A games model of bunched implications

Reference:

McCusker, G. and Pym, D., 2007. A games model of bunched implications. In: Duparc, J. and Henzinger, T. A., eds. Computer Science Logic: Proceedings of 21st International Workshop, CSL 2007, 16th Annual Conference of the EACSL. Vol. 4646. Berlin, Germany: Springer, pp. 573-588. (Lecture Notes in Computer Science)

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Official URL:

http://dx.doi.org/10.1007/978-3-540-74915-8_42

Abstract

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.

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