Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae

  • Authors:
  • Ofer Arieli

  • Affiliations:
  • The Academic College of Tel-Aviv, Tel-Aviv, Israel

  • Venue:
  • ACM Transactions on Computational Logic (TOCL)
  • Year:
  • 2007

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Abstract

We introduce a uniform approach of representing a variety ofparaconsistent nonmonotonic formalisms by quantified Booleanformulae (QBFs) in the context of multiple-valued logics. We showthat this framework provides a useful platform for capturing, in asimple and natural way, a wide range of methods for preferentialreasoning. The outcome is a subtle approach to represent theunderlying formalisms, which induces a straightforward way tocompute the corresponding entailments: By incorporatingoff-the-shelf QBF solvers it is possible to simulate within ourframework various kinds of preferential formalisms, among which arePriest's logic LPm of reasoning with minimal inconsistency, Batens'adaptive logic ACLuNs2, Besnard and Schaub's inference relation&vbar;=n, a variety of formula-preferentialsystems, some bilattice-based preferential relations (e.g.,&vbar;=I1 and&vbar;=I2), and consequencerelations for reasoning with graded uncertainty, such as thefour-valued logic &vbar;=4c.