Entailment Semantics for Rules with Priorities

We define a new general rule-based non-monotonic framework which allows an external acyclic priority relation between rules to be interpreted in several ways. Several entailment semantics are defined via a constructive digraph, with one being given a declarative fixed-point characterisation as well. Each of these semantics satisfies Principle 1 of [Brewka and Eiter 1999]. The framework encompasses Default Logic [Reiter 1980], ground Answer Set Programming (ASP) [Baral 2003], and Defeasible Logic [Nute 1994]. Default Logic is provided with a new semantics which is ambiguity blocking, rather than the usual ambiguity propagating semantics. Also Reiterextensions are given a new fixed-point characterisation; and Lukaszewicz's [1990] m-extensions are given a much simpler construction and fixed-point characterisation.