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
-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 (
). This hypothesis allows us to discuss typological parameters in universal grammar in terms of the presence/absence of a certain directional combinators.