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<Paper uid="W04-1308">
  <Title>Modelling syntactic development in a cross-linguistic context</Title>
  <Section position="4" start_page="54" end_page="55" type="metho">
    <SectionTitle>
3 The optional-infinitive phenomenon
</SectionTitle>
    <Paragraph position="0"> Between two and three years of age, children learning English often produce utterances that appear to lack inflections, such as past tense markers or third person singular agreement markers. For example, children may produce utterances as:  (1a) That go there* (2a) He walk home* instead of: (1b) That goes there (2b) He walked home  Traditionally, such utterances have been interpreted in terms of absence of knowledge of the appropriate inflections (Brown, 1973) or the dropping of inflections as a result of performance limitations in production (L. Bloom, 1970; P. Bloom, 1990; Pinker, 1984; Valian, 1991). More recently, however, it has been argued that they reflect the child s optional use of (root) infinitives (e.g. go) in contexts where a finite form (e.g. went, goes) is obligatory in the adult language (Wexler, 1994, 1998).</Paragraph>
    <Paragraph position="1"> This interpretation reflects the fact that children produce (root) infinitives not only in English, where the infinitive is a zero-marked form, but also in languages such as Dutch where the infinitive carries its own infinitival marker. For instance,  children learning Dutch may produce utterances such as:  (3a) Pappa eten* (Daddy to eat) (4a) Mamma drinken* (Mummy to drink) instead of: (3b) Pappa eet (Daddy eats) (4b) Mamma drinkt (Mummy drinks)  The optional infinitive phenomenon is particularly interesting as it occurs in languages that differ considerably in their underlying grammar, and is subject to considerable developmental and cross-linguistic variation. It is also intriguing because children in the optional infinitive stage typically make few other grammatical errors. For example, they make few errors in their use of the basic word order of their language: English-speaking children may say he go, but not go he.</Paragraph>
    <Paragraph position="2"> Technically, the optional infinitive phenomenon revolves around the notion of finiteness . Finite forms are forms that are marked for Tense and/or Agreement (e.g. went, goes). Non-finite forms are forms that are not marked for Tense or Agreement. This includes the infinitive form (go), the past participle (gone), and the progressive participle (going). In English, finiteness marking increases with development: as they grow older, children produce an increasing proportion of unambiguous finite forms.</Paragraph>
  </Section>
  <Section position="5" start_page="55" end_page="59" type="metho">
    <SectionTitle>
4 Description of the model
</SectionTitle>
    <Paragraph position="0"> MOSAIC is a computational model that analyses the distributional characteristics present in the input. It learns to produce increasingly long utterances from naturalistic (child-directed) input, and produces output consisting of actual utterances, which can be directly compared to children s speech. This allows for a direct comparison of the output of the model at different stages with the children s developmental data.</Paragraph>
    <Paragraph position="1"> The model learns from text-based input (i.e., it is assumed that the phonological stream has been segmented into words). Utterances are processed in a left to right fashion. MOSAIC uses two learning mechanisms, based on discrimination and generalisation, respectively. The first mechanism grows an n-ary discrimination network (Feigenbaum &amp; Simon, 1984; Gobet et al., 2001) consisting of nodes connected by test links. Nodes encode single words or phrases. Test links encode the difference between the contents of consecutive nodes. (Figure 1 illustrates the structure of the type of discrimination net used.) As the model sees more and more input, the number of nodes and links increases, and so does the amount of information held in the nodes, and, as a consequence, the average length of the phrases it can output. The node creation probability (NCP) is computed as follows:</Paragraph>
    <Paragraph position="3"> where M is a parameter arbitrarily set to 70,000 in the English and Spanish simulations, N = number of nodes in the net (N M), and L = length of the phrase being encoded. Node creation probability is thus dependent both on the length of the utterance (longer utterances are less likely to yield learning) and on the amount of knowledge already acquired.</Paragraph>
    <Paragraph position="4"> In a small net, learning is slow. When the number of nodes in the net increases, the node creation probability increases and, as a result, the learning rate also increases. This is consistent with data showing that children learn new words more easily as they get older (Bates &amp; Carnavale, 1993).</Paragraph>
    <Paragraph position="5">  net. The Figure also illustrates how an utterance can be generated. Because she and he have a generative link, the model can output the novel utterance she sings. (For simplicity, preceding context is ignored in this Figure.) While the first learning mechanism is based on discrimination, the second is based on generalisation. When two nodes share a certain percentage (set to 10% for these simulations) of nodes (phrases) following and preceding them, a new type of link, a generative link is created between them (see Figure 1 for an example). Generative links connect words that have occurred in similar contexts in the input, and thus are likely to be of the same word class. As no linguistic constructs are given to the model, the development of approximate linguistic classes, such as those of noun or verb, is an emergent property of the distributional analysis of the input. An important feature of MOSAIC is that the creation and removal of generative links is dynamic. Since new nodes are constantly being created in the network, the percentage overlap between two nodes varies over time; as a  consequence, a generative link may drop below the threshold and so be removed.</Paragraph>
    <Paragraph position="6"> The model generates output by traversing the network and outputting the contents of the visited links. When the model traverses test links only, the utterances it produces must have been present in the input. Where the model traverses generative links during output, novel utterances can be generated. An utterance is generated only if its final word was the final word in the utterance when it was encoded (this is accomplished by the use of an  end marker). Thus, the model is biased towards generating utterances from sentence final position, which is consistent with empirical data from language-learning children (Naigles &amp; Hoff-Ginsberg, 1998; Shady &amp; Gerken, 1999; Wijnen, Kempen, &amp; Gillis, 2001).</Paragraph>
    <Paragraph position="7"> 5 Modelling the optional-infinitive phenomenon in English  Despite the theoretical interest of the optional-infinitive phenomenon, there is, to our knowledge, no quantitative description of the developmental dynamics of the use of optional infinitives in English, with detail comparable to that provided in other languages, such as Dutch (Wijnen et al., 2001). The following analyses fill this gap.</Paragraph>
    <Section position="1" start_page="56" end_page="56" type="sub_section">
      <SectionTitle>
5.1 Children s data: Methods
</SectionTitle>
      <Paragraph position="0"> We selected the speech of two children (Anne, from 1 year 10 months to 2 years 9 months; and Becky, from 2 years to 2 years 11 months). These data were taken from the Manchester corpus (Theakston, Lieven, Pine, &amp; Rowland, 2001), which is available in the CHILDES data base (MacWhinney, 2000). Recordings were made twice every three weeks over a period of one year and lasted for approximately one hour per session. Given that optional-infinitive phenomena are harder to identify in English than in languages such as Dutch or German (due to the relatively low number of unambiguous finite forms), the analysis focused on the subset of utterances that contain a verb with he, she, it, this (one), or that (one) as its subject. Restricting the analysis in this way avoids utterances such as I go, which could be classified both as non-finite and finite, and therefore makes it possible to more clearly separate non-finites, simple finites, compound finites, and ambiguous utterances. null Identical (automatic) analyses of the data and model were carried out in a way consistent with previous work on Dutch (Wijnen et al., 2001). Utterances that had the copula (i.e., forms of the verb to be) as a main verb were removed. Utterances that contained a non-finite form as the only verb were classified as non-finites. Utterances with an unambiguous finite form (walks, went) were counted as finite, while those containing a finite verb form plus a non-finite form (has gone) were classified as compound finites. The remaining utterances were classified as ambiguous and counted separately; they contained an ambiguous form (such as bought in he bought) as the main verb, which can be classified either as a finite past tense form or as a (non-finite) perfect participle (in the phrase he bought, the word has may have been omitted).</Paragraph>
    </Section>
    <Section position="2" start_page="56" end_page="56" type="sub_section">
      <SectionTitle>
5.2 Children s data: Results
</SectionTitle>
      <Paragraph position="0"> The children s speech was partitioned into three developmental stages, defined by mean length of utterance (MLU). The resulting distributions, portrayed in Figure 2, show that the proportion of non-finites decreases as a function of MLU, while the proportion of compound finites increases. There is also a slight increase in the proportion of simple finites, although this is much less pronounced than the increase in the proportion of compound finites.</Paragraph>
    </Section>
    <Section position="3" start_page="56" end_page="59" type="sub_section">
      <SectionTitle>
5.3 Simulations
</SectionTitle>
      <Paragraph position="0"> The model received as input speech from the children s respective mothers. The size of the input was 33,000 utterances for Anne s model, and 27,000 for Becky s model. Note that, while the analyses are restricted to a subset of the children s corpora, the entire mothers corpora were used as input during learning. The input was fed through the model several times, and output was generated after every run of the model, until the MLU of the output was comparable to that of the end stage in the two children. The output files were then compared to the children s data on the basis of MLU.</Paragraph>
      <Paragraph position="1"> The model shows a steady decline in the proportion of non-finites as a function of MLU coupled with a steady increase in the proportion of compound finites (Figure 3). On average, the model s production of optional infinitives in third person singular contexts drops from an average of 31.5% to 16% compared with 47% to 12.5% in children.</Paragraph>
      <Paragraph position="2"> MOSAIC thus provides a good fit to the developmental pattern in the children s data (not including the ambiguous category: r2 = .65, p &lt; .01, RMSD = 0.096 for Anne and her model; r2 = .88, p &lt; .001, RMSD = 0.104 for Becky and her model). One obvious discrepancy between the model s and the children s output is that both models at MLU 2.1 produce too many simple finite utterances. Further inspection of these utterances reveals that they contain a relatively high proportion of finite modals such as can and will and finite forms of the dummy modal do such as does and did. These forms are unlikely to be used as the only verb in children s early utterances as their function is to</Paragraph>
      <Paragraph position="4"/>
      <Paragraph position="6"> compound finites, and ambiguous utterances for Anne and Becky as a function of developmental phase. Only utterances with he, she, it, that (one), or this (one) as a subject are included.</Paragraph>
      <Paragraph position="8"/>
      <Paragraph position="10"> compound finites, and ambiguous utterances for the models of Anne and Becky as a function of developmental phase. Only utterances with he, she, it, that (one), or this (one) as a subject are included.</Paragraph>
      <Paragraph position="11"> modulate the meaning of the main verb rather than to encode the central relational meaning of the sentence. null An important reason why MOSAIC accounts for the data is that it is biased towards producing sentence final utterances. In English, non-finite utterances can be learned from compound finite questions in which finiteness is marked on the auxiliary rather than the lexical verb. A phrase like He walk home can be learned from Did he walk home?, and a phrase like That go there can be learned from Does that go there? As MLU increases, the relative frequency of non-finite utterances in the output decreases, because the model learns to produce more and more of the compound finite utterances from which these utterances have been learned.</Paragraph>
      <Paragraph position="12"> MOSAIC therefore predicts that as the proportion of non-finite utterances decreases, there will be a complementary increase in the proportion of compound finites.</Paragraph>
      <Paragraph position="13"> 6 Modelling optional infinitives in Dutch Children acquiring Dutch seem to use a larger proportion of non-finite verbs in finite contexts (e.g., hij lopen, bal trappen) than children learning English. Thus, in Dutch, a very high percentage of children s early utterances with verbs (about 80%) are optional-infinitive errors. This percentage decreases to around 20% by MLU 3.5 (Wijnen, Kempen &amp; Gillis, 2001).</Paragraph>
      <Paragraph position="14"> As in English, optional infinitives in Dutch can be learned from compound finites (auxiliary/modal + infinitive). However, an important difference between English and Dutch is that in Dutch verb position is dependent on finiteness. Thus, in the simple finite utterance Hij drinkt koffie (He drinks coffee) the finite verb form drinkt precedes its object argument koffie whereas in the compound finite utterance Hij wil koffie drinken (He wants coffee drink), the non-finite verb form drinken is restricted to utterance final position and is hence preceded by its object argument: koffie. Interestingly, children appear to be sensitive to this feature of Dutch from very early in development and MOSAIC is able to simulate this sensitivity. However, the fact that verb position is dependent on finiteness in Dutch also means that whereas non-finite verb forms are restricted to sentence final position, finite verb forms tend to occur earlier in the utterance. MOSAIC therefore simulates the very high proportion of optional infinitives in early child Dutch as a function of the interaction between its utterance final bias and increasing MLU.</Paragraph>
      <Paragraph position="15"> That is, the high proportion of non-finites early on is explained by the fact that the model mostly produces sentence-final phrases, which, as a result of  Dutch grammar, have a large proportion of nonfinites. null As shown in Figure 4, the model s production of optional infinitives drops from 69% to 28% compared with 77% to 18% in the data of the child on whose input data the model had been trained. In these simulations, the input data consisted of a sample of approximately 13,000 utterances of child-directed speech. Because of the lower input size, the M used in the NCP formula was set to  and compound finites for Peter and his model, as a function of developmental phase.</Paragraph>
      <Paragraph position="16"> 7 Modelling optional infinitives in Spanish Wexler (1994, 1998) argues that the optional-infinitive stage does not occur in pro-drop languages, that is, languages like Spanish in which verbs do not require an overt subject. Whether MOSAIC can simulate the low frequency of optional-infinitive errors in early child Spanish is therefore of considerable theoretical interest, since the ability of Wexler s theory to explain cross-linguistic data is presented as one of its main strengths. Note that simulating the pattern of finiteness marking in early child Spanish is not a trivial task. This is because although optional-infinitive errors are much less common in Spanish than they are in Dutch, compound finites are actually more common in Spanish child-directed speech than they are in Dutch child-directed speech (in the corpora we have used, they make up 36% and 30% of all parents utterances including verbs, respectively).</Paragraph>
      <Paragraph position="17">  and compound finites for Juan and his model, as a function of developmental phase.</Paragraph>
      <Paragraph position="18"> Figure 5a shows the data for a Spanish child, Juan (Aguado Orea &amp; Pine, 2002), and Figure 5b the outcome of the simulations run using MOSAIC. The parental corpus used as input consisted of about 27,000 utterances. The model s production of optional infinitives drops from 21% to 13% compared with 23% to 4% in the child.</Paragraph>
      <Paragraph position="19"> Both the child and the model show a lower proportion of optional-infinitive errors than in Dutch. The presence of (some rare) optional-infinitive errors in the model s output is explained by the same mechanism as in English and Dutch: a bias towards learning the end of utterances. For example, the input ?Quieres beber cafO? (Do you want to drink coffee?) may later lead to the production of beber cafO. But why does the model produce so few optional-infinitive errors in Spanish when the Spanish input data contain so many compound finites? The answer is that finite verb forms are much more likely to occur in utterance final position in Spanish than they are in Dutch, which makes them much easier to learn.</Paragraph>
    </Section>
  </Section>
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