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Games and full completeness for multiplicative linear logic

Published online by Cambridge University Press:  12 March 2014

Samson Abramsky  and
Radha Jagadeesan
Samson Abramsky
Affiliation:
Department of Computing, Imperial College of Science, Technology and Medicine, London, SW7 2BZ, England, E-mail: sa@doc.ic.ac.uk
Radha Jagadeesan
Affiliation:
Department of Mathematical Sciences, Loyola University, Chicago, E-mail: radha@feldberg.math.luc.edu
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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 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 543 - 574
Copyright
Copyright © Association for Symbolic Logic 1994

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