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Representing Argumentation Frameworks in Answer Set Programming

Sakama C., Rienstra T.

Fundamenta Informaticae

2017

Vol. 155, nr 3

261--292

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.

Abducible Semantics and Argumentation

Osorio M., Carballido J. L., Zepeda C.

Fundamenta Informaticae

2017

Vol. 155, nr 3

293--319

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.