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Commodious Axiomatization of Quantifiers in Multiple-Valued Logic

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Abstract

We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers.

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  1. Institute for Logic, Complexity and Deduction Systems Dept. of Computer Science, University of Karlsruhe, 76128, Karlsruhe, Germany

    Reiner Hähnle

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  1. Reiner Hähnle
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Hähnle, R. Commodious Axiomatization of Quantifiers in Multiple-Valued Logic. Studia Logica 61, 101–121 (1998). https://doi.org/10.1023/A:1005086415447

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