HL2, an Inconsistency-adaptive and Inconsistency-resolving Logic for General Statements that might have Exceptions

Abstract

ABSTRACT The present paper offers a new approach to non-monotonic logics and their reconstruction in terms of inconsistency-adaptive logics. By applying a special technique, universally quantified formulas are assigned instances that, given the paraconsistent framework, do not cause triviality even if they conflict with knowledge deriving from other sources. From the special instances, the usual instances may be derived conditionally, viz. provided they are not contradicted by statements derived with a higher preference ranking.