Fundamenta Informaticae - Volume 155, issue 3

Authors: Gaggl, Sarah Alice | Nieves, Juan Carlos | Strass, Hannes | Torroni, Paolo

Article Type: Other

DOI: 10.3233/FI-2017-1583

Citation: Fundamenta Informaticae, vol. 155, no. 3, pp. i-iii, 2017

Authors: Maher, Michael J.

Article Type: Research Article

Abstract: There are a wide variety of formalisms for defeasible reasoning that can be seen as implementing concrete argumentation on defeasible rules. However there has been little work on the relationship between such languages and Dung’s abstract argumentation. In this paper we identify two small fragments of defeasible rule languages on which many concrete defeasible formalisms agree. The two fragments are closely related, as we show. Both arise as ways to express abstract argumentation frameworks in the concrete formalisms. Using these fragments, we establish a close relationship between abstract argumentation under semantics based on complete extensions, and ambiguity blocking logics in …the framework of Antoniou et al. These results support a uniform approach to deriving complexity lower bounds for defeasible formalisms, where a lower bound is established for abstract argumentation and can then be extended “for free” to corresponding concrete defeasible formalisms. Show more

DOI: 10.3233/FI-2017-1584

Citation: Fundamenta Informaticae, vol. 155, no. 3, pp. 233-260, 2017

Authors: Sakama, Chiaki | Rienstra, Tjitze

Article Type: Research Article

Abstract: This paper studies representation of argumentation frameworks (AFs) in answer set programming (ASP). Four different transformations from AFs to logic programs are provided under the complete semantics, stable semantics, grounded semantics and preferred semantics. The proposed transformations encode labelling-based argumentation semantics in a simple manner, and different semantics of AFs are uniformly characterized by stable models of transformed programs. We apply transformed programs to solving AF problems such as query-answering, enforcement of arguments, agreement or equivalence of different AFs. Logic programming encodings of AFs are also used for representing assumption-based argumentation (ABA) in ASP. The results of this paper exploit …new connections between argumentation theory and logic programming, and enable one to perform various argumentation tasks using existing answer set solvers. Show more

Keywords: argumentation framework, answer set programming, transformation

DOI: 10.3233/FI-2017-1585

Citation: Fundamenta Informaticae, vol. 155, no. 3, pp. 261-292, 2017

Authors: Osorio, Mauricio | Carballido, José Luis | Zepeda, Claudia

Article Type: Research Article

Abstract: We extend further the relationship that exists between logic programming semantics and some of the semantics of extensions defined on argumentation frameworks. We define a new logic programming semantics based on the addition of abducible atoms to those normal logic programs that do not have stable models, and consider the argumentation extensions that result from it when using a well-known translation mapping between argumentation frameworks and normal programs. We call this programming semantics the stable m-ab-m logic programming semantics. This semantics defines a new type of semantics of extensions on argumentation frameworks that is not comparable to the semi-stable argumentation …semantics, yet both argumentation semantics share several properties, since they both generalize the stable semantics of extensions. We also define a semantics for normal logic programs based on minimal classical two-valued models and the Gelfond-Lifschitz reduct. This semantics corresponds to the semi-stable extensions in argumentation frameworks according to the mapping mentioned before; this way we obtain a general version of a semi-stable semantics for normal logic programs. Each of these new semantics has the property of being non-empty for any normal logic program or argumentation framework, and each of them agrees with the respective stable semantics in the case where the stable semantics is a non-empty set. Show more

Keywords: Argumentation framework, argumentation semantics, logic programming semantics

DOI: 10.3233/FI-2017-1586

Citation: Fundamenta Informaticae, vol. 155, no. 3, pp. 293-319, 2017