The Rényi-Ulam games and many-valued logics

In this paper we introduce complete game semantics for Product, Gödel, BL and SBL logics (game semantics for Łukasiewicz logic are well-known). For each of these logics we introduce a variant of the Rényi-Ulam game whose states are equipped in a natural way with an algebraic structure. Moreover we prove that each logic is complete with respect to the algebras of the states for the corresponding game.