Signed Systems for Paraconsistent Reasoning

  • Authors:
  • Ph. Besnard;T. Schaub

  • Affiliations:
  • IRISA, Campus de Beaulieu, F-35042 Rennes Cedex;LERIA, Faculté des Sciences, Université d’Angers, 2 boulevard Lavoisier, F-49045 Angers Cedex 01

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 1998

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Abstract

We present a novel approach to paraconsistent reasoning, that is, toreasoning from inconsistent information. The basic idea is the following. Wetransform an inconsistent theory into a consistent one by renaming allliterals occurring in the theory. Then, we restore some of the originalcontents of the theory by introducing progressively formal equivalenceslinking the original literals to their renamings. This is done as long asconsistency is preserved. The restoration of the original contents of thetheory is done by appeal to default logic. The overall approach provides uswith a family of paraconsistent consequence relations.Our approach is semantical because it works at the level of thepropositions; it deals with the semantical link between a proposition andits negation. The approach is therefore independent of the combination ofthe connectives that are actually applied to the propositions in order toform entire formulas.