*David Billington*

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. The framework encompasses Default Logic, ground Answer Set Programming (ASP), and Defeasible Logic. Default Logic is provided with a new semantics which is ambiguity blocking, rather than the usual ambiguity propagating semantics. Also Reiter-extensions are given a new fixed-point characterisation; and Lukaszewicz’s m-extensions are given a much simpler construction and fixed-point characterisation.