Foundations of Paraconsistent Resolution

Authors:
Norihiro Kamide
Affiliations:
Department of Philosophy, Keio University, 2-15-45 Mita, Minatoku, Tokyo, 108-8345, Japan. E-mail: kamide@mtc.biglobe.ne.jp
Venue:
Fundamenta Informaticae
Year:
2006

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Abstract

An extended first-order predicate sequent calculus PLK with two kinds of negation is introduced as a basis of a new resolution calculus PRC (paraconsistent resolution calculus) for handling the property of paraconsistency. Herbrand theorem, completeness theorem (with respect to a classical-like semantics) and cut-elimination theorem are proved for PLK. The correspondence between PLK and PRC is shown by using a faithful embedding of PLK into the sequent calculus LK for classical logic.