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. © 2011 Springer-Verlag.
CITATION STYLE
Bekki, D. (2011). Combinatory categorial grammar as a substructural logic - Preliminary remarks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6797 LNAI, pp. 16–29). https://doi.org/10.1007/978-3-642-25655-4_3
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