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Games and full completeness for multiplicative linear logic

  • Samson Abramsky (a1) and Radha Jagadeesan (a2)
Abstract
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.

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[Abr93] S. Abramsky , Computational interpretations of linear logic, Theoretical Computer Science, vol. 111 (1993), pp. 357, revised version of Imperial College Technical Report DoC 90/20, October 1990.

[BFSS90] S. Bainbridge , P. J. Freyd , A. Scedrov , and P. Scott , Functorial polymorphism, Theoretical Computer Science, vol. 70 (1990), pp. 3564.

[Bla92b] A. Blass , A game semantics for linear logic, Annals of Pure and Applied Logic, vol. 56 (1992), pp. 183220.

[DP90] B. A. Davey and H. A. Priestley , Introduction to lattices and order, Cambridge University Press, London and New York, 1990.

[DR89] V. Danos and L. Regnier , The structure of multiplicatives, Archive for Mathematical Logic, vol. 28 (1989), pp. 181203.

[Gir86] J.-Y. Girard , The system F of variable types, fifteen years later, Theoretical Computer Science, vol. 45 (1986), pp. 159192.

[Gir87] J.-Y. Girard , Linear logic, Theoretical Computer Science, vol. 50 (1987), pp. 1102.

[HRR89] J. M. E. Hyland , E. P. Robinson , and G. Rosolini , Algebraic types in per models, Fifth conference on mathematical foundations in programming semantics, Lecture Notes in Computer Science, vol. 442, Springer-Verlag, Berlin and New York, 1989, pp. 333350.

[LS91] Y. Lafont and T. Streicher , Games semantics for linear logic, Proceedings of the sixth annual symposium on logic in computer science, Computer Society Press, Rockville, Maryland, 1991, pp. 4351.

[Plo77] G. D. Plotkin , LCF considered as a programming language, Theoretical Computer Science, vol. 5 (1977), pp. 223255.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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