Matematicheskie Trudy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskie Trudy, 2017, Volume 20, Number 2, Pages 3–34
DOI: https://doi.org/10.17377/mattrudy.2017.20.201
(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
Full-text PDF (376 kB) Citations (1)
References:
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.
Received: 21.03.2016
English version:
Siberian Advances in Mathematics, 2018, Volume 28, Issue 2, Pages 79–100
DOI: https://doi.org/10.3103/S1055134418020013
Bibliographic databases:
Document Type: Article
UDC: 510.644+510.662
Language: Russian
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}
Linking options:
  • https://www.mathnet.ru/eng/mt321
  • https://www.mathnet.ru/eng/mt/v20/i2/p3
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
    Statistics & downloads:
    Abstract page:279
    Full-text PDF :110
    References:41
    First page:7
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024