On Semantic Games for Łukasiewicz Logic

Authors: C. Fermüller, Ondrej Majer
Publication year: 2018
Publication type: Kapitola v monografii
Periodical: Jaakko Hintikka on Knowledge and Game-Theoretical Semantics
Projects: A Multivalued Approach to Optima and Equilibria in Economics
Bibliographic citation: FERMÜLLER, C., MAJER, Ondrej. On Semantic Games for Łukasiewicz Logic. In: VAN DITMARSCH, H., SANDU, G., eds. Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Cham: Springer, 2018, S. 263-278. Outstanding Contributions to Logic, 12. ISBN 978-3-319-62863-9
Dostupné z: doi:10.1007/978-3-319-62864-6_10.
DOI: 10.1007/978-3-319-62864-6_10
ID: 495556
Online record: View online record

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.