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Double Negation Operator in Logic N ∗

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We obtain an axiomatization of the double Routley negation operator as a necessity operator in the logic N ∗. We introduce the logic N # describing the behavior of the double Routley negation operator, define the Kripke semantics of N #, prove the completeness, and the establish the finite approximation property and decidability. We also compare constructive properties of the logics N ∗ and N #.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, pr. Akad. Koptyuga, Novosibirsk, 630090, Russia

    S. A. Drobyshevich

  2. Novosibirsk State University, 2, ul. Pirogova, Novosibirsk, 630090, Russia

    S. A. Drobyshevich

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  1. S. A. Drobyshevich
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Correspondence to S. A. Drobyshevich.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13, No. 4, 2013, pp. 68–83.

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Drobyshevich, S.A. Double Negation Operator in Logic N ∗ . J Math Sci 205, 389–402 (2015). https://doi.org/10.1007/s10958-015-2254-3

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  • DOI: https://doi.org/10.1007/s10958-015-2254-3

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