On semantic games for Łukasiewicz logic

Christian G. Fermüller

Ondrej Majer

pp. 263-278

in: Hans van Ditmarsch, Paul-Gabriel Sandu (eds), Jaakko Hintikka on knowledge and game-theoretical semantics, Berlin, Springer, 2018

Abstract

We explore different ways to generalize Hintikka's classic game theoretic semantics to a many-valued setting, where the unit interval is taken as the set of truth values. In this manner a plethora of characterizations of Łukasiewicz logic arise. Among the described semantic games is Giles's dialogue and betting game, presented in a manner that makes the relation to Hintikka's game more transparent. Moreover, we explain a so-called explicit evaluation game and a "bargaining game" variant of it. We also describe a recently introduced backtracking game as well as a game with random choices for Łukasiewicz logic.

Cited authors

Łukasiewicz Jan