---
title: "Entailment Semantics for Rules with Priorities"
authors:
  - "David Billington"
doi: ""
url: "https://ijcai.org/proceedings/2007/39"
pdf: "https://ijcai.org/proceedings/2007/0039.pdf"
venue: "Proceedings of the Twentieth International Joint Conference on Artificial Intelligence"
year: 2007
pages: "256-260"
track: ""
keywords:
---

# Entailment Semantics for Rules with Priorities

David Billington

*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence*, pages 256-260.

## Abstract

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.