Abstract
Connections between games and logic are quite common in the literature: for example, to every analytic proof system with the subformula property (hence admitting cut-elimination) one can associate a game in which a player tries to find a cut-free proof and his opponent can attack parts of the proof constructed since then. Along these lines, formulas correspond to games and proofs correspond to winning strategies. A first connection between many-valued logic and games was discovered by Giles in [9]. A variant of such semantics was used in [4] in order to obtain a uniform proof system with a game-theoretical interpretation for Łukasiewicz, product and Gödel logics. The above mentioned papers are extremely interesting, but we would say that the interest of this game semantics is more proof-theoretical than game-theoretical.
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Jenei, S., Montagna, F. (2007). Rényi-Ulam Game Semantics for Product Logic and for the Logic of Cancellative Hoops. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_14
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