Abstract
Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a representation of arbitrary games as modal or first-order evaluation games. We probe how far our analysis extends to product operations on games. We also discuss some more general consequences of this new perspective for standard logic.
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References
Abramsky, S., 1996, ‘Semantics of Interaction: an Introduction to Game Semantics’, in P. Dybjer and A. Pitts, (eds.), Proceedings 1996 CLiCS Summer School, Isaac Newton Institute, Cambridge University Press, Cambridge, pp. 1-31.
Abramsky, A., 1997, Games in the Semantics of Programming Languages, invited lecture, 11th Amsterdam Colloquium, Amsterdam.
Van Benthem, J., 1996, Exploring Logical Dynamics, CSLI Publications, Stanford.
Van Benthem, J., 1999 onward, Logic in Games, electronic lecture notes, ILLC Amsterdam & CSLI Stanford (printed version 2001).
Van Benthem, J., 2000A, ‘Hintikka Self-Applied’, to appear in L. Hahn, (ed.), Jaakko Hintikka, Library of Living Philosophers, Southern Illinois University.
Van Benthem, J., 2000B, ‘Logical Evaluation Games are Complete for the Game Algebra of Forcing Relations’, ILLC Amsterdam, the original version of this paper.
Van Benthem, J., 2001, ‘Games in Dynamic Epistemic Logic’, Bulletin of Economic Research 53:4, 219-248.
Van Benthem, J., 2002A, ‘Extensive Games as Process Models’, Journal of Logic, Language and Information 11, 289-313.
Van Benthem, J., 2002B, ‘Notes on Product Games’, manuscript, ILLC Amsterdam.
Van Den Berg, M., 1996, The Dynamics of Nominal Anaphora, dissertation DS 1996-03, ILLC Amsterdam.
Berwanger, D., and E. GrÄdel, 2002, ‘The Variable Hierarchy of the μ-Calculus’, Department of Informatics, RWTH Aachen.
Goranko, V., 2000, ‘The Basic Algebra of Game Equivalences’, Preprint 2000-12, ILLC Amsterdam.
Hintikka, J., 1973, Logic, Language Games, and Information, Clarendon Press, Oxford.
Hintikka, J., and G. Sandu, 1997, ‘Game-Theoretical Semantics’, in J. van Benthem and A. ter Meulen, (eds.), Handbook of Logic and Language, Elsevier, Amsterdam, pp. 361-410.
W. Hodges, 1998, An Invitation to Logical Games, lecture notes, department of mathematics, Queen Mary's College, London.
R. Parikh, 1985, ‘The Logic of Games and its Applications’, Annals of Discrete Mathematics 24, 111-140.
M. Pauly, 2001, Logic for Social Software, dissertation DS 2001-10, ILLC Amsterdam.
C. Stirling, 1999, ‘Bisimulation, Modal Logic, and Model Checking Games’, Logic Journal of the IGPL 7, 103-124.
Venema, Y., 2003, ‘Representation of Game Algebras’, Studia Logica 75, 239-256.
Visser, A., 1995, ‘Relational Validity and Dynamic Predicate Logic’, preprint 144, Logic Group, Department of Philosophy, Utrecht University.
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van Benthem, J. Logic Games are Complete for Game Logics. Studia Logica 75, 183–203 (2003). https://doi.org/10.1023/A:1027306910434
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DOI: https://doi.org/10.1023/A:1027306910434