The lattice of Belnapian modal logics: Special extensions and counterparts

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

Сперанский С. О.

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.

Ключевые слова: strong negation, paraconsistent logic, algebraic logic, many-valued modal logic