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Mat. Tr., 2017, Volume 20, Number 2, Pages 3–34 (Mi mt321)  

This article is cited in 1 scientific paper (total in 1 paper)

Infinite-valued first-order Łukasiewicz logic: hypersequent calculi without structural rules and proof search for sentences in the prenex form

A. S. Gerasimov


Abstract: The rational first-order Pavelka logic is an expansion of the infinite-valued first-order Łukasiewicz logic Ł$\forall$ by truth constants. For this logic, we introduce a cumulative hypersequent calculus G$^1$Ł$\forall$ and a noncumulative hypersequent calculus G$^2$Ł$\forall$ without structural inference rules. We compare these calculi with the Baaz–Metcalfe hypersequent calculus GŁ$\forall$ with structural rules. In particular, we show that every GŁ$\forall$-provable sentence is G$^1$Ł$\forall$-provable and a Ł$\forall$-sentence in the prenex form is GŁ$\forall$-provable if and only if it is G$^2$Ł$\forall$-provable. For a tableau version of the calculus G$^2$Ł$\forall$, we describe a family of proof search algorithms that allow us to construct a proof of each G$^2$Ł$\forall$-provable sentence in the prenex form.

Key words: fuzzy logic, infinite-valued first-order Łukasiewicz logic, rational first-order Pavelka logic, hypersequent calculus, proof search algorithm.

DOI: https://doi.org/10.17377/mattrudy.2017.20.201

Full text: PDF file (376 kB)
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English version:
Siberian Advances in Mathematics, 2018, 28:2, 79–100

UDC: 510.644+510.662
Received: 21.03.2016

Citation: A. S. Gerasimov, “Infinite-valued first-order Łukasiewicz logic: hypersequent calculi without structural rules and proof search for sentences in the prenex form”, Mat. Tr., 20:2 (2017), 3–34; Siberian Adv. Math., 28:2 (2018), 79–100

Citation in format AMSBIB
\Bibitem{Ger17}
\by A.~S.~Gerasimov
\paper Infinite-valued first-order {\L}ukasiewicz logic: hypersequent calculi without structural rules and proof search for sentences in the prenex form
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 2
\pages 3--34
\mathnet{http://mi.mathnet.ru/mt321}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.201}
\elib{https://elibrary.ru/item.asp?id=29145398}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 2
\pages 79--100
\crossref{https://doi.org/10.3103/S1055134418020013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048020013}


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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, “Repetition-free and infinitary analytic calculi for first-order rational Pavelka logic”, Sib. elektron. matem. izv., 17 (2020), 1869–1899  mathnet  crossref
  • Математические труды Siberian Advances in Mathematics
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