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Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency

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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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Authors and Affiliations

  1. Dpto. de Historia y Filosofía de la CC, la Ed. y el Leng., Universidad de La Laguna, Facultad de Filosofía, Campus de Guajara, 38071, La Laguna, Tenerife, Spain

    Gemma Robles

  2. Universidad de Salamanca, Campus Unamuno, Edificio FES, 37007, Salamanca, Spain

    José M. Méndez

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  1. Gemma Robles
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  2. José M. Méndez
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Correspondence to Gemma Robles.

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Robles, G., Méndez, J.M. Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency. J of Log Lang and Inf 18, 357–402 (2009). https://doi.org/10.1007/s10849-009-9085-x

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  • DOI: https://doi.org/10.1007/s10849-009-9085-x

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