Basic Quasi-Boolean Expansions of Relevance Logics

Journal of Philosophical Logic 50 (4):727-754 (2021)
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Abstract

The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.

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Author Profiles

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca

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Universal Logic.Ross Brady - 2006 - CSLI Publications.
Natural 3-valued logics—characterization and proof theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Universal Logic.Ross Brady - 2007 - Bulletin of Symbolic Logic 13 (4):544-547.
Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.

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