A Games Model of Bunched Implications

A game semantics of the (−−∗, →)-fragment of the logic of bunched implications, BI, is presented. To date, categorical models of BI have been restricted to two kinds: functor category models; and the category Cat itself. The game model is not of this kind. Rather, it is based on Hyland-Ong-Nickau-style games and embodies a careful analysis of the notions of resource sharing and separation inherent in BI. The key to distinguishing between the additive and multiplicative connectives of BI is a semantic notion of separation. The main result of the paper is that the model is fully complete: every finite, total strategy in the model is the denotation of a term of the αλ-calculus, the term language for the fragment of BI under consideration.

• Type: Conference
• Year: 2007
• Where: CSL
• Authors: Guy McCusker, David J. Pym
• Keywords: Categorical Models, CSL 2007, Functor Category Models, Game Semantics