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The lattice of Belnapian modal logics: Special extensions and counterparts

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Odintsov S. P., Speranski S. O.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 1
3-33
EN
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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