Preferential and Preferential-discriminative Consequence relations
Résumé
The present paper follows the line of research which consists in investigating consequence relations that are both paraconsistent and plausible (generally non-monotonic too). More precisely, we lay the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations (such as in Non-monotonic Reasoning). The first purpose of the paper is to provide characterizations for families of them, in a general framework that covers e.g. the ones of the well-known paraconsistent logics J3 and FOUR. The second and main purpose is to provide, again in a general framework, characterizations for families of preferential-discriminative consequence relations. The latter are defined exactly as the plain versions, except that among the conclusions, a formula is rejected if its negation is also present.