We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

In this paper, we investigate the revision of argumentation systems a la Dung. We focus on revision as minimal change of the arguments status. Contrarily to most of the previous works on the topic, the addition of new arguments is not allowed in the revision process, so that the revised system has to be obtained by modifying the attack relation only. We introduce a language of revision formulae which is expressive enough for enabling the representation of complex conditions on the acceptability of arguments in the revised system. We show how AGM belief revision postulates can be translated to the case of argumentation systems. We provide a corresponding representation theorem in terms of minimal change of the arguments statuses. Several distance-based revision operators satisfying the postulates are also pointed out, along with some methods to build revised argumentation systems. We also discuss some computational aspects of those methods.

/pdf/on-the-revision-of-argumentation-systems-minimal-change-of-4a57djk6zi.pdf

On the revision of argumentation systems: minimal change of arguments statuses

Characteristics of multiple viewpoints in abstract argumentation

In this chapter we give an overview of the core computational problems arising in formal argumentation together with a complexity analysis highlighting different sources of computational complexity. To this end we consider three of the previously discussed formalisms, that are Dung’s abstract argumentation frameworks, assumption-based argumentation, and abstract dialectical frameworks, each of which allows to highlight different sources of computational complexity in formal argumentation. As most of these problems turn out to be of high complexity we also consider properties of instances, like being in a specific graph class, that reduce the complexity and thus allow for more efficient algorithms. Finally, we also show how to apply techniques from parametrized complexity that allow for a more fine-grained complexity classification.

Computational Problems in Formal Argumentation and their Complexity.

argumentation offers an appealing way of representing and evaluating arguments
and counterarguments. This approach can be enhanced by considering probability
assignments on arguments, allowing for a quantitative treatment of formal argumentation.
In this paper, we regard the assignment as denoting the degree of belief that an agent
has in an argument being acceptable. While there are various interpretations of this, an
example is how it could be applied to a deductive argument. Here, the degree of belief that
an agent has in an argument being acceptable is a combination of the degree to which it
believes the premises, the claim, and the derivation of the claim from the premises. We
consider constraints on these probability assignments, inspired by crisp notions from classical
abstract argumentation frameworks and discuss the issue of probabilistic reasoning
with abstract argumentation frameworks. Moreover, we consider the scenario when assessments
on the probabilities of a subset of the arguments are given and the probabilities
of the remaining arguments have to be derived, taking both the topology of the argumentation
framework and principles of probabilistic reasoning into account. We generalise
this scenario by also considering inconsistent assessments, i.e., assessments that contradict
the topology of the argumentation framework. Building on approaches to inconsistency
measurement, we present a general framework to measure the amount of conflict of these
assessments and provide a method for inconsistency-tolerant reasoning.

/pdf/probabilistic-reasoning-with-abstract-argumentation-f01zwssxhj.pdf

Probabilistic Reasoning with Abstract Argumentation Frameworks

Argumentation is an inherently dynamic process. Consequently, recent years have witnessed tremendous research efforts towards an understanding of how the seminal AGM theory of belief change can be applied to argumentation, in particular for Dung's abstract argumentation frameworks (AFs). However, none of the attempts has yet succeeded in handling the natural situation where the revision of an AF is guaranteed to be representable by an AF as well. In this work, we present a generic solution to this problem which applies to many prominent I-maximal argumentation semantics. In order to prove a full representation theorem, we make use of recent advances in both areas of argumentation and belief change. In particular, we utilize the concepts of realizability in argumentation and the notion of compliance as used in Horn revision.

/pdf/an-extension-based-approach-to-belief-revision-in-abstract-icjapmzifx.pdf

An extension-based approach to belief revision in abstract argumentation

Design and results of the Second International Competition on Computational Models of Argumentation

argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.

/pdf/compact-argumentation-frameworks-3o2afvvm7b.pdf

Thomas Linsbichler

Papers

Characteristics of multiple viewpoints in abstract argumentation

An extension-based approach to belief revision in abstract argumentation

Design and results of the Second International Competition on Computational Models of Argumentation

Compact argumentation frameworks

Compact Argumentation Frameworks