Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency

Journal of Logic, Language and Information 18 (3):357-402 (2009)
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Abstract

In a standard sense, consistency and paraconsistency are understood as the absence of any contradiction and as the absence of the ECQ (‘E contradictione quodlibet’) rule, respectively. The concepts of weak consistency (in two different senses) as well as that of F -consistency have been defined by the authors. The aim of this paper is (a) to define alternative (to the standard one) concepts of paraconsistency in respect of the aforementioned notions of weak consistency and F -consistency; (b) to define the concept of strong paraconsistency; (c) to build up a series of strongly paraconsistent logics; (d) to define the basic constructive logic adequate to a rather weak sense of consistency. All logics treated in this paper are strongly paraconsistent. All of them are sound and complete in respect a modification of Routley and Meyer’s ternary relational semantics for relevant logics (no logic in this paper is relevant).

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Author Profiles

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

Citations of this work

Paraconsistent logics included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):442-466.

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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.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.

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