Constraint-Based Categorial Grammar

Constraint-Based Categorial Grammar Gosse Bouma and Gertjan van Noord Alfa-informatica and Behavorial and Cognitive Neurosciences, Rijksuniversiteit Groningen {gosse,vannoord} @let.rug.nl Abstract We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recur- sive constraints. In particular, the introduction of re- lational constraints allows one to capture the effects of (recursive) lexical rules in a computationally attractive manner. We illustrate the linguistic merits of the new approach by showing how it accounts for the syntax of Dutch cross-serial dependencies and the position and scope of adjuncts in such constructions. Delayed evalu- ation is used to process grammars containing recursive constraints. 1 Introduction Combinations of Categorial Grammar (co) and unifica- tion naturally lead to the introduction of polymorphic categories. Thus, Karttunen (1989) categorizes NP's as X/X, where x is a verbal category, Zeevat el al. (1987) assign the category X/(NP\X) to NP's, and Emms (1993) extends the Lambek-calculus with polymorphic cate- gories to account for coordination, quantifier scope, and extraction. The role of polymorphism has been restricted, how- ever, by the fact that in previous work categories were defined as feature structures using the simple, non- recursive, constraints familiar from feature description languages such as PATR. Relational constraints can be used to define a range of polymorphic categories that are beyond the expressive capabilities of previous ap- proaches. In particular, the introduction of relational con- straints captures the effects of (recursive) lexical rules in a computationally attractive manner. The addition of such rules makes it feasible to consider truly 'lexical- ist' grammars, in which a powerful lexical component is accompanied by a highly restricted syntactic compo- nent, consisting of application only. 2 Recursive Constraints In cG, many grammatical concepts can only be de- fined recursively. Dowty (1982) defines grammatical functions such as subject and object as being the ul- timate and penultimate 'argument-in' of a verbal cate- gory. Hoeksema (1984) defines verbs as exocentric cat- egories reducible to s. Lexical rules frequently refer to such concepts. For instance, a categorial lexical rule of passive applies to verbs selecting an object and must remove the subject. In standard unification-based formalisms, these con- cepts and the rules referring to such concepts cannot be expressed directly. 2.1 Subject-verb agreement Consider a categorial treatment of subject-verb agree- ment with intransitive ( NP[NOM]\S ) and transitive ((NP[NOM]\S)/NP[ACC]) verbs defined as follows: (1) lez(walks,X):- iv(X). /ez(kisses, X) :- tv(X). vat[ eat s ] iv( dir'\' arg [ catnp ] )" case nora iv( val dir '/' vat[ cats ] dir '\' arg [ cat np ] case nom arg [ cal np ] case aCE Subject-verb agreement can be incorporated easily if one reduces agreement to a form of subcategorization. 147 If, however, one wishes to distinguish these two pieces of information (to avoid a proliferation of subcategoriza- tion types or for morphological reasons, for instance), it is not obvious how this could be done without recursive constraints. For intransitive verbs one needs the con- straint that (arg agr) = Agr (where Agr …

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