Laurent Dekydtspotter

Jon C Hathorn

Quelque chose … de remarquable in English-French acquisition: mandatory, informationally encapsulated computations in second language interpretation

 1999) contention that interlanguage knowledge is constrained by a mental organization in which Universal Grammar provides the contents of a largely universal processor devoted to language.

I A severe poverty of the stimulus problem

In French, unlike in English, the existential quantifier quelque chose 'something' may take an adjectival restriction introduced by the particle de.

This adjectival restriction may appear together with the quantifier as in (1) or may be separated from it as in (2) [START_REF] Huot | Constructions infinitives du français: le subordonnant 'de[END_REF][START_REF] Azoulay-Vicente | Les tours comportant l'expression de + adjectif[END_REF][START_REF] Birdsong | Constraints on the structure de + modifier in French[END_REF][START_REF] Hulk | Accord et opérateurs nuls dans les projections adjectivales [Agreement and null operators in adjectival projections[END_REF].

1) Quelque chose de remarquable a été observé par chacun des chercheurs. something of remarkable was observed by each of-the researchers 'Something remarkable was observed by each of the researchers.'

2) Quelque chose a été observé de remarquable par chacun des chercheurs.

something was observed of remarkable by each of-the researchers 'Something remarkable was observed by each of the researchers.'

The permutation of the continuous quantifier in (1) into the discontinuous quantifier in (2) is accompanied by very subtle interpretive effects of a pragmatic nature. As a French speaker in a speech situation, if you hear the continuous sentence in (1), a range of situations seems possible: It could be that all the researchers witnessed a different remarkable object or that all the researchers witnessed the same remarkable object, or any case in between. In contrast, out of the blue, the discontinuous sentence in (2) implies that the researchers did not observe the same thing. This implication can, however, be defeated. That is to say, one can assert (2) without taking it as true in the context that the researchers did not observe the same thing. Therefore, (2) may be followed by (3), which denies the implication, without the resulting discourse being contradictory.

3) En fait, la même chose a été observée par tous les chercheurs.

in fact the same thing was observed by all the researchers 'In fact, the same thing was observed by all the researchers.'

The implication that the researchers did not observe the same thing is, hence, not part of the literal semantics, but arises as a pragmatic implicature. The paradigm of situations and syntactic structures (with the implicature taken as true) is presented in Table 1. A (second) language acquirer must come to know that the discontinuous sentence (2) a priori excludes situations where the same object was observed by all researchers. However, there are serious obstacles in the path of the learner. If the learner extends the interpretation of the familiar continuous quantifier structure in (1) to the unfamiliar discontinuous quantifier structure in (2), no evidence will ever inform the learner that the discontinuous quantifier structure in (2) is not interpretively a variant of the continuous quantifier structure in (1). This is because in every situation where a discontinuous quantifier structure as in ( 2) is used, the continuous quantifier structure as in (1) may be used as well. The learner thus never encounters a situation where only discontinuous quantifier structures can be used.

Even if the learner does not analogize discontinuous quantifier structures to continuous quantifier structures, severe problems remain. Situations of use do not unambiguously reflect the form-meaning relations in Table 1. The implication that the same remarkable object was not observed by all researchers can be suspended by additionally uttering the corrective statement (3). Such corrective statements confuse form-meaning relations in actual use, because the learner will not reliably encounter the discontinuous quantifier structure in (2) only in situations where each researcher observed (at least) a different remarkable object. This is because the discontinuous sentence in (2) can be followed by sentence (3) which specifies that the same object was observed by all. Additionally, the corrective statement in (3) is also compatible with the continuous sentence in (1). Hence, corrective statements do not uniquely flag the interpretation of sentences with discontinuous quantifiers, since they can be found across the continuous/discontinuous dimension.

Thus, the highly unstable correspondences between sentence structure and situations make the likelihood of grasping the eccentric pattern in Table 1 exceedingly remote in actual use. Additionally, ambiguity in situations of use may come from the fact that the information known to the interlocutors is partial, so that the learner's information state may be compatible with a range of interpretations. In particular, one interlocutor could take a sentence as true on one interpretation, while the other interlocutor takes it as true on a different interpretation without recognizing Laurent Dekydtspotter and Jon C. Hathorn 293 that their interpretations are different. Partiality will prevent the learner from honing in on the interpretation in the general case.

In addition to problems in the character of the environment, learning problems also arise as a function of the learner. If learning proceeds inductively by making inferences that can be disconfirmed by further evidence, (erroneous) beliefs about the facts under discussion can cause unlearning at any point of acquisition. Induction, therefore, cannot guarantee that the relevant grammatical properties will arise in the general case. Hence, if such properties arise predictably in the course of development, then these properties are more feasibly viewed as an expression of a specific mental organization inherent in the learner.

Further, we note that the discontinuous structure in ( 2) is subject to stylistic constraints that make it unlikely to be part of the daily exposure in relatively early classroom acquisition. This adds to the complexities facing inductive acquisition in actual situations of use. In the context of (adult) English-French acquisition where instruction might play a role, it is also important to note that the construction and its interpretation are not the topic of instruction, and that native speakers are not consciously aware of the grammatical properties under discussion.

II Scalar implicatures: syntax, semantics and pragmatics

The interpretation of discontinuous sentences seems to require semantically constrained computations beyond syntax-semantics mappings.

To see this, we consider the semantic representations resulting from scope interactions among the quantifiers and their truth conditions. Both continuous (1) and discontinuous (2) introduce an existential quantifier quelque chose 'something' (analysed with existential ∃) and a universal quantifier chacun des chercheurs 'everyone of the researchers' (analysed with universal ∀). These quantifiers bind variables in the theta positions of the verb's semantic representation and interact with one another. The existential quantifier quelque chose takes scope either under the universal quantifier chacun des chercheurs as in the ∀∃ representation (4) or over it as in the ∃∀ representation (5). Abstracting away from tense, the representations in (4) and ( 5) thus constitute the range of scope-dependent semantic representations potentially available to (1) and (2). 'For every researcher there is a remarkable thing such that he/she observed it.'

5) ∃x [ thing(x) ^remarkable(x) ^∀y [ researcher(y) → [ observe(x)(y)]]]

'There is a remarkable thing such that every researcher observed it.'

The semantic differences between (4) and ( 5) reside in the scope of the quantifiers. In (4) quelque chose takes scope under the universal quantifier chacun des chercheurs. In (5) quelque chose takes scope over the universal quantifier chacun des chercheurs. On the ∀∃ representation in (4), the sentence is true of (past) situations where each researcher is such that some remarkable thing was observed (but not necessarily the same object). On the ∃∀ representation in (5), the sentence is true of (past) situations where some (unique) remarkable thing is such that every researcher observed it. Thus, (4) denotes the set of (past) situations where for every researcher there is a remarkable object that he or she observed. The representation in (5) denotes the set of (past) situations where for some (unique) remarkable object it is the case that every researcher observed it. Hence, the representations in ( 4) and ( 5) are both true of (past) situations where the same remarkable object was observed by every researcher, but (5) exclusively specifies such situations. Semantically, the representations in (4) and ( 5) stand in an asymmetrical entailment relation: whenever (5) is true, (4) is true, but not the other way around. The entailment relation follows from the fact that the situations that make (5) true and the situations that make (4) true stand in the inclusion relation in ( 6): The set of situations that verify the representation (5) with the quantifiers in the ∃∀ scope relation (i.e., the set of situations where the same remarkable object is observed by each researcher) is a subset of the set of situations that verify the representation (4) with the quantifiers in the ∀∃ scope relation (i.e., the set of situations where each researcher observed some remarkable object, and possibly the same one).

6) {s | s is characterized by (5)} ʕ {s | s is characterized by (4)} Given that the ∀∃ representation in (4) and ∃∀ representation in (5) together constitute the space of possible semantic representations for both the continuous sentence in (1) and the discontinuous sentence in (2), the asymmetry between (1) and (2) in Table 1 is unexpected on the basis of possible semantic representations alone. This is because both (4) and ( 5) will be true in situations where the same remarkable object was observed by all the researchers, yet the sentences (1) and ( 2) are not equally acceptable in this context. Thus, the interpretive intuitions in Table 1 must require pragmatically induced computations beyond Logical Form (LF) representations, as we now show.

Since [START_REF] Grice | Logic and conversation[END_REF], language use is assumed to be governed by domain-general principles of conversational cooperation. In particular, the Maxim of Quantity (7) requires that the strongest statement consistent with what is known be made. 7) Maxim of Quantity: make your contribution as informative as required, and no more informative than is required. [START_REF] Grice | Logic and conversation[END_REF] Horn (1985; 1989; 1992) shows that informational strength relations play a significant role in determining how Grice's principles apply on specific domains such as quantification. Given the semantics of quantification, the ∃∀ representation (5) asymmetrically entails the ∀∃ representation (4). This asymmetric entailment creates an informational scale in which the entailing ('subset') representation ( 5) is informationally stronger than the entailed ('superset') ∀∃ representation (4). The ∃∀ representation (5) uniquely characterizes the speech context, whereas the ∀∃ representation (4) allows for other possibilities. Given that (5) is informationally stronger than (4), the Maxim of Quantity (7) would seem to require that in a context where the ∃∀ representation (5) is true, (5) -as the more informative statement -should be the LF representation. Conversely, on the assumption that the Maxim of Quantity is satisfied, the ∀∃ representation (4) at the LF-interface should trigger the implicature that the stronger statement (5) is not verified. In other words, if you could have made the stronger statement (5), you would have. Since you did not make the stronger statement, it must not be true. We now turn to the manner in which the word order asymmetries arise in French. First, an idiosyncratic syntax-semantics (LF-interface) mapping is required. The fact that discontinuous (2) a priori describes a situation where each researcher observed a different object requires the ∀∃ representation (4), because (4) is the only representation that allows for such situations. Following de Swart's work (1992) on constructions with discontinuous constituents, we adopt the interface constraint in (8).

The constraint in (8) fixes the scope of a discontinuous quantifier (Q 2 ) in terms of the placement of its restriction with respect to some other scope-bearing element. The syntactic constraint in (8) is necessary but not sufficient to account for the pattern in Table 1. This is because the ∀∃ representation in (4), forced by the constraint in (8), is true not only of situations where each researcher observed a potentially different object, but also of situations where it turns out that the same object was observed. The mapping in (8) is, therefore, necessarily accompanied by a pragmatic inference. Hence, (8) must be supplemented by Gricean interpretive computations that lead to the exclusion of the set of situations described by (5).

In sum, the interpretive differences between (1) and (2) follow if:

• the sentence (1) maps to the ∀∃ semantic representation in (4) or the ∃∀ semantic representation in (5) at the LF-interface, whereas sentence

(2) maps uniquely to the ∀∃ representation (4) at the LF interface; and

• a scalar implicature "(5) does not hold" is induced by the ∀∃ repre- sentation (4) at LF, satisfying the Gricean Maxim of Quantity through a grammatically provided semantic scale.

In other words, the pattern in Table 1 arises because a grammatically calculated scalar implicature supervenes on the syntax-linked LFrepresentation (4) of the discontinuous sentence in (2) in order to satisfy principles of conversational cooperation. The continuous sentence in (1) receives the ∀∃ representation in (4) or the ∃∀ representation in (5), whereas the discontinuous sentence in (2) receives the ∀∃ representation in (4) at LF by virtue of the constraint in (8). The representation in (4) at the LF-interface pragmatically implies "and not (5)" by the Maxim of Quantity [START_REF] Grice | Logic and conversation[END_REF] in a grammatically provided, entailment-based informational scale. In the absence of the computation of an implicature as part of interpretive knowledge, no asymmetry in the interpretation of (1) and (2) could arise. If an asymmetry arises, it is because an implicature is mandatorily calculated. The derivation of scalar implicatures described above crucially relies on asymmetric scope relations. There are other asymmetries that support the idiosyncratic derivation of a scope-induced implicature through a grammatically provided informational scale. Only universal quantifiers (such as toujours 'always') trigger the implicature, yielding an asymmetry between (9a) and (9b). Existential quantifiers (such as parfois 'sometimes') do not yield such an asymmetry between (10a) and (10b). 9) a. Quelque chose a toujours été observé de remarquable le soir. something has always been observed of remarkable evenings. 'Something remarkable was always observed in the evenings.' b. Quelque chose de remarquable a toujours été observé le soir. something of remarkable has always been observed evenings. 'Something remarkable was always observed in the evenings.' 10) a. Quelque chose a parfois été observé de remarquable le soir. something has sometimes been observed of remarkable evenings. 'Something remarkable was sometimes observed in the evenings.' b. Quelque chose de remarquable a parfois été observé le soir. something of remarkable has sometimes been observed evenings. 'Something remarkable was sometimes observed in the evenings.' With the universal event quantifier toujours, an implicature is generated by virtue of the semantics of the scopal interactions between the universal quantifier toujours and the existential quantifier quelque chose. In (9), the alternative scopes have truth-conditional import, so that the situations corresponding to the stronger ∃∀ representation are excluded under the Gricean Maxim of Quantity, given the ∀∃ representation at LF. Thus (9a) and (9b) subtly contrast in the relative availability of the same object reading (out of the blue). That is to say, if you know that the same remarkable object is always observed, then (9b) is a better characterization than (9a), although again (9a) is not an impossible statement, as discussed above. The contrast in (9) follows if the discontinuous syntax requires the ∀∃ representation at LF, and if the LF ∀∃ representation triggers an implicature that the ∃∀ representation is not verified.

With the existential quantifiers parfois and quelque chose, there is no truth conditional import of the relative scopes of quelque chose and parfois: The representations map to the same set of situations on either scope of parfois with respect to quelque chose. Because scope relations do not lead to asymmetric truth conditions in (10), no implicature is generated. Thus, if you think of the same object per relevant observation, both (10a) and (10b) are possible characterizations out of the blue. The asymmetry that exists between (9a) and (9b) does not exist between (10a) and (10b). Hence, the implicatures that concern us here are crucially computed through scales determined by asymmetric entailment relations. We return to the importance of computations through scales in a discussion of informational encapsulation (see section IV).

III A second language acquisition experiment 1 Methods

Our experiment investigated English-French learners' acceptance of continuous and discontinuous sentences in situations where there was one and the same object for all human participants vs. situations where there were different objects per human participant. Our respondents included a group of 40 adult classroom learners of French enrolled in the third semester of the basic language program at Indiana University. Our respondents also included a group of 20 students enrolled in sixth semester French language proficiency courses at Indiana University. [START_REF] Magnan | Accessing speaking proficiency in the undergraduate curriculum: data from French[END_REF] found that most English-speaking students having completed one year of university study are concentrated at the intermediate low/mid levels in French language proficiency on the ACTFL (American Council of the Teaching of Foreign Languages) scale. Those having completed two and one half years are concentrated on the intermediate high level on the ACTFL scale. Thus, we refer to the 40 classroom learners of French in third semester French as the low/mid intermediate group, and we refer to the 20 classroom learners of French in the sixth semester of French language proficiency as the high intermediate group. The respondents provided background information on their native language, on their exposure to French and on any other languages they had studied or acquired. We excluded from consideration volunteers whose first language (L1) was not English. Our native comparison group included (adult) native French students, who were like our experimental groups: linguistically naive young adults. These native French speakers were completing coursework for the Bachelor of Arts (Licence) degree in English at the Université de Lille in France. They were enrolled in English language proficiency in their third year of university studies. This group provides evidence of the ability of our instrument to capture reflexes of mental organization in a group of respondents whose knowledge of French is not in dispute.

Experimental items consisted of eight sets of quadruples. Each quadruple included continuous vs. discontinuous sentences crossed with stories involving a different object or the same object for all human participants. The request for information was a constant. The lexical material within a given quadruple was identical. It was limited to vocabulary familiar to respondents even at the most elementary level investigated. Thus, each narrative (one providing a scenario with a different object, and one providing the same object for all human participants) appeared twice: once paired with a sentence exemplifying a continuous sentence in response to the request for information and once paired with a sentence exemplifying a discontinuous sentence in response to the same request for information. Eighteen fillers were blended in with the rest of the task to offset the expected imbalance between the positive and negative responses, yielding a total of 50 items. The 50 items were presented in three distinct random orders.

Respondents were told that they were judges for an (imaginary) comprehension exercise in Madame Goyette's English class. As judges, respondents were presented with excerpts from the transcripts of the comprehension exercise. Each experimental item consisted of a story told in English to French pupils by a character, named Mrs Briggs. When the story was being told, the pupils' teacher, Madame Goyette, was not in the room. After the story had been told, Madame Goyette prompted the pupils with a question in French about the story that Mrs Briggs told: Qu'est-ce qui s'est donc passé? ('So, what happened?'). Following this question, a pupil's answer in response to Madame Goyette's information request was provided to the respondents. Respondents indicated whether the answer was an adequate response to the information query. The respondents were told that an adequate response need not be complete and that it need not have all the details of the relevant aspects of the story. 1 It merely should not mislead the hearer about the facts. Examples sensitized the respondents to the types of inferences that would mislead a hearer. The following examples illustrate the test methodology. (The full list of sentences is provided in Appendix 1.) Sample Test Item 1: Different objects with continuous answer

Mrs Briggs:

Having landed on the planet Omega, the three scientists of the interstellar expedition separated to begin their exploration of the planet. The first scientist observed a new life form. The second scientist observed the fast growth of interesting crystals. The third scientist looked up from his notebook just in time to observe a meteor crash into the surface of the planet.

Mme Goyette: Qu'est-ce qui s'est donc passé?

Élève:

Quelque chose -de remarquable -a été observé par chacun des scientifiques.

IS THIS AN ADEQUATE RESPONSE? YES NO CANNOT DECIDE

Sample Test Item 2: Different objects with discontinuous answer

Mrs Briggs:

Having landed on the planet Omega, the three scientists of the interstellar expedition separated to begin their exploration of the planet. The first scientist observed a new life form. The second scientist observed the fast growth of interesting crystals. The third scientist looked up from his notebook just in time to observe a meteor crash into the surface of the planet.

Mme Goyette: Qu'est-ce qui s'est donc passé?

Élève:

Quelque chose a été observé -de remarquable -par chacun des scientifiques.

IS THIS AN ADEQUATE RESPONSE? YES NO CANNOT DECIDE

The English narratives ensured that all respondents unambiguously understood the context in which the answer was uttered. This allowed us to study learners at low levels of proficiency, since such learners might not be able to deal with an entire context in the target language.

It could be argued that using English might also detract from learner performance, since it requires switching from one mode of expression to another. However, in the study of knowledge of interpretive effects where understanding of the situation is crucial, the English scenarios nearly guarantee that the respondent is in the relevant information state. As a final methodological note relevant to the interpretation of results, we note that any interpretive asymmetry of the type considered in Table 1 logically requires that an implicature mandatorily accompany the ∀∃ LF representation. Unless the implicature is mandatorily generated, no asymmetry is expected at all, given the range of possible semantic representations at LF. In contradistinction, the lack of a detectable asymmetry does not demonstrate the absence of implicature. Only the presence of an asymmetry along the lines discussed above is revealing of learners' knowledge. We first consider the ability of our instrument to detect the pattern previously shown in Table 1 in a group of native speakers. We then discuss our English-French results.

Results and discussion

The results for our group of French native speakers in Table 2 reveal a relevant pattern of asymmetries: there is no significant difference between continuous answers and discontinuous answers in differentobject contexts (t(15) ϭ 1.15, p ϭ .267), but there is a crucial significant difference between continuous answers and discontinuous answers in same-object contexts (t(15) ϭ 2.50, p ϭ .025). The French native speakers' acceptance rates of continuous answers in same-object vs. differentobject scenarios are virtually flat (t(15) ϭ .09, p ϭ .930). In contrast, acceptance rates of discontinuous answers in same-object versus different-object scenarios differ significantly (t(15) ϭ 2.16, p ϭ .048).

Crucially, the asymmetries in the response pattern in Table 2 cannot logically be accounted for unless implicatures are calculated. We note that if implicatures were not systematically calculated in accordance with Gricean cooperation maxims, no difference between the acceptance of answers in different-object vs. same-object contexts would be expected at all. This is because ∀∃ representations hold true of both types of situations. Hence, a post-LF pragmatic calculation must supervene on ∀∃ LF representations for there to be any effect whatsoever in same-object contexts.

302 Mandatory, informationally encapsulated computations We now consider the English-French learners. T-tests were performed for each subgroup. We, therefore, adopt a Bonferroni protection level of ␣ ϭ .05/2 ϭ .025. As shown in Table 3, the low/mid intermediate learners (n ϭ 40) accepted continuous and discontinuous answers with scenarios involving a different object per participant at very similar rates (t(39) ϭ .70, p ϭ .489). They also accepted continuous and discontinuous answers in the same-object condition at similar rates (t(39) ϭ .15, p ϭ .881). Low/mid intermediate learners were biased against accepting the answers in same-object context when compared to different-object contexts in both conditions: for continuous answers (t(39) ϭ 3.97, p Ͻ .0005) and for discontinuous answers (t(39) ϭ 3.11, p ϭ .003).

Thus, no effect of word order was found for this population: low/mid intermediate learners interpreted continuous answers and discontinuous answers alike. However, low/mid intermediate learners accepted fewer answers in same-object contexts than in different-object contexts. Again, this contrast is unexpected purely in terms of the semantics of the possible LF representations involved. This is because the semantics predict that the value "true" is returned in same-object situations. Similar acceptance rates are expected in all four cells, contrary to what was found.

Given possible LF representations, the pattern in Table 3 follows only if intermediate low/mid English-French learners typically access ∀∃ representations at LF but typically not ∃∀ representations (see discussion below), and if the situations that correspond to the ∃∀ scope configuration are pragmatically excluded when a ∀∃ representation is derived at LF. Our first conclusion imposed by logical necessity given the range of LF representations is that the pattern of asymmetry found in low/mid English-French learners' interpretation is such that ∀∃ representations at LF induce scalar implicatures in obligatory fashion. Differences between the two groups reveal an acquisition sequence, associated with the interpretation of continuous and discontinuous answers. An independent samples t-test comparing the relative acceptance of continuous answers versus discontinuous answers as descriptions of same-object scenarios confirms that the two groups are indeed statistically distinct (t(58) ϭ 2.09, p ϭ .041). The behaviour of high intermediate learners (contra low/mid intermediate learners) is not unlike the pattern produced by the French native speakers.

Laurent Dekydtspotter and Jon C. Hathorn 303

Thus, for the high intermediate and native groups, a statistically significant difference of means arose between continuous and discontinuous answers in same-object scenarios, but not with different-object scenarios. Given that the range of possible semantic representations cannot alone account for such an asymmetry, we prima facie conclude that high intermediate learners assigned ∀∃ representations of the type in (4) to discontinuous sentences, and that they obligatorily computed implicatures of the type "and not ( 5 from the over-exclusion of situations in same-object contexts with continuous answers only.

We discuss the distribution of individual responses by comparing for each individual the rate of acceptance of discontinuous answers in same-object contexts versus different-object contexts. This distribution is provided in Figure 1. On the axis of abscissa appear the relative measures of acceptance of discontinuous answers in same-object contexts vs. different-object contexts. This is obtained by subtracting the percentage 'yes' responses to discontinuous answers in same-object contexts from the percentage 'yes' responses to discontinuous answers in different-object contexts. A value above (to the right of) zero indicates a higher acceptance of discontinuous answers in different-object contexts vs. same-object contexts. On the axis of the ordinate appears the number of individuals. That there are few respondents falling on the negative side (left of zero) demonstrates a bias against accepting discontinuous answers in same-object contexts. Similar patterns emerged in both learner populations as well. Individual responses showed a bias in the expected direction: There was a greater number of respondents accepting discontinuous answers in different-object contexts over same-object contexts than there were respondents accepting discontinuous answers in same-object contexts over different-object contexts. Figure 2 shows that an asymmetrical distribution was in evidence in the low/mid intermediate learners.

A strongly regimented pattern of behaviour was obvious in the individual distribution of the high intermediate learners, as shown in Figure 3. There was one individual with a marked response pattern in the opposite direction. However, this response pattern was in stark contrast with the rest of the respondents.

Hence, despite the range of factors that may affect performance, the pattern of individual responses in all three groups suggested that mental structure compels respondents to resist accepting discontinuous answers in same-object contexts.

306 Mandatory, informationally encapsulated computations In support of the view that these implicatures arise in entailmentbased scales, we administered a second experiment in which we investigated the interaction of discontinuous quantifiers with the universal quantifier toujours 'always' and the existential quantifier parfois 'sometimes'. In the target language, a sentence of the form Q ∃ … parfois … [restriction of Q ∃ ] is potentially associated with either scenario. However, a sentence of the form Q ∃ … toujours … [restriction of Q ∃ ] pragmatically implies a different object per event. In Experiment 2, discontinuous quantifiers with toujours and parfois were crossed with contexts involving a different object per event and the same object for all events. Forty-seven learners participated in this additional experiment.

As in Experiment 1, each item in the experimental instrument included a story told in English by a character Mrs Briggs. The story provided either a scenario where there was a different object per event or the same theme for all events. This was followed by a request for information about the story, (Qu'est-ce vous avez donc appris? 'So, what did you learn?') from a French-speaking character Madame Goyette, and a discontinuous answer in response to the information request containing either parfois 'sometimes' or toujours 'always'. Respondents were to indicate whether the answer was an adequate response to the information query. Experimental items consisted of eight sets of quadruples. For each quadruple, there was one prose narrative unambiguously involving the same object and another unambiguously involving a different object per event. Each was paired once with a sentence exemplifying a discontinuous answer containing parfois and once with a discontinuous answer containing toujours. An example of a test item follows:

Sample Test Item 3 (different object per event with parfois):

Mrs Briggs:

On three of the five voyages to the planet Omega taken so far, the mission's field scientist observed a truly remarkable thing in the universe: On the first mission, an immense geyser was observed throwing liquid nitrogen twenty miles high into the atmosphere of the planet. On the second mission, an eruption of the universe's largest known volcano was observed. On the third mission, an earthquake over the entire planet was observed. The last two missions however observed nothing of value. Still, NASA wants to organize more missions.

Mme Goyette: Qu'est-ce que vous avez donc appris?

Élève: Sur la planète Oméga, quelque chose a parfois été observé de remarquable.

IS THIS AN ADEQUATE RESPONSE? YES NO CANNOT DECIDE

Eighteen fillers were blended with the rest of the task to offset the expected imbalance between the positive and negative responses. There was thus a total of 50 items presented in three distinct random orders. An independent samples t-test comparing the relative acceptance of discontinuous answers with parfois 'sometimes' vs. discontinuous answers with toujours 'always' in same-object contexts shows that the two groups are indeed statistically distinct (t(47) ϭ 2.52, p ϭ .015). Low/mid intermediate learners (n ϭ 28) showed evidence of sensitivity to scope interactions on this task, as shown by the asymmetry in Table 5. Thus, for (discontinuous) answers with parfois, there was no significant difference in respondents' rates of acceptance having a different object per event versus the same object per event (t(27) ϭ .87, p ϭ .391), but, crucially, for (discontinuous) answers with toujours, the acceptance rate in different-object contexts was significantly greater than the acceptance rate in same-object contexts (t(27) ϭ 3.88, p ϭ .001). This asymmetry is revealing of the role of the quantifier in the derivation of these implicatures. Although the acceptance rate for (discontinuous) answers is lower with toujours than with parfois in same-object contexts, this does not reach statistical significance.

In the case of high intermediate learners (Table 6), the lowest acceptance rate is still associated with answers with toujours in single-object contexts, although the results were not statistically significant. It may be that for (some of) these subjects, the number of events provided in the contexts (three) was not enough for them to consistently accept an answer with toujours. The existence of a response strategy relying on this aspect of context would then obfuscate any difference between different-object contexts and single-object contexts arising from an implicature.

In pursuance of this hypothesis, we considered the behaviour of those high intermediate learners (Group A, n ϭ 8) who accepted toujours in different-object contexts at a rate at least as high as the mean rate of acceptance of parfois in different-object contexts for the whole high intermediate population (84.21%). This was compared to those high intermediate learners (Group B, n ϭ 11) who accepted toujours in Laurent Dekydtspotter and Jon C. Hathorn 309 different-object contexts at a rate lower than the mean rate of acceptance of parfois in different-object contexts. Thus, Group B learners were those who seemed hesitant to use toujours for only three events, whereas Group A learners allowed the use of toujours at least as often as parfois in different object contexts.

For Group A learners, the mean acceptance rate for (discontinuous) answers with toujours in different-object contexts (92.19%) was not significantly different from the mean acceptance rate for (discontinuous) answers with parfois in different-object contexts (82.81%) (t(7) ϭ 1.34, p ϭ .222). However, the acceptance of (discontinuous) answers with toujours (75.31%) versus parfois (88.44%) in same-object contexts contrasted significantly (t(7) ϭ 4.11, p ϭ .005). Furthermore, Group A learners' acceptance rates for answers with parfois in different-object contexts (82.81%) and in same-object contexts (88.44%) did not differ significantly (t(7) ϭ 1.15, p ϭ .287). However, their acceptance of answers with toujours in different-object contexts (92.19%) was significantly greater than in same-object contexts (75.31%) (t(7) ϭ 4.22, p ϭ .004). This suggests that a theoretically significant asymmetry appeared between parfois and toujours answers in different-object versus same object-contexts. Thus, Group A learners' acceptance patterns seem underlain by conversational conclusions that are scope induced and entailment based.

For Group B learners, the mean acceptance rate for (discontinuous) answers with toujours in different-object context (58.18%) was significantly different from their acceptance rate for (discontinuous) answers with parfois in different-object contexts (85.23%) (t(10) ϭ 3.16, p ϭ .010). It indeed seems to be the case that Group B learners were reluctant to accept the use of toujours as a characterization of contexts with only three events. There was no contrast between parfois (78.41%) and toujours (77.27%) in same-object contexts (t(10) ϭ .20, p ϭ .849). No contrast arose between (discontinuous) answers with parfois in different-object contexts (85.23%) versus same-object contexts (78.41%) (t(10) ϭ 1.26, p ϭ .237). But, a contrast in the opposite direction was found with toujours: Group B learners' acceptance of answers with toujours in different-object contexts (68.18%) was significantly lower than their acceptance of answers with toujours in same-object contexts (77.27%) (t(10) ϭ 3.29, p ϭ .008).

In summary, the response pattern of Group A learners seems underlain by implicatures that are derived in entailment-derived informational scales at the output of syntax. In contrast, Group B results follow if aspects of the context constitute the central ingredient of the response pattern. Specifically, three events did not suffice for confident use of toujours in characterizing the scenario, but salience of the same theme for all three events improved the use of toujours in the characterization of what happened. This contrast between Group A and Group B respondents suggests to us that the relevant features of the target language allowing discontinuous quantifiers are not acquired by Group B respondents, so that the interpretive consequences of discontinuous quantifiers were not felt.

That there is a difference in the acquisition of discontinuous quantifiers between Groups A and B finds confirmation in a further analysis of results in Experiment 1.2 Group A respondents evinced the interpretive knowledge associated with the grammaticality of discontinuous quantifiers: they accepted continuous answers (87.50%) and discontinuous answers (85.72%) at similar rates in different-object contexts (t(6) ϭ .13, p ϭ .899). Crucially, their acceptance of continuous answers (87.50%) differed significantly from their acceptance of discontinuous answers (62.50%) in same-object contexts (t(6) ϭ 3.06, p ϭ .022). Again, Group A learners' acceptance of continuous answers in different-object contexts (87.50%) and their acceptance of continuous answers in sameobject contexts (87.50%) were totally flat (t(6) ϭ .00, p ϭ 1), but again, crucially, their acceptance of discontinuous answers in different-object contexts (85.71%) and in same-object contexts (62.50%) contrasted significantly (t(6) ϭ 2.77, p ϭ .032). These results are consonant with the interpretive consequences of a grammar licensing discontinuous quantifiers at the syntax-semantics-pragmatics interfaces.

In contradistinction, the results of Group B respondents on Experiment 1 did not reveal evidence of French-like interpretive knowledge. These learners accepted continuous answers (81.82%) and discontinuous answers (85.23%) at similar rates in both different-object contexts (t(10) ϭ .56, p ϭ .588) and same-object contexts: 77.27% (continuous) and 69.32% (discontinuous) (t(10) ϭ 1.05, p ϭ .319). Their rates for continuous answers in different-object contexts (81.82%) versus same-object contexts (77.27%) are not statistically different (t(10) ϭ .36, p ϭ .727); and neither are their acceptance rates for discontinuous answers in different-object contexts (85.23%) versus same-object contexts (69.32%) (t(10) ϭ 1.26, p ϭ .236).

An independent samples t-test comparing Group A respondents and Group B respondents in terms of their relative acceptance of continuous versus discontinuous answers in same-object contexts provides statistical confirmation that Group A and Group B respondents indeed exhibit distinct response patterns in Experiment 1 (t(16) ϭ 2.30, p ϭ .035).

The French native speakers' results were flat on this task, with all differences far from achieving significance (see Table 7). All sentences on this task are stylistically disfavoured. It is possible that stylistic concerns may have rendered the task more difficult for native speakers. As a more general point, Rex A. Sprouse (personal communication) pointed out to us that for some asymmetry not to arise in a native comparison group in contrast to some nonnative group does not absolve the researcher from exploring the range of possible models for the asymmetry found in second language (L2) acquisition. We agree with him. The fact that a theoretically relevant asymmetry arose in an L2 group cannot be overlooked because logically such an asymmetry reveals that an inference is necessarily made that goes beyond the literal semantics, and that this inference is prima facie sensitive to entailment relations between scope-dependent semantic representations. The fact that L2 learners may exhibit theoretically relevant knowledge that is obfuscated in some other group is a distinct possibility that should not be overlooked. Thus, the very existence of these asymmetries in English-French interpretive knowledge suggests that discontinuous structures receive ∀∃ representations at LF, while the continuous structure allows both ∀∃ and ∃∀ LF representations, and that ∀∃ LF representations trigger the implicature "and the ∃∀ representation is not verified". These conclusions are based on the fact that asymmetries are not predicted from the range of possible LF representations without the constraint in ( 8) and without implicatures supervening on ∀∃ LF representations. If implicatures were not required, no asymmetry would arise in a normal sample. The asymmetries, therefore, reveal both domain-specific constraints on LF representations and mandatory implicatures supervening on ∀∃ LF representations. The results from Experiment 2 support the role of semantic scales in constraining the manner in which the implicatures are computed.

Mandatory, informationally encapsulated computations

Interlanguage asymmetries that follow from constraint (8) and the derivation of LF-triggered and semantically calculated implicatures provide prima facie evidence for a domain-specific, informationally encapsulated algorithm constraining L2 acquisition. We now show that the effects of constraint (8) derive from general principles of movement, so that it never has to be acquired. We then show that only narrowly constrained semantic computations satisfying principles of cooperation in idiosyncratic ways guarantee the appearance of these asymmetries.

IV A domain-specific, informationally encapsulated processor 1 Domain specificity

Assuming with [START_REF] Chomsky | The minimalist program[END_REF] that movement (conceived as copying followed by matching deletions) is driven by the need to satisfy the checking of features and by output requirements, we show that the constraint on the legitimate semantic representations available to continuous and discontinuous quantifiers seems to be a reflex of the theory of movements. We assume that movement to the subject position is driven by the need to satisfy the Extended Projection Principle (EPP) requirements of I, with nominative case a reflex of this satisfaction. Following [START_REF] Hulk | Accord et opérateurs nuls dans les projections adjectivales [Agreement and null operators in adjectival projections[END_REF], we assume that a quantificational [+Q] feature of the de morphology licenses a null [+Q] category in its specifier position, which allows for discontinuous quantification. Thus, the feature requirements of I (i.e., EPP, and Case) can satisfied by the DP quelque chose de remarquable as in (12) or the DP quelque chose as in (13). We assume with [START_REF] Diesing | Indefinites[END_REF] that indefinite expressions such as quelque chose are ambiguous between a quantificational interpretation (associated with the IP domain) that possesses inherent existential force lexically, and an individual variable interpretation (associated with the VP domain) with its existential force provided constructionally by a default Existential Closure operation at the VP-level. The by-phrase introduced by par is treated as an inherently case-marked (VP-external) syntactic adjunct binding the external argument position of the verb. The by-phrase takes scope over the VP-level existential closure but takes scope under the IP-level quantifier.

The derivations in ( 12) and ( 13) interact with deep properties of grammar to determine mappings to semantic representations. Matching deletions in the head or tail position in (12) lead to two possible LF representations: ( 14) and (15). In ( 14), the indefinite is interpreted at the foot of the chain and takes scope under the by phrase. In (15), the indefinite is interpreted at the head of the chain and takes scope over the by phrase. Crucially, once the DP quelque chose is raised to SpecI as in the derivation in (13), the feature-driven movement of the expression [t(quelque chose) de remarquable] out of the VP to SpecI is ruled out by Last Resort (which says that an operation cannot happen unless it is required) because the relevant formal features of I (EPP and case) are already satisfied. Movement for interpretive reasons (i.e., scope taking) is also ruled out, since the trace in the raised DP is not head-governed [START_REF] Lamontagne | The syntax of adjacency[END_REF]. Thus, if quelque chose is raised, further movements of [t(quelque chose) de remarquable] are ruled out. If quelque chose de remarquable is raised to SpecI, then Full Interpretation at the Phonological Form (PF) interface requires that the entire expression quelque chose de remarquable be uttered.

In summary, if the expression quelque chose is raised, the indefinite quelque chose de remarquable is uniquely interpreted within the VP. However, if the whole expression quelque chose de remarquable is raised, the indefinite quelque chose de remarquable may be interpreted either in IP or at the trace. The range of legitimate LF representations need not be acquired, but inheres in a specific grammatical organization.

Informational encapsulation

We now consider that, instead of computations through scales (our position), conversational implications derived on the basis of beliefs might be the source of the asymmetries found in English-French interlanguage. We show that this cannot feasibly be. Thus, in Experiment 1, learners' behaviour would be due to conversational implications derived on the basis of beliefs about events with human actors. Hence, learners would (oddly) share the belief that real world observations (by distinct scientists) typically do not have the same theme. In accordance with this belief, they would exclude from literal interpretations the states of affairs in which all relevant events are observations of the same object. The reasoning would be as follows:

Semantics: For every researcher there is a remarkable thing such that he or she observed it. World Belief 1: Different things get observed by distinct scientists. Conversational conclusion: The observations were not of the same thing.

Such beliefs about events with human actors might be compatible with the learner behaviour observed in Experiment 1, but only if these beliefs were generally held and generally felt to be relevant to the situation of utterance. However, in this latter respect, the information in sameobject scenarios should tell the learner that the current situation is not prototypical, but rather an exception to the belief. Once the belief is irrelevant, the conversational conclusion can no longer be drawn. Hence, no asymmetry should appear.

If beliefs about events determined conversational conclusions, then additionally scope-determined entailment relations would be irrelevant. Therefore, the asymmetry observed in Experiment 2 between the existential quantifier parfois 'sometimes' versus the universal quantifier toujours 'always' would be unexplained. To see that the same expectation for both toujours 'always' and parfois 'sometimes' would hold in the belief-based model, we consider a corollary world belief about scientific observations: that different things get observed on different occasions. World Belief 2 would license a conversational conclusion that excludes the states of affairs in which all relevant observations are of the same object:

Semantics: Sometimes/Always a remarkable thing was observed. World Belief 2: Different things get observed on different occasions. Conversational conclusion: The observations were not of the same thing.

This inference would arise whether the quantifier is parfois 'sometimes' or toujours 'always' because the quantifier scope is irrelevant; only the belief about certain kinds of events matters. In this case, a conversational conclusion would be derived with both parfois 'sometimes' and toujours 'always'. Therefore, acceptance rates in same-object contexts would be significantly depressed with both parfois 'sometimes' or toujours 'always'. No such pattern was found.

In summation, the pragmatic inferences that account for the asymmetries observed in the development of English-French interpretive knowledge do not appear to follow from a belief-dependent strengthening of the informational content of utterances beyond the literal semantics. Rather, these pragmatic inferences in interlanguage interpretation seem to be grammatically triggered and calculated [START_REF] Kadmon | On unique and non-unique reference and asymmetric quantification[END_REF]2000;Horn, 1992;[START_REF] Landman | Plurals and maximalization[END_REF]. Such scalar implicatures follow from general principles of conversational co-operation, but in a domain-specific and informationally encapsulated manner. Hence, the scale-dependent strengthening of literal meanings evident in English-French acquisition of discontinuous quantifiers strongly suggests that aspects of L2 interpretive knowledge are reflexes of an idiosyncratic interface between a specialized language module and general principles of co-operative behaviour in the type of mental architecture explored in [START_REF] Fodor | The modularity of mind[END_REF]2000).

V The source of language specific computations

Given that the range of legitimate mappings to semantic representations derives from the theory of movements, the knowledge accounting for the interpretation of discontinuous quantifiers is naturally instantiated in English, although discontinuous quantifiers of the type found in French are not. As an anonymous Second Language Research reviewer notes, the English sentence Each of the researchers observed a remarkable thing strongly suggests that it was not the same thing that was observed. This intuition also follows from an LF-derived implicature through scales. Thus, one may wonder whether the asymmetries in English-French interpretation reflect a (largely) universal computational module that interacts with the functional lexicon (as investigated above), or whether they can be simply derived from the L1 knowledge, without the need for a universal algorithm (surviving in the adult mind) [START_REF] Schachter | Testing a proposed universal[END_REF][START_REF] Bley-Vroman | The logical problem of second language learning[END_REF]. As [START_REF] Hale | Can UG and L1 be distinguished in L2 acquisition?[END_REF] points out, given the level of generality of principles of Universal Grammar in Minimalist understanding, all grammatical principles are instantiated in all languages. The distinction becomes vitiated since knowledge of the L1 is the product of a parameterized lexicon with general universal principles.

However, the performance of L2 learners on the task might plausibly be due to L1 intuitions, not requiring any learning. Thus, following [START_REF] Dekydtspotter | The interpretive interface in L2 acquisition: the process-result distinction in English-French interlanguage grammars[END_REF], we consider the intuitions that knowledge of English might provide to learners, despite the ungrammaticality of partitive quantifiers with detachable restrictions. In conditions similar to the English-French learner groups, we tested two groups of native English respondents, presenting them with stimuli consisting of continuous and discontinuous sentences. These individuals were selected from first semester French college classes and had no or exceedingly little prior exposure to French.

They were told that they were judges for an (imaginary) final comprehension exercise in Madame Goyette's class populated with French speaking learners of English. As judges, respondents were presented with excerpts from the transcripts of the comprehension exercise consisting of a story told in English and the question "So, what happened?" followed by a pupil's response. Respondents were to indicate whether the answer was an adequate response to the information query. An answer was adequate as long as it did not mislead the hearer about the facts. As this was a comprehension exercise, respondents were told that "the potentially faulty grammar of a pupil's response must not be held against the pupil." Respondents were thus to focus on the informational content conveyed by the answer of the pupil.

One English control group (n ϭ 14) was presented with items as in "Something remarkable was observed by each of the researchers" and "Something was observed remarkable by each of the researchers" that gloss the French items, pace the de morphology. The other control group (n ϭ 10) was presented with sentences as in "Something of remarkable was observed by each of the researchers" and "Something was observed of remarkable by each of the researchers" that gloss the French items verbatim. Tables 8 and9 respectively show similar results for both groups.

In the first task (without of ), English controls accepted continuous and discontinuous answers with scenarios involving a different object per participant at 91.07% and 78.57% respectively (t(13) ϭ 1.49, p ϭ .160). They also accepted continuous and discontinuous answers in the same object condition at 66.07% and 70.54% respectively (t(13) ϭ .59, p ϭ .567). This shows a response bias against accepting answers with scenarios involving the same object for all human participants. Contrasts of means were significant for continuous answers (t(13) ϭ 2.55, p ϭ .024). In the second task (with of ), continuous and discontinuous answers with scenarios involving a different object per participant were accepted at 85.00% and 77.50% respectively (t(9) ϭ .80, p ϭ .443).

318 Mandatory, informationally encapsulated computations Continuous and discontinuous answers were accepted in same object contexts at 55.00% and 56.25% respectively (t(9) ϭ .23, p ϭ .823). English respondents seemed again biased against accepting the answers with scenarios involving the same object for all human participants. Significant contrasts of means appeared for continuous answers (t(9) ϭ 2.84, p ϭ .019). The behaviour of English controls was reminiscent of the low/mid intermediate learners, who showed similar rates of acceptance between continuous and discontinuous answers in same-object contexts and similar rates of acceptance between continuous and discontinuous answers in different-object contexts, with a general bias against same-object interpretations. The results of both control groups and the low/mid intermediate group were compatible with the ungrammaticality of leftbranch extractions: the effects of a (French-like) grammar are simply not felt on interpretation for these groups. This was in stark contrast with the French-like behaviour of high intermediate learners who accepted continuous and discontinuous answers in different-object contexts equally, but accepted continuous answers significantly more than discontinuous answers in same-object contexts.

Hence, English intuitions do not explain the emergence of these asymmetries in English-French acquisition. Rather, we argue that the acquisition of the morphology allowing left-branch extractions in a grammar determines the appearance of the interpretive effects in the strict constraints of the interfaces between syntax, semantics and pragmatics. Our findings, therefore, provide strong support for Schwartz's (1986;[START_REF] Kadmon | On unique and non-unique reference and asymmetric quantification[END_REF]1999) claim that L2 acquisition is constrained by a (largely) universal processor devoted to language, of which Universal Grammar specifies the contents.

VI Conclusions

The interpretation of quantifiers with detachable restrictions in English-French interlanguage shows reflexes of domain specificity in the limits on available LF representations. It also shows reflexes of informational encapsulation in computations at the interface between grammar and principles of conversational cooperation. The interpretation of (dis)continuous quantifiers in English-French interlanguage reveals asymmetries that -given the truth-conditional relations between possible LF representations -require a constraint on the LF representations available to discontinuous constituents and also require semantically constrained pragmatic computations supervening on specific LF representations. These properties of knowledge acquired in English-French acquisition follow naturally if L2 acquisition is constrained by an encapsulated processor with Universal Grammar for its database, as Schwartz (1999) entertains. Such properties are otherwise unexpected if a range of computations are available in L2 acquisition. 7 dis. Quelque chose a été trouvé -de formidable -par chacun des paléontologues. 8 con. Quelque chose -de fantastique -a été démontré par chacun de ces savants. 8 dis. Quelque chose a été démontré -de fantastique -par chacun de ces savants.

  4) ∀y [ researcher(y) → [∃x [thing(x) ^remarkable(x) ^observe(x)(y)]]]

  )". The change between the low/mid intermediate learners and the high intermediate learners seems characterizable in terms of the ability of high intermediate learners to retreat 304 Mandatory, informationally encapsulated computations

Figure 1

 1 Figure 1 Native speakers (n ϭ 16): percentage 'yes' responses to discontinuous answers in different-object contexts minus percentage 'yes' responses to discontinuous answers in same-object contexts Notes: Difference: accepted discontinuous answers in different vs. same-object contexts; SD ϭ 15.95; Mean ϭ 10.2.

Figure 2

 2 Figure 2 Low/mid intermediate learners (n ϭ 40): percentage 'yes' responses to discontinuous answers in different-object contexts minus percentage 'yes' responses to discontinuous answers in same-object contexts Notes: Difference: accepted discontinuous answers in different vs. same-object contexts; SD ϭ 27.98; Mean ϭ 17.2.

Figure 3

 3 Figure 3 High intermediate learners (n ϭ 20): Percentage 'yes' responses to discontinuous answers in different-object contexts minus percentage 'yes' responses to discontinuous answers in same-object contexts Notes: Difference: accepted discontinuous answers in different vs. same-object contexts; SD ϭ 33.07; Mean ϭ 18.8.

  14) [ VP ∀y [researcher(y) → ∃x [ VP observe(x)(y) ^thing (x) ^remarkable (x)]]] 15) [ IP ∃x [thing(x) ^remarkable(x) ^[VP ∀y [ VP researcher(y) → observe (x)(y) ]]]]

Table 1

 1 Interpretive asymmetries in continuous and discontinuous Q de A sentences

	Situations of use	Continuous Q de A	Discontinuous Q de A
		sentence	sentence
	Different object(s)	Yes	Yes
	per researcher
	The same object(s)	Yes	No
	for all researchers

Table 2

 2 French native speakers (n ϭ 16): percentage `yes' on continuous vs.

	discontinuous answers
		Continuous answers	Discontinuous answers
		Mean (%)	SD	Mean (%)	SD
	Different objects	82.81	26.17	71.09	33.76
	The same object	82.03	25.40	61.72	32.43

Table 3

 3 Low/mid intermediate learners (n ϭ 40): percentage `yes' on continuous vs. discontinuous answers In contrast, high intermediate learners (n ϭ 20) exhibit sensitivity to word order in interpretation; this is shown in Table 4. With continuous answers, acceptance rates are statistically flat in different-object and same-object contexts (t(19) ϭ .47, p ϭ .645). With discontinuous answers, however, the acceptance rate in different-object contexts marginally contrasts with the acceptance rate in same-object contexts (t(19) ϭ 2.32, p ϭ .032). The acceptance rates for continuous and discontinuous answers in different-object contexts are completely flat (t(19) ϭ .00, p ϭ 1.00). But, crucially, the acceptance rates for continuous and discontinuous answers in same-object contexts contrast significantly (t(19) ϭ 2.60, p ϭ .017).

		Continuous answers	Discontinuous answers
		Mean (%)	SD	Mean (%)	SD
	Different objects	76.25	21.52	74.06	19.28
	The same object	59.06	22.64	59.69	22.91

Table 4

 4 High intermediate learners (n ϭ 20): percentage `yes' on continuous vs. discontinuous answers

		Continuous answers	Discontinuous answers
		Mean (%)	SD	Mean (%)	SD
	Different objects	84.38	28.64	84.38	21.41
	The same object	80.63	17.43	66.88	25.74

Table 5

 5 Low/mid intermediate learners (n ϭ 28): percentage `yes' on parfois vs. toujours discontinuous answers

		parfois		toujours
		Mean (%)	SD	Mean (%)	SD
	Different objects	75.00	17.68	79.01	19.26
	The same object	71.83	20.39	64.73	21.53

Table 7

 7 Native speakers (n ϭ 16): percentage `yes' on parfois vs. toujours

	discontinuous answers
		parfois		toujours
		Mean (%)	SD	Mean (%)	SD
	Different objects	80.47	22.81	79.75	20.34
	The same object	73.44	17.00	75.00	14.43

  12) [ IP Quelque chose de remarquable a [ VP été observé [ DP t quelque chose de remarquable ]] par chacun des chercheurs] 13) [ IP Quelque chose a [ VP été observé [ DP t quelque chose [de remarquable ]]] par chacun des chercheurs ]

Table 8

 8 English controls (nϭ14): percentage `yes' on continuous vs. discontinuous answers (without of )

		Continuous answers	Discontinuous answers
		Mean (%)	SD	Mean (%)	SD
	Different objects	91.07	19.87	78.57	33.05
	The same object	66.07	29.59	70.54	27.56

Table 9

 9 English controls (n ϭ 10): percentage `yes' on continuous vs. discontinuous answers (with of )

		Continuous answers	Discontinuous answers
		Mean (%)	SD	Mean (%)	SD
	Different objects	85.00	21.08	77.50	28.14
	The same object	55.00	23.72	56.25	30.76

8) In a construction: Q 2j … Q 1 … [ e j [restriction of Q 2 ]] … Q 2 cannot take scope over Q 1 .Semantic formulation: A quantifier Q 1 can only separate a quantifier Q 2 from its restrictive clause if Q 1 has wide scope (or is scopally independent from Q 2 ).

It was suggested to us by anonymous Second Language Research reviewers that the term `adequate' risks potential misinterpretations by respondents, or that our approach would appeal the most to respondents already sensitized to these subtle distinctions by their training. Our respondents were randomly chosen from a population of French classroom learners. Although the subjects were not chosen for their linguistic sophistication in the relevant area, when we administered the practice examples, we found that they could easily determine that a sentence compatible with the facts of the scenarios would nevertheless be misleading to one who had only that sentence to go on, and that they could accept or reject answers on that basis.

One respondent from Group A and two respondents from Group B did not participate in Experiment 1. This is reflected in the degree of freedom values of the t-tests performed on results of Experiment 1 for these two groups.

con. Quelque chose -de terrifiant -a été choisi par chacun des étudiants. 4 dis. Quelque chose a été choisi -de terrifiant -par chacun des étudiants.

con. Quelque chose -de lamentable -a été vu par chacun des enfants. 5 dis. Quelque chose a été vu -de lamentable -par chacun des enfants.

con. Quelque chose -de fabuleux -a été découvert par chacun des voleurs. 6 dis. Quelque chose a été découvert -de fabuleux -par chacun des voleurs.

con. Quelque chose -de formidable -a été trouvé par chacun des paléontologues.

Acknowledgements

This work was funded in part by a Faculty Graduate Research Fund grant from Indiana University administered through the Indiana University Department of French and Italian. We acknowledge the comments of three anonymous Second Language Research reviewers which helped us substantially refine our analysis. We thank Rex A. Sprouse for methodological input during the development stage and Bonnie D. Schwartz for criticism during the drafting stage. We benefited from feedback from audiences during a poster presentation at Generative Approaches to Second Language Acquisition, 6, Université d'Ottawa and from members of the Indiana University second language research group. The final presentation also owes much to Roger Hawkins' editorial advice. Any remaining technical and rhetorical inadequacies are our sole responsibility. Lastly, we would like to thank the subjects, instructors and course administrators for their co-operation. In particular, we acknowledge the help of Kathleen O'Connor with the collection of data from native French respondents in Lille.

Schwartz, B.D. 1986: The epistemological status of second language acquisition. Second Language Research 2, 120-59. --1987: The modular basis of second language acquisition. Unpublished doctoral dissertation, University of Southern California, Los Angeles, CA. --1999: Let's make up your mind: 'special nativist' perspectives on language, modularity of mind, and nonnative language acquisition. Studies in Second Language Acquisition 22, 635-55.

Appendix 1 Test sentences 1 con. Quelque chose -de remarquable -a été observé par chacun des scientifiques. 1 dis. Quelque chose a été observé -de remarquable -par chacun des scientifiques. 2 con. Quelque chose -de très traditionnel -a été selectionné par chacun des architectes. 2 dis. Quelque chose a été selectionné -de très traditionnel -par chacun des architectes. 3 con. Quelque chose -de choquant -a été proposé par chacun des artistes. 3 dis. Quelque chose a été proposé -de choquant -par chacun des artistes.


Clarissa Wilks

Paul Meara
email: p.m.meara@swansea.ac.uk

Brent Wolter

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A further note on simulating word association behaviour in a second language Clarissa Wilks Kingston University, Paul Meara University of Wales Swansea and Brent Wolter Idaho State University This article explores some critical methodological and theoretical issues that emerge from recent research into word association behaviour in second language (L2) learners. The studies that we discuss here all use computer simulations as a tool to investigate L2 lexical networks, and to compare these networks with those of first language (L1) speakers. This article broaches some previously unacknowledged complexities in this kind of research, and draws attention to the importance of which assumptions are built into simulation models. The article queries some of the assumptions of our 2002 article [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF], and provides a reinterpretation of some of the data that we presented there. The article argues that simulation modelling forces us to make critical analyses of assumptions in a way that is not always necessary in less exacting experimental environments.

I Introduction

In an earlier article published in this journal [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF], we reported data from an experiment in which we tested the ability of first language (L1) English speakers to recognize associated pairs in small sets of French words. These students (Ss) were first year university students, who had previously studied French for seven years in school. The material used consisted of a 40-item questionnaire. Each item in the questionnaire comprised a set of five words randomly chosen from the Français Fondamental list: approximately the first thousand most frequent words in French excluding grammatical items (Gougenheim et al., 1956). The participants were instructed to read each set of words and circle any two words in the set that they considered to be associated. Ss were provided with written instructions which asked them to read each set of words and to circle any two words that they considered to be associated, for example: blouse cheminée coûter feu tort

The instructions stipulated that where informants perceived no links between any of the words in the set, they should write nothing. In addition, the instructions stated that where they considered more than two of the words of the set to be associated they should circle the two with the strongest link. Ss were instructed to work instinctively and to spend no more than 20 minutes on the entire exercise. Instructions were given in English to the learners of French who participated in the study and in French to the French native speakers. These instructions were developed over a number of studies, and seem not to encourage frivolous responses. A typical item might look like example one below:

1) blouse cheminée coûter feu tort

If they saw more than one pair of associated words in the set, the participants were instructed to circle only the two words with the strongest link. In example (1), for instance, they might circle cheminée (chimney) and feu (fire). If they found no links between any of the words they were instructed to write nothing, and continue to the next item. Alongside this group of L1 English speakers, we also ran a group of L1 French speakers, who carried out the same task. Our intention was to compare the data of the L1 English speakers with the native speakers of French, and we expected, of course, to find that our L1 English speakers were less adept at identifying associated pairs than the L1 French speakers were. Not surprisingly, this turned out to be the case (t ϭ 6.47, p Ͻ .001). The data we reported are presented in Table 1.

These data clearly confirm that there is a difference between the two subject groups, and the most obvious explanation of this difference is that the association network of the L1 group is 'denser' than that of the second language (L2) group, in the sense that L1 words have more associative connections than L2 words do. This density metaphor is one that frequently occurs in the literature on L2 word associations, but its implications are rarely developed. Aitchison (1987), for example, talks about the lexicon as 'a gigantic multidimensional cobweb', and most researchers appear content to operate on this descriptive level. Wilks and Meara, however, attempted to show that it was possible to move beyond imprecise metaphorical descriptions, and to develop more specific quantitative models instead. We did this by comparing the experimental data with data generated by an association simulator.

The simulator was a computer program that modelled a small lexicon in which each word was linked with a number of other words in the lexicon. The number of links between each word and the rest of the lexicon -the NLinks parameter -could be varied, and Wilks and Meara showed that the probability of two associated words appearing in a small set of words varied with the value of this parameter. We then used this data to look again at the data generated by real subjects, and estimated what the real data implied about the density of interword connections in the mental lexicons of our test-takers. Our initial guess had been that the L1 English speakers would have relatively few connections between words in their L2 lexicons, perhaps as few as four or five. However, the results generated by the simulator forced us to revise that estimate. We concluded that the data implied a much denser set of connections, even for L2 speakers, perhaps as many as 30 or 40 links for each word. [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF] considered the implications of this for the way we normally interpret word association data generated by L2 speakers, and we concluded that the density of connections between words would have to be considerably higher than most researchers assumed it to be. This had significant implications for the way we thought about word association networks in an L2.

II Rethinking the simulator

A number of people, notably Brent Wolter, the third author of this article, pointed out to us that our simulator had in fact made some very severe assumptions about the way associations in a lexicon might work, and that this might have resulted in unrealistically high estimates for the number of links between words. In order to clarify this objection, we need to explain the detailed workings of the simulator.

Basically the simulator consists of a large array of numbers. We set the size of this array at 1000, an arbitrary number, but one which is sufficiently large for us to argue that our results did not merely apply to very small lexicons. Each element in the array represents one 'word' in the lexicon. The items are not in fact real words, merely numbers that stand in for real words. Next we set the NLinks parameter, which determines the number of associations each word has. Let us suppose, for the purposes of illustration, that this parameter is set at three. The program next selects three random numbers between 1 and 1000 for the first 'word' in the lexicon. These random numbers point to three other 'words' in the lexicon, and represent the three associates of word number 1. The program then repeats this selection process for all the other words in the lexicon. The result is a structure that looks like Table 2.

For this particular simulation, word 1 is linked with words 123, 145 and 160; word 2 is connected to words 99, 182 and 279, and so on. Other runs, making different random choices, would produce different numbers, but the basic structure would be the same. Setting the NLinks parameter at a different value, say 5, would generate five associations for each word rather than three.

The critical next step is for the simulator program to select sets of five words and check whether or not they contain a pair of associated words (a "hit event"). In [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF] we determined that a hit event had occurred if the number that identified one of the five selected words also appeared in the association list of another word in a set. This is shown in example ( 2 In example (2), we have a set of five words -29, 367, 456, 552 and 699 -each directly linked to six other words in the lexicon. Word 29 appears in the association list for word 367, and this is taken to mean that there is a direct association between word 29 and word 367. Given these data, the simulator program would record a hit. Compare this with what we find in example (3). Here, we have the same set of five target words -29, 367, 456, 552, and 699 -but we have altered the association lists, and none of these words appears in the association list of the other words in the set. Given the data in example (3), the simulator program would record a NoHit event.

3 Our thinking at the time was that a strong associative link between two words would normally result in the index of one word appearing in the association list of the other. For instance, if word 29 had been BLUE, and word 367 had been SEA, we might well expect one of these words to appear in the association list of the other: associations of this type are easily identified in word association norm lists (e.g., [START_REF] Postman | Norms of word association[END_REF]). In modelling terms, 29 might appear in the association list for word 367, and 367 might appear in the association list of word 29. Either event would have been sufficient for the program to register a hit. We assumed that most of the associations recognized by our Ss would be strong associations of this type, and that this interpretation of an associative link was a reasonable way of modelling association behaviour.

Wolter argued that this is actually a very narrow interpretation of association behaviour. It is certainly the case that some common associations have close connections of this kind: RED elicits BLUE, for example, or BIG elicits LITTLE in this way. In terms of our model, this would mean that BLUE would appear in the association list for RED, and LITTLE would appear in the association list of BIG, and the word association norms confirm that this is the case. However, not all associations are of this type. Test-takers are relatively consistent in the Clarissa Wilks,Paul Meara and Brent Wolter 363 associations that they produce, but they appear to be much less consistent in the associations that they recognize. In recognition experiments, the number of idiosyncratic associations is generally rather high, and test-takers will often find associations between words that are only loosely connected with each other. For example, test-takers will frequently identify pairs of words as associates, even when the pairs do not appear in the standard word association lists. Given a word set like RUN, SLEEP, BUS, BLUE, CLOUD, test-takers will sometimes identify RUN~BUS as an associated pair (because they sometimes run for the bus), or SLEEP~BUS (because they usually sleep on the bus), or BLUE~BUS (because the buses in their town happen to be painted blue). Loose associations of this type are particularly likely to be reported if there are no other stronger associations available. This behaviour clearly implies a much looser definition of an association than the one we were working with in [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF].

Wolter suggested that one obvious possibility for scoring looser associations of this sort would be to recognize that real associations between words often rely on a common link shared with a third word. For example, BIRD might be associated with AEROPLANE because they both FLY. This association feels like a strong one, even though BIRD is not commonly associated with AEROPLANE, and AERO-PLANE is not commonly associated with BIRD. The Edinburgh Associative Thesaurus [START_REF] Kiss | An associative thesaurus of English and its computer analysis[END_REF] reveals that no-one offered AEROPLANE as a response to BIRD or vice versa in that dataset. Wolter further pointed out that it would be relatively straightforward to reprogram our simulator so that its definition of a hit event reflected these looser associative connections. Specifically he suggested that the simulator might be reprogrammed to register a hit if any one of the words associated with word X also occurred in the list of associates for word Y. In example (4), for instance, word 138 occurs in the association set for word 29 and for word 456, and this might be interpreted as showing that word 29 and word 456 are linked together indirectly in some way. Suppose word 29 was BIRD, and word 138 was FLY and word 456 was AEROPLANE, then the simulator would register that both BIRD and AEROPLANE share a common associate FLY.

III Results

Wolter's hunch that it would be easy to adapt our simulator to operate in this way is correct, and Table 3 presents a set of data that shows what happens when we make this adjustment.

The data is the probability that the simulator program will register at least one hit in a set of five randomly selected words when the number of associated words for each entry in the lexicon varies from 1 to 20. Each figure in the table is based on 1000 simulated word sets.

It is immediately obvious that these probabilities are considerably higher than the figures we reported in [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF]. The data suggests that the probability of a hit increases rapidly as the NLinks parameter varies between 2 and 14; for values of NLinks above 15, the probability of finding a hit in a set of 5 words is very close to 1.

We can now use these figures to re-interpret the data we reported in [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF]. Wilks and Meara reported that their L1 French speakers, the Native Speaker group, registered a hit on approximately 30 of their 40 trials, i.e., about 75%, but with a substantial standard deviation from this mean. The closest match to these figures in Table 3 is when the NLinks parameter is set to 11 links per word. Wilks and Meara reported that their L1 English speakers, the Non-native Speaker group, returned a mean hit rate of 19/40 (ϭ47.5%) but with a very substantial standard deviation from this mean score. The closest match to these figures in Table 3 is when the NLinks parameter is set to 7 links per word. Table 4 shows Wilks and Meara's original data alongside some further data generated by the revised simulator program. In this simulation, we ran a set of 60 cases. For half these cases, the NLinks parameter was set at 7, and for the other half, the NLinks parameter was set at 11. Each case consisted of 40 five-word stimulus sets. In this way, the simulation is an exact parallel of the real data collected in Wilks and Meara's study. Table 4 shows that the mean scores in the simulated data and the real data are very close, but the simulator seems to generate smaller standard deviations, which are about half the size of the standard deviations in the real data.

Clarissa Wilks, Paul Meara and Brent Wolter 365

These results suggest that our new model generates data that is a reasonably close fit to the data generated by real test-takers. However, the implications of this new dataset suggest rather different conclusions from the ones we drew from our earlier attempt at modelling associations in L2 speakers. In our earlier model, the chances of finding a hit in a random set of five words is fairly low, and the only way to account for the relatively high numbers of matches reported by our test-takers is to argue that the number of links between words must be correspondingly high. In our new model, relatively high hit rates can be achieved with relatively small numbers of connections between the words in the lexicon. Clearly, this changes the game substantially. In our new model, it looks as though 11 links per word is sufficient to account for the native speaker data, while 7 links per word is sufficient to account for the data generated by the L2 speakers. The difference between L1 speakers and L2 speakers is still real, but it now appears to be much smaller than the difference we were suggesting in our earlier account.

366 Simulating word association behaviour in an L2

IV Discussion

Two general points seem to emerge out of this re-evaluation of our [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF] data.

Simulations as a test bed for research tools

The first general point is that simulations clearly have a role in the development of testing instruments that has not been exploited hitherto in SLA research. Specifically, simulations can sometimes be useful because they allow us to identify what experimental conditions are necessary to test the hypotheses that we are working with.

As a simple example of this problem, consider the large amount of research that has looked at incidental vocabulary acquisition in L2. Typically, this work has measured take-up of vocabulary as a result of reading extended texts (see also [START_REF] Huckin | Incidental vocabulary acquisition in a second language: a review[END_REF], and it has done this by presenting Ss with a short list of target words that the Ss did not know when they started to read the text, and measured whether they did know them as a result of having read the text. On the face of it, this looks like a good design: if Ss acquire words by reading, then they should have higher scores on the post-test than they do on the pre-test. In practice, however, most studies of this type report only minimal increases in vocabulary knowledge. It is not difficult to work out why this result keeps recurring. Simply by quantifying what we mean by incidental vocabulary acquisition, we can easily see that some testing instruments will not be sensitive enough to pick up vocabulary growth even if it really exists. Let us suppose that there is a 5% chance of an S picking up a new word from a single encounter in a text [START_REF] Nagy | Incidental vs. instructional approaches to increasing reading vocabulary[END_REF]. Now suppose that we run an experiment that involves 20 target vocabulary items each repeated once in the text that the Ss read. How much improvement would we expect to find between the pre-test and post-test? The answer is about 5% of 20 words, that is, just one word would be expected to show an improvement. Clearly, a difference of this size is very likely to be swamped by variation within the subject group, and would be very unlikely to show up as a reliable improvement in a set of experimental scores. Even if we tested 100 words in this way, we would still expect to find an increase of only five words between pre-test and post-test. This simple quantitative model, then, allows us to say unequivocally that a testing instrument that uses a small number of target words (e.g., the 12-item test used in Hulstijn, 1992: Experiment 1) is not going to be adequate as a tool for evaluating this particular hypothesis.

When it comes to evaluating more complex claims about lexical organization, it becomes more difficult to develop relevant armchair simulations like the one described in the previous paragraph. For example, most people agree that the lexical organization of L2 speakers is different from the lexical organization of L1 speakers, and that the association structure of advanced L2 speakers will be rather different from that of less advanced L2 speakers, but it has proved rather difficult to pin down these differences in practice. The data reported in this article suggests that word association tasks might be capable in principle of demonstrating a difference of this sort, but considerable care needs to be taken in designing experiments to test these claims.

Suppose, for instance, that we have a general hypothesis that lexical organization becomes more complex when language learners spend an extended period in a country where their target language is spoken, and let us suppose that we want to test this hypothesis using a word association recognition task. Now let us suppose that we have a group of students who, before spending a period abroad, score 38% on a test like the one we described in Section III, i.e., they behave as if their L2 lexicons have an average of six links per word. If, as the simulations suggest, the difference between native speakers and advanced learners is typically about four additional associative links, then we might expect that an extended period abroad would increase the average number of links slightly, so let us hypothesize that our learners increase their lexical links from six to seven words as a result of their stay abroad. With a test like the one [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF] used, this improvement ought to show up as an increase in the test scores from 38% to 44%. On a 50-item test, however, this difference is a mere three additional hits: an improvement that would be very difficult to detect in noisy data. Even with a 100-item test, the model suggests that we would expect to measure an improvement of only 6 additional hits. The point here is that relatively small differences in the overt behaviour of the test-takers could be pointers to quite significant changes in the underlying structure of their lexicons.

Arguments like this suggest that developing good test instruments for evaluating hypotheses about vocabulary development may be more difficult than we have typically supposed. Simply comparing the associations of L2 learners and native speakers, using ad hoc lists of words, as much of the research in this area has done, begins to look like a very unsatisfactory approach to assessing L2 lexical competence. Indeed, blunt research tools of this kind may be intrinsically incapable of evaluating the hypotheses we think we are researching. Careful simulation studies provide a way of testing out the capabilities of these instruments before they are widely used in real experiments.

The complexities of simulation research

The second general point to emerge from this study is that working with simulations is perhaps not as straightforward as it might seem to be. Clearly, the results we get from a simulation study are only as good as the assumptions that go into the simulator. If the assumptions are totally wrong, then the results of the simulation that uses them will be completely meaningless. Fortunately, cases of this sort are generally easy to identify. More difficult to work with are cases, like the one reported here, where the assumptions built into the simulation model are not exactly wrong, but limit the possible range of outcomes in some significant way. In the simulations in [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF], we chose to model association processes by looking for stimulus words that occurred in the association list of other stimulus words. This was one of a number of plausible implementations that we could have chosen as a way of modelling the association process and, at the time, it did not strike us as problematical or contentious to model these processes in this way.

With hindsight, it is obvious that the very large number of connections between words implied by the results of that simulation should have made us query this particular set of assumptions sooner. The fact that we did not do this perhaps suggests that researching with simulations is very different from the kind of research that we are used to in SLA. Typically, SLA research involves developing a loosely formulated but broadly testable theoretical position, and evaluating it by collecting data from groups of L2 learners. Because empirical data of this kind is generally hard to collect, it is highly valued, and we often accept data that is partial and fragmentary (small groups of Ss, small numbers of stimulus items, and so on) as a compromise. At the same time, empirical data of this sort is usually treated uncritically: the profession as a whole tends to take empirical findings very much at face value, and it is rare to find data of this sort exposed to close critical scrutiny. Very often we end up accepting data that is really quite unsatisfactory as evidence in support of one theoretical position rather than another.

In simulation research, the relationship between data and theory is much more complex. It is actually very easy to generate vast quantities of data, and because of this, it suddenly becomes very easy to evaluate many different theoretical positions in a way that is logistically impossible using experiments with real L2 learners. However, this facility comes at a price, and the price is that simulations require us to be absolutely explicit about the processes that we think we are modelling, and the actual implementation of a model becomes critical to the research process. The corollary of this is that we need to do much more ground work at the level of theory than we need to do when we are dealing with data collected from human test-takers. Specifically, we can afford to pay much more attention to the details of our theoretical assumptions, simply because the implications of these assumptions can be evaluated much more easily. Potentially, this introduces a significant shift into the way we think about second language acquisition in general, and second language lexicons in particular. Simulations force us to explore the effects of building different assumptions into our theories: by modelling in different ways the processes we are interested in, we can explore in considerable depth exactly how these processes contribute to the performance of our model. This, in turn, can often force us to reevaluate some of the fundamental assumptions that we are working with, and this process, when pushed hard enough, can significantly alter the way we look at things.

In these studies, we have been attempting to model the underlying structures that generate word associations. Most work in this field takes it for granted that word associations are the result of direct connections between one word and another in a mental lexicon. Our first simulation showed that this specific assumption only works if we allow very large numbers of connections between words. Our second simulation showed that a model with fewer connections will also work, but only if we significantly redefine what we mean by an association. On balance, we think that the second model is a more plausible model than the one we developed in [START_REF] Wilks | Untangling word webs: graph theory and the notion of density in second language word association networks[END_REF]: it is mathematically more tractable than the earlier model, and it suggests that the learning burden faced by L2 learners is perhaps not that big. However, it also suggests that previous work on L2 word associations may have been very naive in assuming that word association behaviour was a direct reflection of the immediate connections between words. If this assumption is not correct, then much of the early work on word associations -and not just the work on L2 word associations -may need to be re-evaluated. This is clearly a far-reaching outcome, and bearing in mind the relatively small scale of these simulations, it clearly illustrates the power of this kind of work.

V Conclusions

Ideally, simulation research is an iterative process, in which we formulate many different models, and test them against each other in a competitive environment. Unfortunately, we do not really have a tradition of this kind of work in SLA. Research in L2 vocabulary acquisition, at least, is dominated by a relatively informal attitude towards theory, and the literature predominantly consists of a huge number of one-off studies (see [START_REF] Meara | Vocabulary in a second language[END_REF], which tend to reinforce the general lack of theory. These two factors have prevented the development of the kind of on-going, critical dialogue that is required to allow the vocabulary field to move forward in theoretical terms. The position is made all the more difficult by the fact that few people have the computational skills necessary to work critically through the implications of a simulation model, or to suggest how the behaviour of a model might be affected by changing its fundamental assumptions. The obvious solution to this problem would be for simulation research to become a standard component in the training received by young SLA researchers. We hope that this article will stimulate some readers to think about providing training of this kind in future.

VI References

Aitchison, J. 1987: Words in the mind. Oxford: Basil Blackwell. Gougenheim, G., Michéa, R., Rivenc, P. and Sauvageot, A. 1956:

L'élaboration du français élémentaire. Paris: Didier.

Table 1

 1 Mean hit rate per group

		Non-native speakers	Native speakers
	Mean hits	19.00	30.90
	Standard deviation	7.65	5.74
	Number of items	40	40
	Number of Ss	30

Table 2

 2 Part of a simulated lexicon with the association parameter set at 3

	word 1	123	145	160
	word 2	99	182	279
	word 3	129	182	761
	...
	word 999	135	856	687
	word 1000	72	65

Table 3

 3 Probability of registering an associated pair in a random set of five words

	Number of links	1	2	3	4	5	6	7	8	9	10
	per word
	p (hit)	.037 .077 .143 .195 .310 .382 .442 .563 .654 .714
	Number of links	11	12	13	14	15	16	17	18	19	20
	per word

Table 4

 4 Real and simulated data, 60 cases, each tested on 40 five-word stimulus sets

		Mean hits	SD
	Real data
	Native-speaker group	30.90	5.74
	Non-native-speaker group	19.00	7.65
	Simulation
	NLinks ϭ 11	29.90	3.17
	NLinks ϭ 7	18.56	3.54

p (hit) .772 .819 .852 .909 .926 .957 .962 .979 .980 .983