Theoretical Computer Science
The syntactic process
Logic of Information Structures
Logic of Information Structures
The Non-Associative Lambek Calculus with Product in Polynomial Time
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Natural Deduction for Intuitionistic Non-communicative Linear Logic
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Wide-coverage semantic representations from a CCG parser
COLING '04 Proceedings of the 20th international conference on Computational Linguistics
Lambda-Calculus and Combinators: An Introduction
Lambda-Calculus and Combinators: An Introduction
Toward the formulation of presupposition by illative combinatory logic
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
Extractability as the deduction theorem in subdirectional combinatory logic
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
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This paper aims to provide a logical background for Combinatory Categorial Grammar (CCG) and its typological discussions. Based on the Curry-Howard correspondence between Gentzen-style proof systems and Lambek Lamda Calculi, and those between Hilbert-style proof systems and substructural BCWK-logic, I define a new class of logic which provides subclasses for each of the substructural combinatory logics, called Subdirectional Combinatory Logic, and propose that CCG is a subdirectional logic of a relevance logic (Combinatory Hypothesis). This hypothesis allows us to discuss typological parameters in universal grammar in terms of the presence/absence of a certain directional combinators.