From Semantic Games to Provability: The Case of Gödel Logic

Abstract We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about relative order of truth degrees complex formulas to atomic ones. The paper builds on previously developed with projection operator in Fermüller et al . (in: M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, A. Wilbik, B. Bouchon-Meunier, R.R. Yager, (eds.), Information processing management uncertainty knowledge-based systems , Springer, Cham, 2020, pp. 257–270). This is extended cover involutive negations constants, then lifted provability using concept disjunctive strategies. Winning strategies game, without constants negations, turn out correspond analytic proofs version $$\text{ SeqGZL } $$ SeqGZL (A. Ciabattoni, T. Vetterlein, Fuzzy Sets Systems 161(14):1941–1958, 2010) sequent-of-relations calculus (M. Baaz, Ch.G. Fermüller, in: N.V. Murray, (ed.), Automated reasoning tableaux related methods Berlin, 1999, 36–51) respectively.