Lorenzen, in the late 1950s, was the first to introduce a game semantics. Since then, numerous sorts of game semantics have been introduced and studied in logic. The primary motivation for Lorenz and his student Lorenzen was to find a game-semantical, or dialogue-semantical (as they preferred to call it) justification for intuitionistic logic. Felscher's work signified a climax of this "game semantics for intuitionistic logic" line. Blass was the first to observe connections between game semantics and linear logic. The "game semantics for linear logic" approach was further developed or modified by Abramsky, Jagadeesan, Hyland, Ong and others. Japaridze started treating games as foundational entities in their own right, elaborating a concept of games meant to formalize the intuitive notion of interactive computational problems, and basing his computability logic on such games.
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