Game Semantics

Game semantics (German: dialogische Logik, translated as dialogical logic) 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, somewhat resembling Socratic dialogues or medieval theory of Obligationes. In the late 1950s Paul Lorenzen was the first to introduce a game semantics for logic, and it was further developed by Kuno Lorenz. At almost the same time as Lorenzen, Jaakko Hintikka developed a model-theoretical approach known in the literature as GTS. Since then, a number of different game semantics have been studied in logic. Shahid Rahman (Lille) and collaborators developed dialogic into a general framework for the study of logical and philosophical issues related to logical pluralism. At around 1995 this triggered a kind of Renaissance with lasting consequences. Actually this new philosophical impulse experienced a parallel renewal in the fields of theoretical computer science, computational linguistics, artificial intelligence and the formal semantics of programming languages triggered by the work of Johan van Benthem and collaborators in Amsterdam who looked thoroughly at the interface between logic and games. New results in linear logic by J-Y. Girard in the interfaces between mathematical game theory and logic on one hand and argumentation theory and logic on the other hand resulted in the work of many others, including S. Abramsky, J. van Benthem, A. Blass, D. Gabbay, M. Hyland, W. Hodges, R. Jagadeesan, G. Japaridze, E. Krabbe, L. Ong, H. Prakken, G. Sandu D. Walton, and J. Woods who placed game semantics at the center of a new concept in logic in which logic is understood as a dynamic instrument of inference.