The lattice of Belnapian modal logics: Special extensions and counterparts

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



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Stanislav Speranski
St. Petersburg State University

References found in this work

An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - New York: Cambridge University Press.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.

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