Journal of Logic, Language and Information

, Volume 17, Issue 1, pp 89–107 | Cite as

The basic constructive logic for a weak sense of consistency

  • Gemma RoblesEmail author
  • José M. Méndez
Original Article


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.


Constructive negation Substructural logics Ternary relational semantics Paraconsistent Logic 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.c Los OsoriosLeónSpain
  2. 2.Universidad de SalamancaSalamancaSpain

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