Embedding Defeasible Logic into Logic Programming

TL;DR

This paper establishes a formal connection between defeasible logic and logic programming by translating defeasible theories into meta-programs, linking their semantics under certain conditions.

Contribution

It introduces a translation method from defeasible logic to logic programming and relates their semantics, especially under the condition of decisiveness.

Findings

Defeasible consequences correspond to stable model conclusions under certain conditions.

The translation is exact under the decisiveness condition.

Kunen semantics can be used for a complete embedding in the general case.

Abstract

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.