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A paraconsistent extension of Sylvan’s logic

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Abstract

We deal with Sylvan’s logic CCω. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension of Sylvan’s logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.

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Authors and Affiliations

  1. Pirogov st., 16-321, Novosibirsk, 630090, Russia

    A. B. Gordienko

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  1. A. B. Gordienko
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Correspondence to A. B. Gordienko.

Additional information

Supported by RFBR grant No. 06-01-00358 and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.

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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 533–547, September–October, 2007.

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Gordienko, A.B. A paraconsistent extension of Sylvan’s logic. Algebra Logic 46, 289–296 (2007). https://doi.org/10.1007/s10469-007-0029-8

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  • DOI: https://doi.org/10.1007/s10469-007-0029-8

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