We provide uniform and invertible logical rules in a framework of relational hypersequents for the three fundamental t-norm based fuzzy logics i.e., LŁukasiewicz logic, Gödel logic, and Product logic. Relational hypersequents generalize both hypersequents and sequents-of-relations. Such a framework can be interpreted via a particular class of dialogue games combined with bets, where the rules reflect possible moves in the game. The problem of determining the validity of atomic relational hypersequents is shown to be polynomial for each logic, allowing us to develop Co-NP calculi. We also present calculi with very simple initial relational hypersequents that vary only in the structural rules for the logics. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Ciabattoni, A., Fermüller, C. G., & Metcalfe, G. (2005). Uniform rules and dialogue games for fuzzy logics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3452 LNAI, pp. 496–510). Springer Verlag. https://doi.org/10.1007/978-3-540-32275-7_33
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