On matrices, Nmatrices and games

Hintikka’s semantic game for classical logic is generalized to the family of all finite valued matrices. This in turn serves as a springboard for developing game semantics for all propositional formulas with respect to arbitrary finite non-deterministic matrices. In this approach a new concept of non-deterministic valuation, called ‘liberal valuation’, emerges that augments the usually employed static and dynamic valuations in a natural manner. Liberal valuation is shown to correspond to unrestricted semantic games, while the characterization of static and dynamic valuations involves certain restrictions of the game that are handled by an interactive pruning procedure.