Non-monotonic Syntax-Based Entailment: A Classification of Consequence Relations

The purpose of this paper is to provide a comparative study of nonmonotonic syntax-basedconsequencerelations, from different points of view. Starting from a (not necessarily consistent) belief baseE and a pre-ordering on E, we first remind different mechanisms for selecting preferred consistent subbases in syntax-based approaches.Then, we present three entailment principles in order to cope with these multiple subbases. The crossing point of each generation mechanism and each principle defines a syntax-based consequence relation. Pursuing previous work of the authors concerning the computational complexity point of view, we first provide a comparison from the cautiousness point of view. Our proposal restates previous results [18] in a single framework and provides new results. In the last part of this paper, we study the validity of deduction rules (such as those introduced by [15, 12]). Results are discussed in the conclusion.