Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Theoretical Computer Science
Parsing and derivational equivalence
EACL '89 Proceedings of the fourth conference on European chapter of the Association for Computational Linguistics
ACL '89 Proceedings of the 27th annual meeting on Association for Computational Linguistics
Normal form theorem proving for the Lambek Calculus
COLING '90 Proceedings of the 13th conference on Computational linguistics - Volume 2
Tuples, discontinuity, and gapping in categorial grammar
EACL '93 Proceedings of the sixth conference on European chapter of the Association for Computational Linguistics
Mixing modes of linguistic description in Categorial Grammar
EACL '95 Proceedings of the seventh conference on European chapter of the Association for Computational Linguistics
Efficient incremental processing with categorial grammar
ACL '91 Proceedings of the 29th annual meeting on Association for Computational Linguistics
Discontinuity and the Lambek calculus
COLING '94 Proceedings of the 15th conference on Computational linguistics - Volume 2
Chart parsing Lambek grammars: modal extensions and incrementality
COLING '92 Proceedings of the 14th conference on Computational linguistics - Volume 1
Journal of Logic, Language and Information
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Use of Lambek's (1958) categorial grammar for linguistic work has generally been rather limited. There appear to be two main reasons for this: the notations most commonly used can sometimes obscure the structure of proofs and fail to clearly convey linguistic structure, and the calculus as it stands is apparently not powerful enough to describe many phenomena encountered in natural language.In this paper we suggest ways of dealing with both these deficiencies. Firstly, we reformulate Lambek's system using proof figures based on the 'natural deduction' notation commonly used for derivations in logic, and discuss some of the related proof-theory. Natural deduction is generally regarded as the most economical and comprehensible system for working on proofs by hand, and we suggest that the same advantages hold for a similar presentation of categorial derivations. Secondly, we introduce devices called structural modalities, based on the structural rules found in logic, for the characterization of commutation, iteration and optionality. This permits the description of linguistic phenomena which Lambek's system does not capture with the desired sensitivity and generality.