On the Complexity of Non-monotonic Entailment in Syntax-based Approaches

The purpose of this paper is to outline various results regarding the computational complexity of non-monotonic entailment in diierent syntax-based approaches. Starting from a (non necessarily consistent) belief base E and a pre-ordering on E, we rst remind diierent mechanisms for selecting preferred consistent subsets in syntax-based approaches. Then we present diierent entailment principles in order to manage these multiple subsets. The crossing point of each generation mechanism m and each entailment principle p deenes an entailment relation (E;)j p;m which we study from the computational complexity point of view. The obtained results are not very encouraging since the complexity of all these non-monotonic entailment relations is, even in the most restricted languages, larger than the complexity of monotonic entailment.