Asynchronous games 4: a fully complete model of propositional linear logic

We construct a denotational model of propositional linear logic based on asynchronous games and winning uniform innocent strategies. Every formula A is interpreted as an asynchronous game [A] and every proof /spl pi/ of A is interpreted as a winning uniform innocent strategy [/spl pi/] of the game [A]. We show that the resulting model is fully complete: every winning uniform innocent strategy /spl sigma/ of the asynchronous game [A] is the denotation [/spl pi/] of a proof /spl pi/ of the formula A.

[1]  Martin Hyland,et al.  Abstract Games for Linear Logic , 1999, CTCS.

[2]  Samson Abramsky,et al.  A fully abstract game semantics for general references , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[3]  Martin Hyland,et al.  Games on Graphs and Sequentially Realizable Functionals , 2002, LICS 2002.

[4]  Jean-Yves Girard,et al.  A new constructive logic: classic logic , 1991, Mathematical Structures in Computer Science.

[5]  Paul-André Melliès,et al.  Asynchronous games 2: The true concurrency of innocence , 2006, Theor. Comput. Sci..

[6]  Pierre-Louis Curien.  On the Symmetry of Sequentiality , 1993, MFPS.

[7]  Uday S. Reddy,et al.  Global state considered unnecessary: An introduction to object-based semantics , 1996, LISP Symb. Comput..

[8]  S. Abramsky.  Game Semantics , 1999 .

[9]  Thomas Ehrhard,et al.  Believe it or not, AJM's games model is a model of classical linear logic , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[10]  Martin Hyland.  Semantics and Logics of Computation: Game Semantics , 1997 .

[11]  Eric Goubault,et al.  Geometry and concurrency: a user's guide , 2000, Mathematical Structures in Computer Science.

[12]  Peter Selinger,et al.  Control categories and duality: on the categorical semantics of the lambda-mu calculus , 2001, Mathematical Structures in Computer Science.

[13]  Hanno Nickau.  Hereditarily Sequential Functionals , 1994, LFCS.

[14]  Samson Abramsky,et al.  Handbook of logic in computer science. , 1992 .

[15]  Paul-André Melliès.  Categorical models of linear logic revisited , 2002 .

[16]  Glynn Winskel,et al.  Models for Concurrency , 1994 .

[17]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[18]  Paul-André Melliès.  Asynchronous Games 3 An Innocent Model of Linear Logic , 2004, CTCS.

[19]  Pierre-Louis Curien,et al.  Sequential Algorithms on Concrete Data Structures , 1982, Theor. Comput. Sci..

[20]  R. A. G. Seely,et al.  Linear Logic, -Autonomous Categories and Cofree Coalgebras , 1989 .

[21]  Bart Jacobs,et al.  Semantics of Weakening and Contraction , 1994, Ann. Pure Appl. Log..

[22]  Samson Abramsky.  Linearity‚ Sharing and State: a fully abstract game semantics for Idealized Algol , 1997 .

[23]  Radha Jagadeesan,et al.  Games and full completeness for multiplicative linear logic , 1992, Journal of Symbolic Logic.

[24]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[25]  Samson Abramsky,et al.  Concurrent games and full completeness , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[26]  Guy McCusker.  Games and Full Abstraction for a Functional Metalanguage with Recursive Types , 1998, Distinguished Dissertations.

[27]  Samson Abramsky.  Axioms for definability and full completeness , 2000, Proof, Language, and Interaction.

[28]  Prakash Panangaden,et al.  Stability and Sequentiality in Dataflow Networks , 1990, ICALP.

[29]  Andreas Blass,et al.  A Game Semantics for Linear Logic , 1992, Ann. Pure Appl. Log..

[30]  Glynn Winskel,et al.  Categories of Models for Concurrency , 1984, Seminar on Concurrency.

[31]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[32]  C.-H. Luke Ong,et al.  On Full Abstraction for PCF: I, II, and III , 2000, Inf. Comput..

[33]  Jean-Yves Girard,et al.  Geometry of Interaction 1: Interpretation of System F , 1989 .

[34]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.