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Logic and Logical Philosophy

The lattice of Belnapian modal logics: Special extensions and counterparts
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The lattice of Belnapian modal logics: Special extensions and counterparts

Authors

  • Sergei P. Odintsov Sobolev Institute of Mathematics, Novosibirsk
  • Stanislav O. Speranski Sobolev Institute of Mathematics, Novosibirsk

DOI:

https://doi.org/10.12775/LLP.2016.002

Keywords

algebraic logic, paraconsistent logic, many-valued modal logic, strong negation

Abstract

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on:

• introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics;

• assigning to every normal modal logic three special conservative extensions in these classes;

• associating with every Belnapian modal logic its explosive, complete and classical counterparts.

We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.

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Logic and Logical Philosophy

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Published

2016-02-25

How to Cite

1.
ODINTSOV, Sergei P. and SPERANSKI, Stanislav O. The lattice of Belnapian modal logics: Special extensions and counterparts. Logic and Logical Philosophy. Online. 25 February 2016. Vol. 25, no. 1, pp. 3-33. [Accessed 1 July 2025]. DOI 10.12775/LLP.2016.002.
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