Abstract argumentation and answer set programming: two faces of Nelson's logic

TL;DR

This paper demonstrates that logic programming and abstract argumentation frameworks can be unified under Nelson's constructive logic N4 by formalizing principles like non-contradictory inference and a strengthened closed world assumption.

Contribution

It introduces a modular translation of logic programming and argumentation frameworks into Nelson's logic N4, using a new implication connective and strong negation.

Findings

Unified formalization of logic programming and argumentation in N4

Introduction of a new implication connective based on non-contradictory inference

Representation of attacks using strong negation in the translation

Abstract

In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and using the object language. Logic programming implication and abstract argumentation supports become, in the translation, a new implication connective following the non-contradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP).