On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach

TL;DR

This paper establishes a logic programming method to relate various extended argumentation frameworks to partial stable models, enabling a uniform semantic characterization and the definition of new frameworks.

Contribution

It introduces a translation from extended AF frameworks to logic programs, linking their semantics to partial stable models, and supports defining semantics for novel AF extensions.

Findings

AF frameworks can be translated into logic programs.

Semantics of AF extensions coincide with subsets of PSMs.

Supports defining semantics for new AF-based frameworks.

Abstract

Recently there has been an increasing interest in frameworks extending Dung's abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF. In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework $\Delta$ can be translated into a logic program $P_\Delta$ so that the extensions prescribed by different semantics of $\Delta$ coincide with subsets of the PSMs of $P_\Delta$. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports. Under consideration for publication in Theory and Practice of Logic Programming.