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Algebra Logika, 2004, Volume 43, Number 2, Pages 235–252 (Mi al68)  

This article is cited in 10 scientific papers (total in 10 papers)

The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic

M. V. Stukacheva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider the disjunction property, $\mathbf{DP}$, in the class of extensions of minimal logic $\mathbf{L}_{j}$. Conditions are described under which $\mathbf{DP}$ is translated from the class $\mathbf{PAR}$ of properly paraconsistent extensions of the logics of class $\mathbf{L}_{j}$ into the class $\mathbf{INT}$ of intermediate extensions and the class $\mathbf{NEG}$ of negative extensions, and conditions for its being translated back into $\mathbf{PAR}$. The logic $\mathbf{L}_{F}$ in $\mathbf{PAR}$, which specifies conditions for $\mathbf{DP}$ to be translated from $\mathbf{PAR}$ into $\mathbf{NEG}$, is defined and is characterized in terms of $j$-algebras and Kripke frames. Moreover, we show that ${\mathbf L}_F$ is decidable and possesses the disjunction property.

Keywords: paraconsistent extension of minimal logic, $j$-algebra - Kripke frame, disjunction property

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English version:
Algebra and Logic, 2004, 43:2, 132–141

Bibliographic databases:

UDC: 510.64
Received: 09.10.2002
Revised: 16.04.2003

Citation: M. V. Stukacheva, “The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic”, Algebra Logika, 43:2 (2004), 235–252; Algebra and Logic, 43:2 (2004), 132–141

Citation in format AMSBIB
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\by M.~V.~Stukacheva
\paper The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic
\jour Algebra Logika
\yr 2004
\vol 43
\issue 2
\pages 235--252
\mathnet{http://mi.mathnet.ru/al68}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2072574}
\zmath{https://zbmath.org/?q=an:1061.03032}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 2
\pages 132--141
\crossref{https://doi.org/10.1023/B:ALLO.0000020851.15017.5e}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42349101471}


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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. M. V. Stukacheva, “Nekotorye zamechaniya o konstruktivnykh rasshireniyakh minimalnoi logiki”, Vestn. NGU. Ser. matem., mekh., inform., 5:3 (2005), 75–88  mathnet
    2. L. L. Maksimova, “A method of proving interpolation in paraconsistent extensions of the minimal logic”, Algebra and Logic, 46:5 (2007), 341–353  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Stukacheva, “O modelyakh paraneprotivorechivoi logiki s aksiomami Kraizelya–Patnema i Skotta”, Sib. elektron. matem. izv., 5 (2008), 407–416  mathnet  mathscinet
    4. L. L. Maksimova, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132  mathnet  crossref  mathscinet  zmath  isi
    5. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267  crossref  mathscinet  zmath  isi  elib  scopus
    6. L. L. Maksimova, “The decidability of craig's interpolation property in well-composed $\mathrm J$-logics”, Siberian Math. J., 53:5 (2012), 839–852  mathnet  crossref  mathscinet  isi
    7. L. L. Maksimova, V. F. Yun, “Recognizable logics”, Algebra and Logic, 54:2 (2015), 167–182  mathnet  crossref  crossref  mathscinet  isi
    8. V. F. Yun, “Recognizability of all WIP-minimal logics”, Siberian Math. J., 59:1 (2018), 179–188  mathnet  crossref  crossref  isi  elib
    9. L. L. Maksimova, V. F. Yun, “Uznavaemost v predgeitingovykh i stroinykh logikakh”, Sib. elektron. matem. izv., 16 (2019), 427–434  mathnet  crossref
    10. L. L. Maksimova, V. F. Yun, “Perceptibility in pre-Heyting logics”, Sib. elektron. matem. izv., 17 (2020), 1064–1072  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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