In this paper I present two new strategies for inconsistencyadaptive logics: the reliable sufficient information strategy of ACLuN3 andthe minimally abnormal sufficient information strategy of ACLuN4. I giveproof theory and semantics for both ACLuN3 and ACLuN4. I also compare them with the well-known inconsistency-adaptive logics ACLuN1 andACLuN2.

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.