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Sibirsk. Mat. Zh., 2018, Volume 59, Number 2, Pages 468–476 (Mi smj2987)  

Irreflexive modality, the Dummett logic, and continual chains

A. D. Yashin, A. G. Makarov

Moscow State University of Psychology and Education, Moscow, Russia

Abstract: We construct a countable family of extensions of the logic of finite chains (the Dummett logic) in the language containing the standard logical connectives and a new connective (irreflexive modality), each of which determines in the Dummett logic a new logical connective in the sense of Novikov. Two arbitrary logics on this list are incompatible over the Dummett logic; i.e., their union contains a formula absent from the Dummett logic.

Keywords: new logical connective, Novikov's approach, Dummett logic, irreflexive modality.

DOI: https://doi.org/10.17377/smzh.2018.59.220

Full text: PDF file (302 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2018, 59:2, 368–374

Bibliographic databases:

UDC: 517.11
MSC: 35R30
Received: 20.01.2017

Citation: A. D. Yashin, A. G. Makarov, “Irreflexive modality, the Dummett logic, and continual chains”, Sibirsk. Mat. Zh., 59:2 (2018), 468–476; Siberian Math. J., 59:2 (2018), 368–374

Citation in format AMSBIB
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\paper Irreflexive modality, the Dummett logic, and continual chains
\jour Sibirsk. Mat. Zh.
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\issue 2
\pages 468--476
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\crossref{https://doi.org/10.17377/smzh.2018.59.220}
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\jour Siberian Math. J.
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\vol 59
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\pages 368--374
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