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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 138–155 (Mi smj12)  

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

On extensions of Nelson's logic satisfying Dummett's axiom

S. P. Odintsov

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

Abstract: The class of extensions is completely described of the logic obtained by adding Dummett's axiom to the paraconsistent Nelson logic. Moreover, we prove that every extension of this logic is finitely axiomatizable and decidable and, given a formula, it is possible to determine which extension is axiomatized by this formula.

Keywords: Nelson's logic, Dummett's axiom, paraconsistency, constructive negation.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 112–125

Bibliographic databases:

UDC: 510.64
Received: 30.11.2005
Revised: 12.05.2006

Citation: S. P. Odintsov, “On extensions of Nelson's logic satisfying Dummett's axiom”, Sibirsk. Mat. Zh., 48:1 (2007), 138–155; Siberian Math. J., 48:1 (2007), 112–125

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Odintsov S., “on the Equivalence of Paraconsistent and Explosive Versions of Nelson Logic”, Logic, Computation, Hierarchies, Ontos Mathematical Logic, 4, eds. Brattka V., Diener H., Spreen D., Walter de Gruyter Gmbh, 2014, 259–272  mathscinet  isi
    2. Czelakowski J., “Paraconsistent Constructive Logic With Strong Negation as a Contraction-Free Relevant Logic”, Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science, Outstanding Contributions to Logic, 16, ed. Czelakowski J., Springer, 2018, 323–379  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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