Abstract
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.
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