[START_REF] Heim | Semantics in Generative Grammar[END_REF].

Another idea that was advanced in the linguistic literature is that function words involve higher types than lexical items (cf.[START_REF] Partee | Syntactic categories and semantic type[END_REF]. See also[START_REF] Macfarlane | Logical constants[END_REF] for a review of the philosophical literature on logical constants.

This proposal uses[START_REF] Asher | Lexical Meaning in Context[END_REF] formal framework in which presuppositions of lexical items are thought of as semantic (type)-presuppositions. However, the gist of the idea could also be

More complex methods attempt to build a distributional representation in step with the syntactic derivation(Coecke et al

. 2010,[START_REF] Baroni | Frege in space: A program for compositional distributional semantics[END_REF], or use neural networks (e.g.[START_REF] Socher | Semantic compositionality through recursive matrix-vector spaces[END_REF].

Acknowledgments

I am grateful for an anonymous reviewer for excellent suggestions that helped to improve the article considerably, as well as Nicholas Asher, Judit Gervain and Giorgio Magri for their insightful comments. The research reported here was supported by a Marie Curie FP7 Career Integration Grant, Grant Agreement Number PCIG13-GA-2013-618550 as well as by the institutional grants ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL.


Ghylène Goudet

Philippe Liere

Lydie Nadal-Desbarats

Antoine Pianos

Doryan Grivault

Cécile Douet

Christophe Staub

Eric Venturi

Jonathan Savoie

Stéphane Ferchaud

Florence Maupertuis

Antoine Roinsard

Sylviane Boulot

Armelle Prunier

Steroidome and metabolome analysis in saliva from immature to pubertal gilts to identify potential biomarkers of receptivity to boar effect

Our objective was to develop alternatives to hormones for estrus synchronization in gilts. Gilts exhibit a prepuberty period with high urinary estrone concentration during which boar exposure could induce the first ovulation. We searched for salivary biomarkers of this period. Urine and saliva were collected on six 140day-old gilts until puberty for estrone assay, metabolome and steroidome analysis. We identified 23 metabolites and 28 steroids in saliva. The concentration of 8 of them showed significant variations at the pre-puberty period, they were candidate biomarkers. Saliva was collected from 30 gilts exposed to a boar and subjected to estrus detection from 150 to 175 days of age. Metabolome and steroidome analyses allowed the identification of 33 metabolites and 29 steroids in saliva. Their concentrations were not significantly different between receptive and non-receptive gilts. Thus, we could not identify salivary biomarkers of the period of receptivity to the boar effect.

Introduction

Effective methods for synchronizing estrus in gilts are important for batch management. Batches enables allin/all-out systems that allows a better disease control, a tight control at the crucial stages of production and a more efficient use of time and materials. Hormonal treatments, such as Altrenogest®, are used in conventional pig farms, but are not allowed in organic farms. Our objective was to develop a strategy to stimulate first estrus of gilts on a date compatible with the sow management. Before puberty, gilts exhibit a pre-puberty period during which boar exposure could induce and synchronize first ovulation [START_REF] Camous | Plasma prolactin, LH, FSH and estrogen excretion patterns in gilts[END_REF]. During this period, urinary estrone levels are high, but urine sampling is difficult in group-housed females. Thus, practical non-invasive tools for identification of the pre-puberty period in farms are lacking. We searched for salivary biomarkers of the pre-puberty period to develop such tools and improve the detection of the gilts to stimulate.

Material and methods

Two experiments were performed, in order to 1) identify potential salivary biomarkers of the pre-puberty period, 2) check their relevance for the detection of the period of receptivity to the boar effect. In the first experiment, six 144 to 147-day-old Large White gilts were subjected to trans-abdominal ultrasound puberty diagnosis 3 times a week until first ovulation. At the same time, urine samples were collected for estrone assay to detect the pre-puberty period and saliva samples were collected for metabolome analysis using 1 H-Nuclear Magnetic Resonance Spectroscopy ( 1 H-NMR) and steroidome analysis using gas chromatography coupled to tandem mass spectrometry (GC/MS/MS) to search for potential biomarkers of the pre-puberty period. Data were analyzed by multivariate and univariate statistical analyses and repeated measures one-way ANOVA. In the second experiment, saliva samples were collected from 30 Large White x Landrace crossbred gilts that were exposed to a boar twice a day and subjected to estrus detection from 150 to 175 days of age. Among the 30 gilts, 10 were detected in estrus 4 to 7 days after introduction of the boar and were considered receptive to the boar effect, 14 were detected in estrus more than 8 days after boar introduction, 6 did not show estrus and were considered non-receptive. Saliva samples from 6 receptive and 6 non-receptive gilts were analysed for steroidome and metabolome. Four saliva samples per gilt were analysed: 26 days and 11 days before boar introduction, the day of boar introduction, 3 days later for receptive gilts or 7 days later for non-receptive gilts. Similar statistical analyses were performed.

Results

In the first experiment, puberty of the gilts occurred between 182 and 192 days. Urinary estrone concentration significantly increased 2 weeks before puberty. This period with higher estrone levels was considered as the pre-puberty period. In order to identify potential salivary biomarkers of this period, metabolome and steroidome analysis were performed on gilts saliva. Metabolome analysis allowed the identification and quantification of 23 low-molecular-weight metabolites in porcine saliva. Steroidome analysis allowed the identification and quantification of 28 steroids in porcine saliva. The concentration of some metabolites (butyrate and hydroxyvalerate, formate, malonate, propionate, dehydroepiandrosterone) and steroids (17-estradiol and 5-dihydroprogesterone) showed significant variations at the beginning of the pre-puberty period. Thus, these metabolites and steroids were considered as candidate salivary biomarkers of the pre-puberty period. These results show that non-invasive saliva sampling could be a welfare-friendly tool for the identification of the physiological status of the gilts. In the second experiment, metabolome and steroidome analyses allowed the identification of 33 metabolites and 29 steroids in gilt saliva. When we looked for biomarkers candidates that could differentiate gilts that will be receptive to boar effect from non-receptive gilts, the concentrations of several metabolites and steroids tended to be different in receptive gilts compared to non-receptive gilts in saliva collected 25 and 11 days before boar exposure. However, no significant differences could be highlighted, including for candidate biomarkers, due to the large variability between gilts. Thus, in our conditions, we could not identify salivary biomarkers that could differentiate gilts that will be receptive to the boar effect from non-receptive gilts.

Discussion

These results show that non-invasive painless sampling of saliva could allow the identification of the physiological hormonal status of the gilts from immature to pubertal stage. However, we could not identify relevant salivary biomarkers to the effectiveness of the boar to stimulate puberty in our experimental conditions. Our study was an exploratory experiment with a small number of experimental gilts, making the assumption that at least one biomarker will show a marked difference between receptive and non-receptive gilts. This was not the case. Therefore, research for salivary biomarkers should continue using a higher number of animals and time points provided the existence of rapid and cheap analytical methods. Other omics approaches, such as proteomics or lipidomics, could also be of interest to search for salivary biomarkers of the period of receptivity to boar effect.