This paper establishes a dual theory about knowledge and argumentation. Our idea is rooted at both epistemic logic and argumentation theory, and we aim to merge these two fields, not just in a superficial way but to thoroughly disclose the intrinsic relevance between knowledge and argumentation. Specifically, we define epistemic Kripke models and argument Kripke models as a dual pair, and then work out a two-way generation method between these two types of Kripke models. Such generation is rigorously justified by a duality theorem on modal formulae's invariance. We also provide realistic examples to demonstrate our generation, through which our framework's practical utility gets strongly advocated. We finally propose a philosophical thesis that knowledge is essentially dynamic, and we draw certain connection to Maxwell's demon as well as the well-known proverb "knowledge is power".

We provide a logical analysis of abstract argumentation frameworks and their dynamics. Following previous work, we express attack relation and argument status by means of propositional variables and define acceptability criteria by formulas of propositional logic. We here study the dynamics of argumentation frameworks in terms of basic operations on these propositional variables, viz.

During the first step of practical reasoning, i.e. deliberation, an intelligent agent generates a set of pursuable goals and then selects which of them he commits to achieve. An intelligent agent may in general generate multiple pursuable goals, which may be incompatible among them. In this paper, we focus on the definition, identification and resolution of these incompatibilities. The suggested approach considers the three forms of incompatibility introduced by Castelfranchi and Paglieri, namely the terminal incompatibility, the instrumental or resources incompatibility and the superfluity. We characterise computationally these forms of incompatibility by means of arguments that represent the plans that allow an agent to achieve his goals. Thus, the incompatibility among goals is defined based on the conflicts among their plans, which are represented by means of attacks in an argumentation framework. We also work on the problem of goals selection; we propose to use abstract argumentation theory to deal with this problem, i.e. by applying argumentation semantics. We use a modified version of the "cleaner world" scenario in order to illustrate the performance of our proposal.

In ASPIC-style structured argumentation an argument can rebut another argument by attacking its conclusion. Two ways of formalizing rebuttal have been proposed: In restricted rebuttal, the attacked conclusion must have been arrived at with a defeasible rule, whereas in unrestricted rebuttal, it may have been arrived at with a strict rule, as long as at least one of the antecedents of this strict rule was already defeasible. One systematic way of choosing between various possible definitions of a framework for structured argumentation is to study what rationality postulates are satisfied by which definition, for example whether the closure postulate holds, i.e. whether the accepted conclusions are closed under strict rules. While having some benefits, the proposal to use unrestricted rebuttal faces the problem that the closure postulate only holds for the grounded semantics but fails when other argumentation semantics are applied, whereas with restricted rebuttal the closure postulate always holds. In this paper we propose that ASPIC-style argumentation can benefit from keeping track not only of the attack relation between arguments, but also the relation of deductive joint support that holds between a set of arguments and an argument that was constructed from that set using a strict rule. By taking this deductive joint support relation into account while determining the extensions, the closure postulate holds with unrestricted rebuttal under all admissibility-based semantics. We define the semantics of deductive joint support through the flattening method.

Dung's abstract argumentation theory plays a guiding role in the field of formal argumentation. The properties of argumentation semantics have been deeply explored in the previous literature. The SCC-recursiveness principle is a property of the extensions which relies on the graph-theoretical notion of strongly connected components. It provides a general recursive schema for argumentation semantics, which is an efficient and incremental algorithm for computing the argumentation semantics. However, in argumentation frameworks with uncertain arguments and uncertain attack relation, the SCC-recursive theory is absence. This paper is an exploration of the SCC-recursive theory in fuzzy argumentation frameworks (FAFs), which add numbers as fuzzy degrees to the arguments and attacks. In this paper, in order to extend the SCC-recursiveness principle to FAFs, we first modify the reinstatement principle and directionality principle to fit the FAFs. Then the SCC-recursiveness principle in FAFs is formalized by the modified principles. Additionally, some illustrating examples show that the SCC-recursiveness principle also provides an efficient and incremental algorithm for simplify the computation of argumentation semantics in FAFs.

Department of Computing Science, Ume a University 90187 Ume a, Sweden Abstract Abstract argumentation has emerged as a method for nonmonotonic reasoning that has gained tremendous traction in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined over the years are typically evaluated from a logics perspective; an analysis that is based on models of ideal, rational decision-making does not exist. In this paper, we close this gap by analyzing abstract argumentation from the perspective of the rational man paradigm in microeconomic theory. To assess under which conditions abstract argumentation-based choice functions can be considered economically rational, we define a new argumentation principle that ensures compliance with the rational man's reference independence property, which stipulates that a rational agent's preferences over two choice options should not be influenced by the absence or presence of additional options. We show that the argumentation semantics as proposed in Dung's classical paper, as well as all of a range of other semantics we evaluate do not fulfill this newly created principle. Consequently, we investigate how structural properties of argumentation frameworks impact the reference independence principle, and propose a restriction to argumentation expansions that allows all of the evaluated semantics to fulfill the requirements for economically rational argumentation-based choice. For this purpose, we define the rational man's expansion as a normal and noncyclic expansion. Finally, we put reference independence into the context of preference-based argumentation and show that for this argumentation variant, which explicitly model preferences, the rational man's expansion cannot ensure reference independence.

This paper studies a fundamental mechanism of how to detect a conflict between arguments given sentiments regarding acceptability of the arguments. We introduce a concept of the inverse problem of the abstract argumentation to tackle the problem. Given noisy sets of acceptable arguments, it aims to find attack relations explaining the sets well in terms of acceptability semantics. It is the inverse of the direct problem corresponding to the traditional problem of the abstract argumentation that focuses on finding sets of acceptable arguments in terms of the semantics given an attack relation between the arguments. We give a probabilistic model handling both of the problems in a way that is faithful to the acceptability semantics. From a theoretical point of view, we show that a solution to both the direct and inverse problems is a special case of the probabilistic inference on the model. We discuss that the model provides a natural extension of the semantics to cope with uncertain attack relations distributed probabilistically. From en empirical point of view, we argue that it reasonably predicts individuals sentiments regarding acceptability of arguments. This paper contributes to lay the foundation for making acceptability semantics data-driven and to provide a way to tackle the knowledge acquisition bottleneck.

Value-based argumentation enhances a classical abstract argumentation graph - in which arguments are modelled as nodes connected by directed arrows called attacks - with labels on arguments, called values, and an ordering on values, called audience, to provide a more fine-grained justification of the attack relation. With more than one agent facing such an argumentation problem, agents may differ in their ranking of values. When needing to reach a collective view, such agents face a dilemma between two equally justifiable approaches: aggregating their views at the level of values, or aggregating their attack relations, remaining therefore at the level of the graphs. We explore the strenghts and limitations of both approaches, employing techniques from preference aggregation and graph aggregation, and propose a third possibility aggregating rankings extracted from given attack relations.

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments. The proposed approach is shown to satisfy some desirable properties which can not be achieved through other "naive" uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitary afs.

We present a novel approach to account for preferences in a well known structured argumentation formalism, Assumption-Based Argumentation (ABA). The new formalism, called ABA+, incorporates object-level preferences (over assumptions) directly into the attack relation to reverse attacks. We give several basic desirable properties of ABA+.