The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial.
Unable to display preview. Download preview PDF.
- D. Batens, Dialectical dynamics within formal logics, Logique et Analyse 29 (1986), pp. 114–173.Google Scholar
- D. Batens, Dynamic dialectical logics, in .Google Scholar
- H. Friedman and R. Meyer, Can we Implement Relevant Arithmetic?, Technical Report TR-ARP-12/88, Automated Reasoning Project, Australian National University, Canberra, 1988.Google Scholar
- G. Priest, Logic of paradox, Journal of Philosophical Logic 8 (1979), pp. 219–241.Google Scholar
- G. Priest, In Contradiction, Nijhoff, 1987.Google Scholar
- G. Priest, Consistency by Default, Technical Report TR-ARP-3/88, Automated Reasoning Project, Australian National University, Canberra, 1988.Google Scholar
- G. Priest, Reductio ad Absurdum et Modus Tollendo Ponens, in .Google Scholar
- G. Priest and R. Routley, On Paraconsistency, #13 Research Series in Logic and Metaphysics, Department of Philosophy. RSSS, Australian National University, 1983. Reprinted as the introductory chapters of .Google Scholar
- G. Priest, R. Routley, and J. Norman, Paraconsistent Logic, Philosophia Verlag, 1989.Google Scholar