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Journal of Logic and Computation
Volume 13, Issue 4, June 2003: pp. 557-580
Reducing Preferential Paraconsistent Reasoning to Classical Entailment
Ofer Arieli1 and Marc Denecker2
1Department of Computer Science, The Academic College of Tel-Aviv, 4 Antokolski street, Tel-Aviv 61161, Israel. E-mail: firstname.lastname@example.org
2Department of Computer Science, The Catholic University of Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium. E-mail: email@example.com
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.
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