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Algebra Logika, 2016, Volume 55, Number 2, Pages 156–191 (Mi al736)  

This article is cited in 2 scientific papers (total in 2 papers)

Free-variable semantic tableaux for the logic of fuzzy inequalities

A. S. Gerasimov

St. Petersburg State University, Universitetskii pr. 28, St. Petersburg, 198504 Russia

Abstract: We present a free-variable tableau calculus for the logic of fuzzy inequalities F$\forall$, which is an extension of infinite-valued first-order Lukasiewicz logic Ł$\forall$. The set of all Ł$\forall$-sentences provable in the hypersequent calculus of Baaz and Metcalfe for Ł$\forall$ is embedded into the set of all F$\forall$-sentences provable in the given tableau calculus. We prove NP-completeness of the problem of checking tableau closability and propose an algorithm, which is based on unification, for solving the problem.

Keywords: fuzzy logic, infinite-valued first-order Lukasiewicz logic, automatic proof search, hypersequent calculus, tableau calculus, tableau closability, NP-complete problem.

DOI: https://doi.org/10.17377/alglog.2016.55.202

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English version:
Algebra and Logic, 2016, 55:2, 103–127

Bibliographic databases:

UDC: 510.644
Received: 26.06.2014
Revised: 21.10.2015

Citation: A. S. Gerasimov, “Free-variable semantic tableaux for the logic of fuzzy inequalities”, Algebra Logika, 55:2 (2016), 156–191; Algebra and Logic, 55:2 (2016), 103–127

Citation in format AMSBIB
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\by A.~S.~Gerasimov
\paper Free-variable semantic tableaux for the logic of fuzzy inequalities
\jour Algebra Logika
\yr 2016
\vol 55
\issue 2
\pages 156--191
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\crossref{https://doi.org/10.17377/alglog.2016.55.202}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 2
\pages 103--127
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Gerasimov, “Infinite-valued first-order Łukasiewicz logic: hypersequent calculi without structural rules and proof search for sentences in the prenex form”, Siberian Adv. Math., 28:2 (2018), 79–100  mathnet  crossref  crossref  elib
    2. A. S. Gerasimov, “Repetition-free and infinitary analytic calculi for first-order rational Pavelka logic”, Sib. elektron. matem. izv., 17 (2020), 1869–1899  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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