The following paper is now available by anonymous ftp from theory.doc.ic.ac.uk, in papers/Abramsky. Anyone needing a hard copy should send me their postal address. -------- \documentstyle[11pt]{article} \begin{document} \bibliographystyle{alpha} \title{Games and Full Completeness for Multiplicative Linear Logic} \author{Samson Abramsky and Radha Jagadeesan \\ Imperial College.} \maketitle \begin{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 {\em 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 {\it et al}. \end{abstract} \end{document} ==============================================================================