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The basic constructive logic for a weak sense of consistency

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Abstract

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

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References

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Authors and Affiliations

  1. c Los Osorios, n 13, 4 izq., 24007, León, Spain

    Gemma Robles

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

    José M. Méndez

Authors
  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. The basic constructive logic for a weak sense of consistency. J of Log Lang and Inf 17, 89–107 (2008). https://doi.org/10.1007/s10849-007-9042-5

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  • DOI: https://doi.org/10.1007/s10849-007-9042-5

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