Boolean games

In this paper Boolean games are introduced as a class of two-player zero-sum games along with a number of operations on them. We argue that Boolean games can be interpreted as modelling the information structures of two-person zero-sum games. As such they comprise games of imperfect information. The algebra of Boolean games modulo strategic equivalence is then proven to be isomorphic to the Lindenbaum algebra of Classical Propositional Logic. A neat match between the game-theoretical notion of a winning strategy and a logical counterpart, however, calls for a refinement of the notion of validity. Pursuing this issue we finally obtain a logical characterization of determinacy for Boolean games.