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arXiv · 1311.6057

Games and Full Completeness for Multiplicative Linear Logic

Samson Abramsky·Radha Jagadeesan
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Abstract

We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of {\em history-free} strategy; strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.

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Samson Abramsky, Radha Jagadeesan. 2013-11-23. Games and Full Completeness for Multiplicative Linear Logic. https://arxiv.org/abs/1311.6057

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