The knowledgebase uncertainty and the argument preferences are considered in this paper. The uncertainty is captured by weighted satisfiability degree, while a preference relation over arguments is derived by the beliefs of an agent.

This manuscript provides the research questions, proposed research plans, as well as expected contributions of my doctoral dissertation. My dissertation is primarily focused on providing computational approaches to study and analyze dialectical reasoning in large-scale online platforms. In particular, I aim to tackle the challenge of developing novel models to automatically classify explanation and argumentation as two different types of reasoning in text of discourse on the Web. The resulting models can be incorporated in the social Web environments to increase participants' awareness of others' reasoning types, which may lead to a more effective dialogue protocol and strategy.

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

In order to emphasize the importance of implemented systems for the field, we also called for system demonstrations; 7 were accepted for the conference, 1 of them associated with a research abstract and 6 of them described in a demonstration extended abstract. At this edition of ICAIL, the Donald H. Berman best student paper award was won by Tran Thi Oanh (Japan Advanced Institute of Science and Technology; JAIST) for the paper entitled "Reference Resolution in Legal Texts" that she wrote with Minh Le Nguyen and Akira Shimazu. Traditionally, ICAIL hosts a lively and varied program of tutorials and workshops. At this conference, there were tutorials covering an introduction to artificial intelligence and law, web ontology and data design, LegalRuleML, and textual information extraction. There were workshops on argumentation, coherence, open and smart data, evidence, e-discovery, e-justice, and network analysis. Also, the international workshop series, Computational Models of Natural Argument, joined ICAIL for its 13th edition (CMNA XIII). The conference was held under the auspices of the Senate of the Italian Republic with as hosting institution the Consiglio Nazionale delle Ricerche (National Research Council of Italy), central unit in Rome. Both AAAI and ACM SIGART were in cooperation. Conference officials were Bart Verheij (program chair), Enrico Francesconi (conference chair), and Anne Gardner (secretary/treasurer).

This paper presents a meta-algorithm for the computation of preferred labellings, based on the general recursive schema for argumentation semantics called SCC-Recursiveness. The idea is to recursively decompose a framework so as to compute semantics labellings on restricted sub-frameworks, in order to reduce the computational effort. The meta-algorithm can be instantiated with a specific "base algorithm", applied to the base case of the recursion, which can be obtained by generalizing existing algorithms in order to compute labellings in restricted sub-frameworks. We devise for this purpose a generalization of a SAT-based algorithm, and provide an empirical investigation to show the significant improvement of performances obtained by exploiting the SCC-recursive schema.

Abstract dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

We contribute to the investigation of possible outcomes of argumentation under semantics formulated using argumentation frameworks (AFs). In particular, we study this question for the labelling-based formulation of such semantics, generalizing previous work which has focused on extensions. In this paper, we restrict attention to the preferred and semi-stable semantics, showing that as long as we have a sufficient number of fresh arguments available, we can in fact argue for anything. That is, for any set of finite labellings there is an AF that enforces exactly this set as the outcome of argumentation.

The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.

The study of extension-based semantics within the seminal abstract argumentation model of Dung has largely focused on definitional, algorithmic and complexity issues. In contrast, matters relating to comparisons of representational limits, in particular, the extent to which given collections of extensions are expressible within the formalism, have been under-developed. As such, little is known concerning conditions under which a candidate set of subsets of arguments are “realistic” in the sense that they correspond to the extensions of some argumentation framework AF for a semantics of interest. In this paper we present a formal basis for examining extension-based semantics in terms of the sets of extensions that these may express within a single AF. We provide a number of characterization theorems which guarantee the existence of AFs whose set of extensions satisfy specific conditions and derive preliminary complexity results for decision problems that require such characterizations.

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. change of their truth values. We describe these operations in a uniform way within a well-known variant of Propositional Dynamic Logic PDL: the Dynamic Logic of Propositional Assignments, DL-PA. The atomic programs of DL-PA are assignments of propositional variables to truth values, and complex programs can be built by means of the connectives of sequential and nondeterministic composition and test. We start by showing that in DL-PA, the construction of extensions can be performed by a DL-PA program that is parametrized by the definition of acceptance. We then mainly focus on how the acceptance of one or more arguments can be enforced and show that this can be achieved by changing the truth values of the propositional variables describing the attack relation in a minimal way.