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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Keywords | Consistency Paraconsistent logics Constructive negation Substructural logics Ternary relational semantics |
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DOI | 10.1007/s10849-009-9085-x |
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References found in this work BETA
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
A Propositional Calculus with Denumerable Matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star).Greg Restall - 1999 - In Dov M. Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers. pp. 53-76.
On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic. [REVIEW]B. J. Copeland - 1979 - Journal of Philosophical Logic 8 (1):399-413.
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Citations of this work BETA
Paraconsistent Logics Included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):442-466.
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