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Uniform rules and dialogue games for fuzzy logics. (English) Zbl 1109.03019
Baader, Franz (ed.) et al., Logic for programming, artificial intelligence, and reasoning. 11th international conference, LPAR 2004, Montevideo, Uruguay, March 14–18, 2005. Proceedings. Berlin: Springer (ISBN 3-540-25236-3/pbk). Lecture Notes in Computer Science 3452. Lecture Notes in Artificial Intelligence, 496-510 (2005).
Summary: We provide uniform and invertible logical rules in a framework of relational hypersequents for the three fundamental t-norm based fuzzy logics i.e., Łukasiewicz 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.
For the entire collection see [Zbl 1070.68001].

MSC:
03B52 Fuzzy logic; logic of vagueness
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