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From Games to Dialogues and Back: Towards a General Frame for Validity

In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical propositional logic and for classical first-order logic, an exact connection between ‘intuitionistic dialogues with hypotheses’ and semantic games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretic and proof-theoretic approaches to the philosophy of logic and mathematics.