The lattice of Belnapian modal logics: Special extensions and counterparts
Journal Title: Logic and Logical Philosophy - Year 2016, Vol 25, Issue 1
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.
Authors and Affiliations
Sergei P. Odintsov, Stanislav O. Speranski
Keywords
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- EP ID EP201102
- DOI 10.12775/LLP.2016.002
- Views 68
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The lattice of Belnapian modal logics: Special extensions and counterparts
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...