Concurrent games and full completeness

A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for Multiplicative-Additive Linear Logic is proved for this semantics.

[1]  Ralph Loader.  Linear logic, totality and full completeness , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[2]  Vincent Danos,et al.  A new deconstructive logic: linear logic , 1997, Journal of Symbolic Logic.

[3]  Samson Abramsky,et al.  Domain Theory in Logical Form , 1991, LICS.

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

[5]  Radha Jagadeesan,et al.  New Foundations for the Geometry of Interaction , 1994, Inf. Comput..

[6]  J. Girard.  PROOF-NETS : THE PARALLEL SYNTAX FOR PROOF-THEORY , 1996 .

[7]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains , 1979, Semantics of Concurrent Computation.

[8]  Radha Jagadeesan,et al.  New foundations for the geometry of interaction , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[9]  Andre Scedrov,et al.  Functorial Polymorphism , 1990, Theor. Comput. Sci..

[10]  Ralph Loader.  Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisati , 1994 .

[11]  Samson Abramsky,et al.  Domain theory , 1995, LICS 1995.

[12]  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.

[13]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

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

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

[16]  Philip J. Scott,et al.  Linear Läuchli Semantics , 1996, Ann. Pure Appl. Log..

[17]  J.-L. Borges.  On the meaning of logical rules II : multiplicatives and additives , 1998 .

[18]  James L. Peterson,et al.  Petri Nets , 1977, CSUR.

[19]  Roberto M. Amadio,et al.  Domains and lambda-calculi , 1998, Cambridge tracts in theoretical computer science.

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

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

[22]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains, Part I , 1981, Theor. Comput. Sci..