Massimiliano Giacomin

Review: an introduction to argumentation semantics

This paper presents an overview on the state of the art of semantics for abstract argumentation, covering both some of the most influential literature proposals and some general issues concerning semantics definition and evaluation. As to the former point, the paper reviews Dungs original notions of complete, grounded, preferred, and stable semantics, as well as subsequently proposed notions like semi-stable, ideal, stage, and CF2 semantics, considering both the extension-based and the labelling-based approaches with respect to their definitions. As to the latter point, the paper presents an extensive set of general properties for semantics evaluation and analyzes the notions of argument justification and skepticism. The final part of the paper is focused on the discussion of some relationships between semantics properties and domain-specific requirements.

SCC-recursiveness: a general schema for argumentation semantics

In argumentation theory, Dungs abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-recursiveness and we show that all Dungs admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dungs preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects.

On principle-based evaluation of extension-based argumentation semantics

The increasing variety of semantics proposed in the context of Dungs theory of argumentation makes more and more inadequate the example-based approach commonly adopted for evaluating and comparing different semantics. To fill this gap, this paper provides two main contributions. First, a set of general criteria for semantics evaluation is introduced by proposing a formal counterpart to several intuitive notions related to the concepts of maximality, defense, directionality, and skepticism. Then, the proposed criteria are applied in a systematic way to a representative set of argumentation semantics available in the literature, namely grounded, complete, preferred, stable, semi-stable, ideal, prudent, and CF2 semantics.

Semantics of Abstract Argument Systems

An abstract argument system or argumentation framework, as introduced in a seminal paper by Dung [13], is simply a pair 〈A ,R〉 consisting of a set A whose elements are called arguments and of a binary relation R on A called attack relation. The set A may be finite or infinite in general, however, given the introductory purpose of this chapter, we will restrict the presentation to the case of finite sets of arguments. An argumentation framework has an obvious representation as a directed graph where nodes are arguments and edges are drawn from attacking to attacked arguments. A simple example of argumentation framework AF1 = 〈{a,b},{(b,a)}〉 is shown in Figure 1. While the word argument may recall several intuitive meanings, like the ones of “line of reasoning leading from some premise to a conclusion” or of “utterance in a dispute”, abstract argument systems are not (even implicitly or indirectly) bound to any of them: an abstract argument is not assumed to have any specific structure but, roughly speaking, an argument is anything that may attack or be attacked by another argument. Accordingly, the argumentation framework depicted in Figure 1 is suitable to represent many different situations. For instance, in a context of reasoning about weather, argument a may be associated with the inferential step

AFRA: Argumentation framework with recursive attacks

The issue of representing attacks to attacks in argumentation is receiving an increasing attention as a useful conceptual modelling tool in several contexts. In this paper we present AFRA, a formalism encompassing unlimited recursive attacks within argumentation frameworks. AFRA satisfies the basic requirements of definition simplicity and rigorous compatibility with Dungs theory of argumentation. This paper provides a complete development of the AFRA formalism complemented by illustrative examples and a detailed comparison with other recursive attack formalizations.

Solving Semantic Problems with Odd-Length Cycles in Argumentation

In the context of Dung’s abstract framework for argumentation, two main semantics have been considered to assign a defeat status to arguments: the grounded semantics and the preferred semantics. While the two semantics agree in most situations, there are cases where the preferred semantics appears to be more powerful. However, we notice that the preferred semantics gives rise to counterintuitive results in some other cases, related to the presence of odd-length cycles in the attack relation between arguments. To solve these problems, we propose a new semantics which preserves the desirable properties of the preferred semantics, while correctly dealing with odd-length cycles. We check the behavior of the proposed semantics in a number of examples and discuss its relationships with both grounded and preferred semantics.

A Fuzzy Extension of Allen`s Interval Algebra

The aim of this work is to integrate the ideas of flexibility and uncertainty into Allens interval-based temporal logic [1], defining a new formalism which extends classical Interval Algebra (IA). Some results obtained in the framework of Fuzzy Constraint Satisfaction Problem (FCSP) approach [3] are used in the specific domain of temporal reasoning. A new fuzzy interval algebra IAfuz is defined. Classical concepts of consistency and minimality are generalized to deal with IAfuz. Path-consistency and branch & bound algorithms are shown. A tractable sub-algebra of IAfuz is defined.

Encompassing Attacks to Attacks in Abstract Argumentation Frameworks

In the traditional definition of Dungs abstract argumentation framework (

Computing Preferred Extensions in Abstract Argumentation: A SAT-Based Approach

\ensuremath{AF}

On the Input/Output behavior of argumentation frameworks

), the notion of attack is understood as a relation between arguments, thus bounding attacks to start from and be directed to arguments. This paper introduces a generalized definition of abstract argumentation framework called