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The lattice of Belnapian modal logics: Special extensions and counterparts

Logic and Logical Philosophy. 2016. Vol. 25. No. 1. P. 3–33.
Speranski S. O.

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.

Language: English
DOI
Keywords: strong negationparaconsistent logicalgebraic logic many-valued modal logic
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