Logic and Logical Philosophy 25 (1):3-33 (2016)

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 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 algebraic logic   paraconsistent logic   many-valued modal logic   strong negation
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DOI 10.12775/LLP.2016.002
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References found in this work BETA

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.

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Citations of this work BETA

Propositional Dynamic Logic with Belnapian Truth Values.Igor Sedlár - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 503-519.

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