Dung's Argumentation Theory Research Articles

A general approach to extension-based semantics in abstract argumentation

After a few decades of development, computational argumentation has become one of the active areas in AI. This paper proposes a general approach to deal with semantic related problems of abstract argumentation frameworks (AAFs, for short) and further develops the graded semantics presented by Grossi and Modgil. We pay attention not only to issues of various extension-based semantics at the object level but also the metatheoretical level. First, an alternative fundamental lemma is given, which generalizes the corresponding result due to Grossi and Modgil by relaxing the constraint on parameters. This lemma provides a new sufficient condition for preserving conflict-freeness and brings a Galois adjunction between admissible sets and complete extensions, which is of vital importance in constructing some special extensions in terms of iterations of the defense function. Applying such a lemma, some flaws in Grossi and Modgil's work are corrected, and the structural property, universal definability of various extension-based semantics and relationships among semantics are considered. Second, the operator ⋂D so-called reduced meet modulo an ultrafilter is presented, which is a simple but powerful tool in exploring infinite AAFs. The neutrality function and the defense function, which play central roles in Dung's abstract argumentation theory, are shown to be distributive over reduced meets modulo any ultrafilter. A variety of fundamental semantics for AAFs (including conflict-free, admissible, complete and stable semantics, etc) and some derived semantics are shown to be closed under this operator. Based on these facts, a number of applications of the operator ⋂D are considered, which show this operator can deal with various aspects of argumentation theory. In particular, we provide a simple and uniform method to prove the universal definability of a family of range related semantics. In addition to these results at the object level, this paper also explores ones at the metatheoretical level. To illustrate the universal applicability of the operator ⋂D as a tool for handling semantic related problems, we introduce the first order language FS(Ω) and establish a connection between ultraproducts of models in model theory and reduced meets of extensions modulo ultrafilters. On the basis of this, we characterize the extension-based semantics that is closed under the operator ⋂D in terms of the FS(Ω)-definability, which provides an example of utilizing model theory to explore the theoretical problems of AAFs and brings a series of metatheorems about extension-based semantics. In a word, our work shows that the operator ⋂D can deal with various problems related to various semantics, which suggests that it provides a general method to study AAFs.

Dealing with Incompatibilities among Procedural Goals under Uncertainty

By considering rational agents, we focus on the problem of selecting goals out of a set of incompatible ones. We consider three forms of incompatibility introduced by Castelfranchi and Paglieri, namely the terminal, the instrumental (or based on resources), and the superfluity. We represent the agent's plans by means of structured arguments whose premises are pervaded with uncertainty. We measure the strength of these arguments in order to determine the set of compatible goals. We propose two novel ways for calculating the strength of these arguments, depending on the kind of incompatibility thatexists between them. The first one is the logical strength value, it is denoted by a three-dimensional vector, which is calculated from a probabilistic interval associated with each argument. The vector represents the precision of the interval, the location of it, and the combination of precision and location. This type of representation and treatment of the strength of a structured argument has not been defined before by the state of the art. The second way for calculating the strength of the argument is based on the cost of the plans (regarding the necessary resources) and the preference of the goals associated with the plans. Considering our novel approach for measuring the strength of structured arguments, we propose a semantics for the selection of plans and goals that is based on Dung's abstract argumentation theory. Finally, we make a theoretical evaluation of our proposal.

Characterizing acceptability semantics of argumentation frameworks with recursive attack and support relations

Over the last decade, several extensions of Dung's Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as necessity. Currently, to determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung's AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung's argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN).