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Combinatory Categorial Grammar as a Substructural Logic

— Preliminary Remarks —
  • Daisuke Bekki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6797)

Abstract

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.

Keywords

Proof System Combinatory Logic Relevant Logic Substructural Logic Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Daisuke Bekki
    • 1
  1. 1.Faculty of Science, Department of Information ScienceOchanomizu UniversityBunkyo-kuJapan

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