Defense semantics of argumentation: encoding reasons for accepting arguments

In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with a new notion of defense equivalence of argument graphs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Then, based on defense semantics, we define two kinds of reasons for accepting arguments, i.e., direct reasons and root reasons, and a notion of root equivalence of argument graphs. Finally, we show how the notion of root equivalence can be used in argumentation summarization.Comment: 14 pages, first submitted on April 30, 2017; 16 pages, revised in terms of the comments from MIREL2017 on August 03, 201

On the equivalence between logic programming semantics and argumentation semantics

This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX$_p$. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin

On the Difference between Assumption-Based Argumentation and Abstract Argumentation

Acknowledgements The first author has been supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSy project). The second and third authors have been supported by CNPq (Universal 2012 - Proc. no. 473110/2012-1), CAPES (PROCAD 2009) and CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPostprin

On the Equivalence between Logic Programming Semantics and Argumentation Semantics

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Modeling time and valuation in structured argumentation frameworks

Temporal Argumentation Frameworks (TAF) represent a recent extension of Dung's abstract argumentation frameworks that consider the temporal availability of arguments. In a TAF, arguments are valid during specific time intervals, called availability intervals, while the attack relation of the framework remains static and permanent in time; thus, in general, when identifying the set of acceptable arguments, the outcome associated with a TAF will vary in time. We introduce an extension of TAF, called Extended Temporal Argumentation Framework (E-TAF), adding the capability of modeling the temporal availability of attacks among arguments, thus modeling special features of arguments varying over time and the possibility that attacks are only available in a given time interval. E-TAF will be enriched by considering Structured Abstract Argumentation, using Dynamic Argumentation Frameworks. The resulting framework, E-TAF∗, provides a suitable model for different time-dependent issues satisfying properties and equivalence results that permit to contrast the expressivity of E-TAF and E-TAF∗ with argumentation based on abstract frameworks. Thus, the main contribution here is to provide an enhanced framework for modeling special features of argumentation varying over time, which are relevant in many real-world situations. The proposal aims at advancing in the integration of time and valuation in the context of argumentation systems as well.Fil: Budan, Maximiliano Celmo David. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación; Argentina. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Gomez Lucero, Mauro Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación; ArgentinaFil: Chesñevar, Carlos Iván. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; Argentina. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación; Argentin