Game semantics for the Lambek-calculus: Capturing directionality and the absence of structural rules

Studia Logica 90 (2):161 - 188 (2008)
Abstract
In this paper, we propose a game semantics for the (associative) Lambek calculus . Compared to the implicational fragment of intuitionistic propositional calculus, the semantics deals with two features of the logic: absence of structural rules, as well as directionality of implication. We investigate the impact of these variations of the logic on its game semantics.
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