Semantic Games with Backtracking for T-norm Based Fuzzy Logics
Christian G. Fermüller
Hintikka’s game theoretic semantics for classical connectives and quantifiers has been generalized to many-valued logics in various ways. We introduce a new type of semantic games, so-called backtracking games, where a stack of formulas is used to store information on how to continue the game after reaching an atomic formula. This mechanism allows one to avoid the explicit reference to truth values, that is characteristic for some evaluation games. Moreover, the indeterminism due to the multiplicity of still to be analyzed formulas that can be observed in Giles’s game for Łukasiewicz logic is dissolved. We present backtracking games for the three fundamental t-norm based logics: Łukasiewicz, Gödel, and Product logic and provide corresponding adequateness theorems.
Keywords: Fuzzy logics, game semantics, evaluation games, t-norm based logic, Łukasiewicz logic, Gödel logic, product logic