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Belnap Constants and Nelson Logic

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The Road to Universal Logic

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

This chapter aims to investigate connections between Belnap’s useful four valued logic and Nelson’s constructive logic with strong negation and the role of adding logical constants to the language. We consider the paraconsistent Nelson’s logic and its expansions obtained by adding to it logical constant’s corresponding to truth values of Belnap’s useful four-valued logic.

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Notes

  1. 1.

    In [4], this logic was denoted as \(\mathbf{eN4}\). We change the denotation to emphasize the connection between the constant b and the truth-value \(\mathit{Both}\).

  2. 2.

    By a dual isomorphism of lattices \({\mathcal{A}}\) and \(\mathcal{B}\) we mean a mapping \(h:{\mathcal{A}}\rightarrow\mathcal{B}\) such that h is an isomorphism of \({\mathcal{A}}\) and \(\mathcal{B}^{op}\), where \(\mathcal{B}^{op}\) is the lattice with the same support as \(\mathcal{B}\), but with the inverse ordering.

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Acknowledgment

This work was supported by Russian Foundation for Basic Research, project No. 12-01-00168-a, and by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-860.2014.1).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russian Federation

    Sergei Odintsov

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  1. Sergei Odintsov
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Correspondence to Sergei Odintsov .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Arnold Koslow

  2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Arthur Buchsbaum

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Odintsov, S. (2015). Belnap Constants and Nelson Logic. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15368-1_22

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