Preferential and Preferential-discriminative Consequence Relations

Abstract

The theory of preferential consequence relations has been investigated extensively in the classical context, where copies of classical valuations serve as the terms of the preference relation. The first purpose of the present paper is to extend the theory to preferential consequence relations in certain three/four-valued contexts, well-known as the paraconsistent logics J3 and FOUR. We give characterizations of several families of preferential consequence relations in these two contexts. Our second and main purpose is to investigate a qualified version of preferential consequence, which we call preferential-discriminative consequence. This is defined to hold between a set Γ of formulae and formula α iff Γ -- α but Γ -- ¬ α where -- is the plain relation. We provide characterizations of several families of such preferential-discriminative consequence relations for all of the classical, three, and four-valued contexts.