Game semantics

Game semantics is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. In this framework, logical formulas are interpreted as defining games between two players. The term encompasses several related but distinct traditions, including dialogical logic (developed by Paul Lorenzen and Kuno Lorenz in Germany starting in the 1950s) and game-theoretical semantics (developed by Jaakko Hintikka in Finland).

Game semantics represents a significant departure from traditional model-theoretic approaches by emphasizing the dynamic, interactive nature of logical reasoning rather than static truth assignments. It provides intuitive interpretations for various logical systems, including classical logic, intuitionistic logic, linear logic, and modal logic. The approach bears conceptual resemblances to ancient Socratic dialogues, medieval theory of Obligationes, and constructive mathematics. Since the 1990s, game semantics has found important applications in theoretical computer science, particularly in the semantics of programming languages, concurrency theory, and the study of computational complexity.