Taking Scope: The Natural Semantics of Quantifiers

Chapter 6 Combinatory Categorial Grammar

Chapter 6 Combinatory Categorial Grammar Alan Greenspan, a former Fed Chairman, said inflation will exceed 10% if the Fed fails to shrink its balance sheet and raise rates, and 3% for a time even if it does. —The Economist, August 15, 2009 The introductory chapters discussed the need for surface-compositional grammars to be strongly lexicalized, in order to be both fully formal and construction-centric, eschewing any distinction between “core” and “periphery .” Combinatory Categorial Grammar (CCG) is a strongly lexicalized theory of grammar in which grammatical categories consist of (a) a syntactic type defining valency (the number and syntactic type of its arguments, if any) and the type of the result, the left-right linear order of those arguments, and the order of their combination, together with (b) a logical form and (c) a phonological form. The Categorial Lexicon is the sole repository of language-specific information . A small universal set of type-driven combinatory syntactic rules projects the sounds and meanings of this language-specific lexicon onto the sounds and meanings of all and only the sentences of the language (Szabolcsi 1992a). I will begin by considering these two components in turn. In the interest of getting the basics across easily, all categories in this chapter are nonnegative polarity and polarity-preserving, so that we can temporarily suppress all syntactic and semantic markers of polarity. 6.1 The Categorial Lexicon The English intransitive verb walks has the following category, which identifies it as a function from (subject) NPs, which the backward slash identifies as having to occur to the left of walks, into sentences of type S:1 (1) walks := S\NP3SG : λx.walk′x 1. This is the “result leftmost” convention for function categories. There is an alternative “result on top” convention, due to Lambek 1958. 78 Chapter 6 The feature value indicated by the subscript 3SG on the subject identifies it as bearing third-person singular agreement. Where agreement is ambiguous, as with walked, or is irrelevant, it is suppressed in examples. As in any other theory of grammar, we must assume that the ensemble of such syntactic category types that can coexist in the lexicon of any human language is subject to universal constraints related to learnability, of a kind investigated for CCG by McConville (2006, 2007) using default inheritance in a hierarchical feature system. The interpretation of categories such as (1) is written as a λ-term associated with the syntactic category by the operator “:”. The English transitive verb admires has the category of a function from (object ) nounphrases (which the forward slash identifies as having to occur to the right of admires) into predicates or intransitive verbs: (2) admires := (S\NP3SG)/NP : λxλy.admire′xy Juxtaposition of function and argument symbols in logical forms as in admire′x indicates function application as before. The usual CCG convention of left associativity holds, according to which admire′xy is equivalent to (admire′x)y. Such predicate-argument structures can therefore be thought of as treestructures like the following, over which a standard notion of structural command can be defined: (3) y x ’ admires In the case of (2), the syntactic type is simply the SVO directional form of the semantic type. In other cases categories may “wrap” arguments into the logical form, in a lexicalized version of the analysis of Bach (1979, 1980), Dowty (1982), and Jacobson (1992). For example, the following is the category of the English ditransitive verb showed:2 (4) showed := ((S\NP)/NP)/ ⋄NP : λxλyλz.showed′yxz CCG differs on this point from the categorial approaches of Bach and colleagues in making WRAP a lexical combinatory operation, rather than a syntactic combinatory rule. One advantage of this analysis, discussed further in SS&I, is that phenomena depending on WRAP, such as anaphor binding and 2. ⋄ modality on the accusative argument of showed prevents overgeneration of heavy shifted datives, as in *We showed a movie a very heavy policeman. Combinatory Categorial Grammar 79 control, are immediately predicted to be bounded phenomena. While this is a departure from the strictest definition of “direct” surface-compositionality, it is entirely harmless, and is known as “direct compositionality by construction” (Jacobson 1999; Barker and Jacobson 2007, 9), as noted in the Preface. The reason for this departure is that it greatly simplifies the account of coordination developed below and in SP and earlier publications...