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Journal of Logic and Computation 2003 13(4):557-580; doi:10.1093/logcom/13.4.557
© 2003 by Oxford University Press
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Original Article

Reducing Preferential Paraconsistent Reasoning to Classical Entailment

Ofer Arieli1 and Marc Denecker2

1 Department of Computer Science, The Academic College of Tel-Aviv, 4 Antokolski street, Tel-Aviv 61161, Israel. E-mail: oarieli{at}mta.ac.il 2 Department of Computer Science, The Catholic University of Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium. E-mail: marcd{at}cs.kuleuven.ac.be

We introduce a general method for paraconsistent reasoning in the context of classical logic. A standard technique for paraconsistent reasoning on inconsistent classical theories is by shifting to multiple-valued logics. We show how these multiple-valued theories can be ‘shifted back’ to two-valued classical theories through a polynomial transformation, and how preferential reasoning based on multiple-valued logic can be represented by classical circumscription-like axioms. By applying this process we provide new ways of implementing multiple-valued paraconsistent reasoning. Standard multiple-valued reasoning can thus be performed through theorem provers for classical logic, and multiple-valued preferential reasoning can be implemented using algorithms for processing circumscriptive theories (such as DLS and SCAN).

Keywords: Paraconsistent reasoning, preferential semantics, circumscription, multiple-valued logics.

Received 6 March 2001.


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