Preferential and Preferential-discriminative Consequence relations

TL;DR

This paper explores non-monotonic, paraconsistent consequence relations called preferential and preferential-discriminative, providing syntactic characterizations and extending their applicability to many-valued logics.

Contribution

It introduces a general framework for preferential and discriminative consequence relations, including new characterizations and applications to many-valued, paraconsistent logics.

Findings

Characterizations of preferential consequence relations

Development of preferential-discriminative relations

Application to many-valued, paraconsistent logics

Abstract

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations. We worked with a general notion of valuation that covers e.g. the classical valuations as well as certain kinds of many-valued valuations. In the many-valued cases, preferential consequence relations are paraconsistant (in addition to be non-monotonic), i.e. they are capable of drawing reasonable conclusions which contain contradictions. The first purpose of this paper is to provide in our general framework syntactic characterizations of several families of preferential relations. The second and main purpose is to provide, again in our general framework, characterizations of several families of preferential discriminative consequence relations. They are defined exactly as the plain version, but any conclusion such that its negation is also a conclusion is rejected (these relations bring something new essentially in the many-valued cases).