From truth degree comparison games to sequents-of-relations calculi for Gödel logic (Q2169133)

Gödel logic is studied from a game semantic point of view. Among the infinite many fuzzy logics, i.e., logics where logical connectives are interpreted in the unit real interval, Gödel logic is the only one in which the comparison of the truth values of two propositions returns ultimately to the order of these values. A truth degree comparison game is introduced. The first player is looking for support for claim that the truth value of proposition \(F\) is smaller or equal to that of proposition \(G\), and the second player attempts to disprove this claim. This game is lifted from individual truth values to a more general level of validity; to comparison claims that hold under every interpretation. The most important new concept is that of disjunctive state, exploiting it leads to a disjunctive winning strategy. Disjunctive winning strategies, in turn are shown to correspond proofs in an analytic proof system called sequents-of-relations calculus introduced by \textit{M. Baaz} and \textit{C. G. Fermüller} [Lect. Notes Comput. Sci. 1617, 36--50 (1999; Zbl 0931.03066)].