A Definite Clause Version of Categorial Grammar

We introduce a first-order version of Categorial Grammar, based on the idea of encoding syntactic types as definite clauses. Thus, we drop all explicit requirements of adjacency between combinable constituents, and we capture wordorder constraints simply by allowing subformulae of complex types to share variables ranging over string positions. We are in this way able to account for constructiods involving discontinuous constituents. Such constructions axe difficult to handle in the more traditional version of Categorial Grammar, which is based on propositional types and on the requirement of strict string adjacency between combinable constituents. We show then how, for this formalism, parsing can be efficiently implemented as theorem proving. Our approach to encoding types:as definite clauses presupposes a modification of standard Horn logic syntax to allow internal implications in definite clauses. This modification is needed to account for the types of higher-order functions and, as a consequence, standard Prolog-like Horn logic theorem proving is not powerful enough. We tackle this * I am indebted to Dale Miller for help and advice. I am also grateful to Aravind Joshi, Mark Steedman, David x, Veir, Bob Frank, Mitch Marcus and Yves Schabes for comments and discussions. Thanks are due to Elsa Grunter and Amy Feh.y for advice on typesetting. Parts of this research were supported by: a Sloan foundation grant to the Cognitive Science Program, Univ. of Pennsylvania; and NSF grants MCS-8219196-GER, IRI-10413 AO2, ARO grants DAA29-84-K-0061, DAA29-84-9-0027 and DARPA grant NOOO14-85-K0018 to CIS, Univ. of Pezmsylvani& t Address for correspondence problem by adopting an intuitionistic treatment of implication, which has already been proposed elsewhere as an extension of Prolog for implementing hypothetical reasoning and modular logic programming. 1 I n t r o d u c t i o n Classical Categorial Grammar (CG) [1] is an approach to natural language syntax where all linguistic information is encoded in the lexicon, via the assignment of syntactic types to lexical items. Such syntactic types can be viewed as expressions of an implicational calculus of propositions, where atomic propositions correspond to atomic types, and implicational propositions account for complex types. A string is grammatical if and only if its syntactic type can be logically derived from the types of its words, assuming certain inference