Cyclic Supports in Recursive Bipolar Argumentation Frameworks: Semantics and LP Mapping

TL;DR

This paper extends argumentation frameworks to include recursive supports and attacks, providing simple, modular semantics and linking them to logic programming, thus addressing previous complexities in cyclic support scenarios.

Contribution

It introduces a unified, modular approach to defining semantics for recursive bipolar argumentation frameworks with cycles, simplifying their interpretation and connection to logic programming.

Findings

Semantics for BAF and Rec-BAF can be defined by simple modifications of AF semantics.

Provides a modular, intuitive framework for handling cycles in argumentation.

Characterizes semantics using logic programming and partial stable models.

Abstract

Dung's Abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in Artificial Intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development of the Bipolar Argumentation Framework (BAF), and recursive attacks and supports, resulting in the Recursive BAF (Rec-BAF). Different interpretations of supports have been proposed, whereas for Rec-BAF (where the target of attacks and supports may also be attacks and supports) even different semantics for attacks have been defined. However, the semantics of these frameworks have either not been defined in the presence of support cycles, or are often quite intricate in terms of the involved definitions. We encompass this limitation and present classical semantics for general BAF and Rec-BAF and show that the semantics for specific BAF and Rec-BAF frameworks can be defined by very simple and intuitive modifications of that defined for the case of AF. This is achieved by providing a modular definition of the sets of defeated and acceptable elements for each AF-based framework. We also characterize, in an elegant and uniform way, the semantics of general BAF and Rec-BAF in terms of logic programming and partial stable model semantics.