Interpreting Propositional Fuzzy Logics via Imperfect Information Games

Equilibrium semantics interprets expected payoffs resulting from Nash equilibria of semantics games with imperfect information (Hintikka-Sandu or HS-games) as truth values. In [1] we showed that all rational truth values in the unit interval can be obtained in this manner from games with just 0 and 1 as possible payoffs in any run of the game. Here, we investigate whether the propositional connectives of various fuzzy logics, in particular of Łukasiewicz, Godel, and Product logic, can be interpreted as operators that combine parallel HS-games into single games. It turns out that the interpretation of different connectives calls for definitions of overall payoffs for combined games that operate at different levels of abstraction.