Abstract
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.
Research supported by C. Bühler-Habilitations-Stipendium H191-N04, FWF Project Nr. P16539-N04, and Marie Curie Fellowship 501043.
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Ciabattoni, A., Fermüller, C.G., Metcalfe, G. (2005). Uniform Rules and Dialogue Games for Fuzzy Logics. In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_33
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DOI: https://doi.org/10.1007/978-3-540-32275-7_33
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