Basic Quasi-Boolean Expansions of Relevance Logics

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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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10.1007/s10992-020-09583-4

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Author Profiles

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

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
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 - 2006 - 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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