Logic and Logical Philosophy
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The lattice of Belnapian modal logics: Special extensions and counterparts
DOI: http://dx.doi.org/10.12775/LLP.2016.002
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.Keywords
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