Equilibrium Semantics for IF Logic and Many-Valued Connectives

Authors: C. Fermüller, Ondrej Majer
Publication year: 2017
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Logic, Language, and Computation
Projects: Modeling vague quantifiers in mathematical fuzzy logic
Bibliographic citation: FERMÜLLER, C., MAJER, Ondrej. Equilibrium Semantics for IF Logic and Many-Valued Connectives. In: HANSEN, H.H., MURRAY, S.E., SADRZADEH, M., ZEEVAT, H., eds. Logic, Language, and Computation. Berlin: Springer, 2017, S. 290-312. Lecture Notes in Computer Science, 10148. ISBN 978-3-662-54331-3. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-662-54332-0_16
DOI: 10.1007/978-3-662-54332-0_16
ID: 472097

Abstract

We connect two different forms of game based semantics: Hintikka’s game for Independence Friendly logic (IF logic) and Giles’s game for Lukasiewicz logic. An interpretation of truth values in [0, 1] as equilibrium values in semantic games of imperfect information emerges for a logic that extends both, Lukasiewicz logic and IF logic. We prove that already on the propositional level all rational truth values can be obtained as equilibrium values.