In logic, game semantics is used to provide a semantic interpretation of logical constructions in terms of strategies for opposing players (a prover and an opponent) to win a game which corresponds to some proposition.
For a brief history, see this comment by Samson Abramsky.
A game theoretic account (explained in terms of ‘dialogues’) of provability was developed by Paul Lorenzen, see
For a survey of this approach see
Walter Felscher, 2002, Dialogues as a foundation for intuitionistic logic, (pdf)
Martin Hyland, Game semantics, in A. Pitts and P. Dybjer, editors, Semantics and Logics of Computation, pages 131–182. Cambridge University Press, 1997. (scanned pdf)
André Joyal, 1977, Remarques sur la théorie des jeux à deux personnes, Gazette des Sciences Mathématiques du Québec 4, 46–52, translated as Remarks on the Theory of Two-Player Games by Robin Houston.
Andreas Blass, Game semantics and linear logic, Annals of Pure and Applied Logic 56 (1992), 183-220.
Samson Abramsky, Radha Jagadeesan, Games and full completeness for multiplicative linear logic, Journal of Symbolic Logic, 59 (1994), 543 - 574
Martin Hyland and Luke Ong?, On full abstraction for PCF, Information and Computation, 163 (2000), 285-408.
Paul-André Melliès, Asynchronous games 3: An innocent model of linear logic, Proceedings of the 10th Conference on Category Theory and Computer Science, Copenhagen, 2004. (pdf)
Robin Cockett, Geoff Cruttwell and K. Saff, Combinatorial Game Categories, (pdf)
For attempts to formulate a game semantics for dependent type theory, see
Matthijs Vákár, Radha Jagadeesan, Samson Abramsky, Game Semantics for Dependent Types, (pdf)
Norihiro Yamada, Game Semantics for Martin-Löf Type Theory, (arXiv:1610.01669)
Last revised on July 18, 2024 at 16:12:55. See the history of this page for a list of all contributions to it.