Argumentation Reasoning via Circumscription with Pyglaf

Issue title: Special issue of the 24th RCRA International Workshop on “Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion”

Guest editors: Marco Maratea, Ivan Serina and Paolo Torroni

Article type: Research Article

Authors: Alviano, Mario^{; *}

Affiliations: Department of Mathematics and Computer Science, University of Calabria, via Pietro Bucci 30B, 87036 Rende (CS), Italy. [email protected]

Correspondence: [*] Address for correspondence: Department of Mathematics and Computer Science, via Pietro Bucci 30B, 87036 Rende (CS), Italy

Abstract: The fundamental mechanism that humans use in argumentation can be formalized in abstract argumentation frameworks. Many semantics are associated with abstract argumentation frameworks, each one consisting of a set of extensions, that is, a set of sets of arguments. Some of these semantics are based on preference relations that essentially impose to maximize or minimize some property. This paper presents the argumentation reasoner PYGLAF, which provides a uniform view of many semantics for abstract argumentation frameworks in terms of circumscription. Specifically, several computational problems of abstract argumentation frameworks are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Finally, grounded extensions are obtained in polynomial time by unit propagation, and acceptance problems are addressed by first checking cardinality optimal models of circumscribed theories, so that the naive extension enumeration is possibly avoided.

Keywords: abstract argumentation frameworks, propositional circumscription, minimal model enumeration, incremental solving

DOI: 10.3233/FI-2019-1808

Journal: Fundamenta Informaticae, vol. 167, no. 1-2, pp. 1-30, 2019