Dungs abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is to identify and study the large class of logic-based instantiations of Dungs theory which correspond to the maxi-consistent operator, i.e. to the function which returns maximal consistent subsets of an inconsistent knowledge base. In other words, we study the class of instantiations where very extension of the argumentation system corresponds to exactly one maximal consistent subset of the knowledge base. We show that an attack relation belonging to this class must be conflict-dependent, must not be valid, must not be conflict-complete, must not be symmetric etc. Then, we show that some attack relations serve as lower or upper bounds of the class (e.g. if an attack relation contains canonical undercut then it is not a member of this class). By using our results, we show for all existing attack relations whether or not they belong to this class. We also define new attack relations which are members of this class. Finally, we interpret our results and discuss more general questions, like: what is the added value of argumentation in such a setting? We believe that this work is a first step towards achieving our long-term goal, which is to better understand the role of argumentation and, particularly, the expressivity of logic-based instantiations of Dung-style argumentation frameworks.

We present a new approach to reasoning about the outcome of an argumentation framework, where an agent's reasoning with a framework and semantics is represented by an inference relation defined over a logical labeling language. We first study a monotonic type of inference which is, in a sense, more general than an acceptance function, but equally expressive. In order to overcome the limitations of this expressiveness, we study a non-monotonic type of inference which allows counterfactual inferences. We precisely characterize the classes of frameworks distinguishable by the non-monotonic inference relation for the admissible semantics.

In this paper we incorporate integrity constraints in Dung-style abstract argumentation frameworks. We show that even for constraints of a very simple form standard conflict-free semantics for argumentation frameworks are not adequate, as conflicts among arguments should sometimes be accepted and tolerated. For this, we use conflict-tolerant semantics and show how corresponding extensions may be represented in terms of propositional formulas.

Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic phrases. This study extends that work to the correspondence between changes in probabilities (updates) and relative probability phrases, such as "much more likely" or "a little less likely." Subjects selected such phrases to best describe numerical probability updates. We examined three hypotheses about the correspondence, and found the most descriptively accurate of these three to be that each such phrase corresponds to a fixed difference in probability (rather than fixed ratio of probabilities or of odds). The empirically derived phrase selection function uses eight phrases and achieved a 72% accuracy in correspondence with the subjects' actual usage.

Our work aims to support decision making in situations where the source of the information on which decisions are based is of varying trustworthiness. Our approach uses formal argumentation to capture the relationships between such information sources and conclusions drawn from them. This allows the decision maker to explore how information from particular sources impacts the decisions they have to make. We describe the formal system that underlies our work, and a prototype implementation of that system, applied to a problem from military decision making.

Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled as a labelled deductive system, in which propositions are doubly labelled with the grounds on which they are based and a representation of the confidence attached to the argument. Argument construction is captured by a generalized argument consequence relation based on the ^,--fragment of minimal logic. Arguments can be aggregated by a variety of numeric and symbolic flattening functions. This approach appears to shed light on the common logical structure of a variety of quantitative, qualitative and defeasible uncertainty calculi.

Distributed knowledge based applications in open domain rely on common sense information which is bound to be uncertain and incomplete. To draw the useful conclusions from ambiguous data, one must address uncertainties and conflicts incurred in a holistic view. No integrated frameworks are viable without an in-depth analysis of conflicts incurred by uncertainties. In this paper, we give such an analysis and based on the result, propose an integrated framework. Our framework extends definite argumentation theory to model uncertainty. It supports three views over conflicting and uncertain knowledge. Thus, knowledge engineers can draw different conclusions depending on the application context (i.e. view). We also give an illustrative example on strategical decision support to show the practical usefulness of our framework.

Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most acceptable arguments for that proposition. In this paper, we investigate different complementary points of view: - an acceptability based on the existence of direct counterarguments, - an acceptability based on the existence of defenders. Pursuing previous work on preference-based argumentation principles, we enforce both points of view by taking into account preference orderings for comparing arguments. Our approach is illustrated in the context of reasoning with stratified knowldge bases.

ConArg is a Constraint Programming-based tool that can be used to model and solve different problems related to Abstract Argumentation Frameworks (AFs). To implement this tool we have used JaCoP, a Java library that provides the user with a Finite Domain Constraint Programming paradigm. ConArg is able to randomly generate networks with small-world properties in order to find conflict-free, admissible, complete, stable grounded, preferred, semi-stable, stage and ideal extensions on such interaction graphs. We present the main features of ConArg and we report the performance in time, showing also a comparison with ASPARTIX [1], a similar tool using Answer Set Programming. The use of techniques for constraint solving can tackle the complexity of the problems presented in [2]. Moreover we suggest semiring-based soft constraints as a mean to parametrically represent and solve Weighted Argumentation Frameworks: different kinds of preference levels related to attacks, e.g., a score representing a "fuzziness", a "cost" or a probability, can be represented by choosing different instantiation of the semiring algebraic structure. The basic idea is to provide a common computational and quantitative framework. Keywords: Abstract Argumentation Frameworks,, Constraint Satisfaction Problems, Weighted Attacks, Tool for Argumentation. 1. Introduction Argumentation [3] is based on the exchange and the evaluation of interacting arguments which may represent information of various kinds, especially beliefs or goals. Argumentation can be used for modeling some aspects of reasoning, decision making, and dialogue.

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and the core semantics defined by Dung can be characterized by specific sub-blocks of the matrix. Furthermore, the elementary permutations of a matrix are employed by which an efficient matrix approach for finding out all extensions under a given semantics is obtained. Different from several established approaches, such as the graph labelling algorithm, Constraint Satisfaction Problem algorithm, the matrix approach not only put the mathematic idea into the investigation for finding out various extensions, but also completely achieve the goal to compute all the extensions needed.