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Many-valued logic and mixed integer programming

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Abstract

We generalize prepositional semantic tableaux for classical and many-valued logics toconstraint tableaux. We show that this technique is a generalization of the standard translation from CNF formulas into integer programming. The main advantages are (i) a relatively efficient satisfiability checking procedure for classical, finitely-valued and, for the first time, for a wide range of infinitely-valued propositional logics; (ii) easy NP-containment proofs for many-valued logics. The standard translation of two-valued CNF formulas into integer programs and Tseitin's structure preserving clause form translation are obtained as a special case of our approach.

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Authors and Affiliations

  1. Institut für Logik, Komplexität und Deduktionssysteme, Fakultät für Informatik, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Reiner Hähnle

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Additional information

Part of the research reported here was carried out while the author was supported by a grant within the DFG Schwerpunktprogramm Deduktion. Preliminary and partial versions of this paper were published as [15, 16].

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Hähnle, R. Many-valued logic and mixed integer programming. Ann Math Artif Intell 12, 231–263 (1994). https://doi.org/10.1007/BF01530787

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