Coupling CCG and Hybrid Logic Dependency Semantics

Coupling CCG and Hybrid Logic Dependency Semantics Jason Baldridge ICCS Division of Informatics 2 Buccleuch Place University of Edinburgh Edinburgh, UK, EH8 9LW jmb@cogsci.ed.ac.uk Geert-Jan M. Kruijff Universit¨at des Saarlandes Computational Linguistics Lehrstuhl Uszkoreit Building 17, Postfach 15 11 50 66041 Saarbr¨ucken, Germany gj@CoLi.Uni-SB.DE Abstract Categorial grammar has traditionally used the λ-calculus to represent meaning. We present an alternative, dependency-based perspective on linguistic meaning and sit- uate it in the computational setting. This perspective is formalized in terms of hy- brid logic and has a rich yet perspicuous propositional ontology that enables a wide variety of semantic phenomena to be rep- resented in a single meaning formalism. Finally, we show how we can couple this formalization to Combinatory Categorial Grammar to produce interpretations com- positionally. 1 Introduction The λ-calculus has enjoyed many years as the stan- dard semantic encoding for categorial grammars and other grammatical frameworks, but recent work has highlighted its inadequacies for both linguistic and computational concerns of representing natural lan- guage semantics (Copestake et al., 1999; Kruijff, 2001). The latter couples a resource-sensitive cate- gorial proof theory (Moortgat, 1997) to hybrid logic (Blackburn, 2000) to formalize a dependency-based perspective on meaning, which we call here Hybrid Logic Dependency Semantics (HLDS). In this pa- per, we situate HLDS in the computational context by explicating its properties as a framework for com- putational semantics and linking it to Combinatory Categorial Grammar (CCG). The structure of the paper is as follows. In x2, we briefly introduce CCG and how it links syntax and semantics, and then discuss semantic represen- tations that use indexes to identify subparts of logi- cal forms. x3 introduces HLDS and evaluates it with respect to the criteria of other computational seman- tics frameworks. x4 shows how we can build HLDS terms using CCG with unification and x5 shows how intonation and information structure can be incorpo- rated into the approach. 2 Indexed semantic representations Traditionally, categorial grammar has captured meaning using a (simply typed) λ-calculus, build- ing semantic structure in parallel to the categorial in- ference (Morrill, 1994; Moortgat, 1997; Steedman, 2000b). For example, a (simplified) CCG lexical en- try for a verb such as wrote is given in (1). (1) wrote ` (snn)=n : λx:λy:write (y;x ) Rules of combination are defined to operate on both categories and λ-terms simultaneously. For exam- ple, the rules allow the following derivation for Ed wrote books. (2) Ed wrote books n:Ed (snn)=n:λx:λy:write (y;x ) n:books > s nn : λy:write (y;books ) < s : write (Ed;books ) Derivations like (2) give rise to the usual sort of predicate-argument structure whereby the order in which the arguments appear (and are bound by the λ’s) is essentially constitutive of their meaning. Thus, the first argument could be taken to corre- spond to the writer, whereas the second argument corresponds to what is being written. Computational Linguistics (ACL), Philadelphia, July 2002, pp. 319-326. Proceedings of the 40th Annual Meeting of the Association for One deficiency of λ-calculus meaning representa- tions …

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