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Logic Games Are Complete for Game Logics

Johan van Benthem
Studia Logica: An International Journal for Symbolic Logic
Vol. 75, No. 2, Game Logic and Game Algebra (Nov., 2003), pp. 183-203
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016550
Page Count: 21
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Logic Games Are Complete for Game Logics
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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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