Interdefinability of defeasible logic and logic programming under the well-founded semantics

TL;DR

This paper establishes a formal connection between defeasible logic and logic programming under well-founded semantics, providing translations and operators that unify their reasoning frameworks and semantics.

Contribution

It introduces translations between defeasible theories and logic programs, and develops operators linking their semantics, unifying ambiguity propagating and blocking defeasible logics with logic programming.

Findings

Defeasible theories under ADL correspond to well-founded semantics of logic programs.

Operators for ADL and NDL relate to the Gelfond-Lifschitz operator for logic programs.

Stable model semantics can be defined for defeasible theories using these operators.

Abstract

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.