Embedding Default Logic in Propositional Argumentation Systems

TL;DR

This paper introduces a linear transformation from propositional default theories to argumentation systems, enabling classical propositional logic methods to compute extensions and reason about default logic.

Contribution

It presents a novel linear transformation that embeds default logic into propositional argumentation systems, unifying reasoning frameworks.

Findings

Transformation is linear in the number of defaults

Allows computation of extensions within propositional logic

Enables reasoning about default logic using classical propositional methods

Abstract

In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of argumentation systems. As a consequence, computing extensions, or determining wether a given formula belongs to one extension or all extensions can be answered without leaving the field of classical propositional logic. The transformation proposed is linear in the number of defaults.