Paraconsistent logics?

  title={Paraconsistent logics?},
  author={Barry Hartley Slater},
  journal={Journal of Philosophical Logic},
  • B. Slater
  • Published 1995
  • Philosophy
  • Journal of Philosophical Logic
If we called what is now 'red', 'blue', and vice versa, would that show that pillar boxes are blue, and the sea is red? Surely the facts wouldn't change, only the mode of expression of them. Likewise, if we called 'subcontraries', 'contradictories', would that show that 'it's not red' and 'it's not blue' were contradictories? Surely the same point holds. And that point shows that there is no 'paraconsistent' logic. Thus in his article 'The Logic of Paradox', Graham Priest composes a well known… 
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In this note I respond to Hartley Slater's argument [12] to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt
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  • Greg Restall
  • Philosophy, Computer Science
    Notre Dame J. Formal Log.
  • 2002
This paper distinguishes contradictions from other inconsistencies, and shows that several different logics are, in an important sense, “paraconsistent” in virtue of being inconsistency tolerant without thereby being contradiction tolerant.
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Quasi-classical Logic: Non-trivializable classical reasoning from incosistent information
A new paraconsistent logic, called quasi-classical logic (or QC logic) that allows the derivation of non-trivializable classical inferences, and a proof-theoretic definition, and semantics, and shows that the consequence relation observes reflexivity, monotonicity and transitivity, but fails cut and supraclassicality.
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  • Computer Science, Philosophy
    Artif. Intell.
  • 1988
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