GAMES AND FULL COMPLETENESS FOR MULTIPLICATIVE LINEAR LOGIC

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 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.