Chapter 5 Combinatory Categorial Grammar ( Draft 4 . 0 , August 10 , 2003 )

We report a computational study on the CHILDES database for learning a grammar of Turkish nouns, in which a syllable-based model converges to a morphemebased model in terms of overlaps in the set of lexical hypotheses. What allows the model to learn is limited combinatory possibilities of a Universal Grammar (as envisioned by Combinatory Categorial Grammar), and relatively short word forms. The convergence of the syllable model, in which the hypotheses include a learned LF, suggests that morphemehood can be an emergent computational property. Introduction How can the meaning and category of words arise in the mind of a child? On one hand, we have the problem of identifying segments of speech as word-like units. On the other, we have the problem of identifying which meanings go with which substrings in speech. The assumption, common to both generative and cognitive linguistics, is that the child has the innate capacity to associate forms with meaning, and it is a question of acquisition to tackle the problem of deciding which forms go with which meanings. A quick glance over the Turkish fragment of the childdirected speech in the CHILDES database reveals that 44% of the nouns are uninflected; the remaining 56% are inflected by means of affixes and clitics (derivational affixes occur in 4% of these words, which are mostly inflected, hence the percentage changes from 44% to 43% only, if we consider derivational affixes as well). The question then arises as to how the meaning and category of the inflected words, which constitute the majority, are acquired by the child. A common concept, influential at least since Bloomfield (1933), is that words are made up of morphemes, and the morpheme is the minimal meaning-bearing element in natural languages. Nevertheless, although there are clear phonological and prosodic cues for word boundaries (e.g. Jusczyk, 1999; Thiessen & Saffran, 2003), there are no apparent cues for morpheme boundaries, hence the task of learning morpheme meanings to come up with word meanings is not made easier by labeling some items as morphemes in the competence grammar of adults. Aksu-Koc & Slobin (1985); Peters & Menn (1993) report production data of respectively Turkish and English children of age 2;6 and younger, during which the child produces meaningless filler syllables. “[I]t seems that the child attempts to retain some rhythmic picture of complex verbs, incomprehendingly inserting morphemes that sound like passive and causative particles.” (Aksu-Koc & Slobin:847). Peters & Menn data show this is not idiosyncratic to verbs. Contra the remarks of both work for Turkish without a statisThere are indeed phonological and prosodic cues for discerning substrings smaller than words, namely syllables (rhythm), stress and pitch accents. In this work, we report a computational study which starts with the ability to identify syllables, and learns the meaning and category of words and morphemes without the assumption that only words and morphemes have a meaning. The kind of meaning that the system starts with and learns more of is not lexical meanings, such as what it means to be a dog or to sleep (see Tenenbaum & Xu 2000 for a Bayesian way to tackle that problem), but the combinatory meaning and its syntactic reflex in the form of a category, as a lexical hypothesis, for example how pisi-ler-e (kitty-PLU-DAT, Turkish), with the syllables pi·si·le·re, can come to be associated with a logical form such as to′(plu ′cat ′) and the syntactic type N (and others, such as VP modifiers). We show that under a Bayesian scenario of hypothesis revision with the Universal Grammar as the provider of likelihoods and priors, starting with syllables and the assumed ability to associate forms with meanings converges to a lexicalized grammar of words and morphemes, by showing a significant overlap with the lexical hypotheses of a learning model which works with the assumption that only morphemes and words constructed from them have meanings. Universal Grammar Crucially, morphology of words is a hidden variable in our model, and the input to the system are pairs of sequence of syllables (in lieu of phonological form, PF) and a logical form (LF), without any indication as to which syllable contributes to what part of the LF, or which part of the meaning of a morpheme is covered by a syllable. This is unlike the approach of Jack et al. (2006), another syllable-based acquisition model, in which a sequence of syllables is paired not with a possibly ambiguous LF but with a disambiguated representation of world meanings. We do not assume that the child knows pisi is kitty, and ler is plural; she might (wrongly) hypothesize pisi is plural and ler means kitty, or the first syllable of pisi (pi) means kitty, etc. We also differ from Aronoff et al. (2006), whose model detects frequently-occuring sound tic, morpheme and syllable boundaries do not generally coincide. Only 23% of the syllables in nouns (out of 20,433 syllables) are also morphemes in the CHILDES database. If we only match boundaries (the beginning and end of a morpheme align with a syllable boundary, irrespective of whether the syllable and the morpheme are the same), e.g. araba-lar (car-PLU, Turkish) versus the syllables a·ra·ba·lar providing two matches out of 4 syllables, the overlap is 57%. sequences and hypothesizes that they are morphemes. Our model aims to learn the LF of the purported morpheme as well, not just its form. What allows our system to learn with reasonable efficiency is that this task is biased by a Universal Grammar (UG) and the current lexicon, the latter of which is shaped but not entirely determined by UG, and that the input words are relatively short (compared to adult input), so that considering all possibilities of syllable-LF associations is tolerable computationally, as suggested by Steedman & Hockenmaier (2007) for learnability of short utterances involving multiple words. We shall assume that UG comprises a set of principles and a set of universal combinatory rules, which are completely type-dependent, rather than structuredependent. Steedman (2000) shows how Combinatory Categorial Grammar (CCG) can fulfil that role, which gives CCG its explanatory edge compared to structuredependent accounts, to explain the so-called nonstandard constituency in bounded and unbounded dependencies such as in coordination and relativization asymmetries, to integrate intonation structure, information structure and syntactic structure as arising from the same derivational system of projecting (PF, LF) pairs from the lexicon to phrases. Steedman & Hockenmaier (2007) show how CCG can bootstrap and facilitate learning a lexicalized grammar of a natural language, with examples involving the use of words from the stage of 2-word syntax onwards. We will confine ourselves to a few principles related to our work, and to one combinatory rule that seems most relevant to acquiring a word grammar, viz. function application. It is defined as follows: (1) a. Forward Application: X/Y: f Y: a ⇒ X: fa (>) b. Backward Application: Y: a X\Y: f ⇒ X: fa (<) The elements of a CCG lexical hypothesis are: