Valid attacks in argumentation frameworks with recursive attacks

The purpose of this work is to study a generalisation of Dung’s abstract argumentation frameworks that allows representing recursive attacks, that is, a class of attacks whose targets are other attacks. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is extension dependent and which, intuitively, represents a set of “valid attacks” with respect to the extension. The studied theory displays a conservative generalisation of Dung’s semantics (complete, preferred and stable) and also of its principles (conflictfreeness, acceptability and admissibility). Furthermore, despite its conceptual differences, we are also able to show that our theory agrees with the AFRA interpretation of recursive attacks for the complete, preferred and stable semantics

An Axiomatic Approach to Support in Argumentation

International audienceIn the context of bipolar argumentation (argumentation with two kinds of interaction, attacks and supports), we present an axiomatic approach for taking into account a special interpretation of the support relation, the necessary support. We propose constraints that should be imposed to a bipolar argumentation system using this interpretation. Some of these constraints concern the new attack relations, others concern acceptability. We extend basic Dung’s framework in different ways in order to propose frameworks suitable for encoding these constraints. By the way, we propose a formal study of properties of necessary support

A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature

An approach to abstract argumentation with recursive attack and support

This work introduces the Attack-Support Argumentation Framework (ASAF), an approach to abstract argumentation that allows for the representation and combination of attack and support relations. This framework extends the  Argumentation Framework with Recursive Attacks (AFRA) in two ways. Firstly, it adds a support relation enabling to express support for arguments; this support can also be given to attacks, and to the support relation itself. Secondly, it extends AFRA's attack relation by allowing attacks to the aforementioned support  relation. Moreover, since the support relation of the ASAF has a necessity interpretation, the ASAF also extends the Argumentation Framework with Necessities (AFN). Thus, the ASAF provides a unified framework for  representing attack and support for arguments, as well as attack and support for the attack and support relations at any level.Fil: Cohen, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Gottifredi, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: García, Alejandro Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin