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Algebra Logika, 2015, Volume 54, Number 2, Pages 252–274 (Mi al691)  

This article is cited in 15 scientific papers (total in 15 papers)

Recognizable logics

L. L. Maksimovaab, V. F. Yunba

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We look into the recognition problem for extensions of Johansson's minimal logic J. It is proved that certain of the known logics are recognizable over J. Namely, recognizability over J is revealed for all well-composed logics possessing Craig's interpolation property (CIP), the restricted interpolation property (IPR), or the projective Beth property (PBP). It is proved that the logic JF is not reliably recognizable over J. Furthermore, we establish a link between the algebraic and the modified Kripke semantics, and give a criterion for being reliably recognizable in terms of characteristic formulas.

Keywords: Johanssons minimal logic, recognizability, reliable recognizability, interpolation property, characteristic formula.

DOI: https://doi.org/10.17377/alglog.2015.54.208

Full text: PDF file (197 kB)
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English version:
Algebra and Logic, 2015, 54:2, 167–182

Bibliographic databases:

UDC: 510.64
Received: 27.06.2014

Citation: L. L. Maksimova, V. F. Yun, “Recognizable logics”, Algebra Logika, 54:2 (2015), 252–274; Algebra and Logic, 54:2 (2015), 167–182

Citation in format AMSBIB
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\by L.~L.~Maksimova, V.~F.~Yun
\paper Recognizable logics
\jour Algebra Logika
\yr 2015
\vol 54
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\pages 252--274
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\crossref{https://doi.org/10.17377/alglog.2015.54.208}
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\jour Algebra and Logic
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\pages 167--182
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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. L. L. Maksimova, V. F. Yun, “Ischisleniya nad minimalnoi logikoi i nevlozhimost algebr”, Sib. elektron. matem. izv., 13 (2016), 704–715  mathnet  crossref
    2. L. L. Maksimova, V. F. Yun, “Layers over minimal logic”, Algebra and Logic, 55:4 (2016), 295–305  mathnet  crossref  crossref  isi
    3. L. L. Maksimova, “The structure of slices over minimal logic”, Siberian Math. J., 57:5 (2016), 841–848  mathnet  crossref  crossref  isi  elib  elib
    4. L. L. Maksimova, V. F. Yun, “The tabularity problem over the minimal logic”, Siberian Math. J., 57:6 (2016), 1034–1043  mathnet  crossref  crossref  isi  elib
    5. L. Maksimova, “LC and its pretabular relatives”, J. Michael Dunn on Information Based Logics, Outstanding Contributions to Logic, 8, ed. K. Bimbo, Springer, 2016, 81–91  crossref  mathscinet  isi
    6. L. L. Maksimova, “Recognizable and perceptible logics and varieties”, Algebra and Logic, 56:3 (2017), 245–250  mathnet  crossref  crossref  mathscinet  isi
    7. L. L. Maksimova, V. F. Yun, “Strong decidability and strong recognizability”, Algebra and Logic, 56:5 (2017), 370–385  mathnet  crossref  crossref  isi
    8. L. L. Maksimova, V. F. Yun, “Slices and levels of extensions of the minimal logic”, Siberian Math. J., 58:6 (2017), 1042–1051  mathnet  crossref  crossref  isi  elib
    9. L. L. Maksimova, V. F. Yun, “Silnaya vychislimost sloev nad logikoi $\mathrm{GL}$”, Sib. elektron. matem. izv., 15 (2018), 35–47  mathnet  crossref
    10. V. F. Yun, “Recognizability of all WIP-minimal logics”, Siberian Math. J., 59:1 (2018), 179–188  mathnet  crossref  crossref  isi  elib
    11. L. L. Maksimova, V. F. Yun, “Extensions of the minimal logic and the interpolation problem”, Siberian Math. J., 59:4 (2018), 681–693  mathnet  crossref  crossref  isi  elib
    12. L. L. Maksimova, V. F. Yun, “Uznavaemost v predgeitingovykh i stroinykh logikakh”, Sib. elektron. matem. izv., 16 (2019), 427–434  mathnet  crossref
    13. L. L. Maksimova, V. F. Yun, “The interpolation problem in finite-layered pre-Heyting logics”, Algebra and Logic, 58:2 (2019), 144–157  mathnet  crossref  crossref  isi
    14. L. L. Maksimova, “Constructive classifications of modal logics and extensions of minimal logic”, Algebra and Logic, 58:6 (2020), 540–545  mathnet  crossref  crossref  isi
    15. L. L. Maksimova, V. F. Yun, “Perceptibility in pre-Heyting logics”, Sib. elektron. matem. izv., 17 (2020), 1064–1072  mathnet  crossref
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