Cyclic Supports in Recursive Bipolar Argumentation Frameworks: Semantics and LP Mapping
Gianvincenzo Alfano, Sergio Greco, Francesco Parisi, Irina Trubitsyna
TL;DR
This work addresses the challenge of defining coherent semantics for Bipolar Argumentation Frameworks (BAF) and Recursive BAFs (Rec-BAF) in the presence of cycles in supports and recursive attacks. It introduces classical, modular semantics that extend the AF-based notions of defeated and acceptable elements to general BAF and Rec-BAF, including self-support-exclusion principles. The authors show that any general BAF or Rec-BAF can be mapped to a propositional logic program $P_ extDelta$ such that the extensions correspond to partial stable models ${ m PS}(P_ extDelta)$, enabling uniform LP-based computation across frameworks. They analyze the computational complexity of verification and credulous/skeptical acceptance under the four standard semantics (${ t gr}$, ${ t co}$, ${ t st}$, ${ t pr}$), obtaining results parallel to AF. The approach integrates with existing formalisms (AFN, AFD, ASAF, RAFN, RAFD, AFRAD) and provides a principled, self-contained route to ASP/LP-based reasoning for complex argumentation structures, with potential for practical tool support and broader applicability in AI reasoning about conflicting information.
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.