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We formulate discussion graph semantics of first-order logic with equality for reasoning about discussion and argumentation as naturally as we would reason about sentences. While there are a few existing proposals to use a formal logic for reasoning about argumentation, they are constructed bottom-up and specialised to the argumentation model by Dung. There is indeed a conspicuous lack of a formal reasoning framework for handling general discussion and argumentation models. We achieve the generality through a top-down formulation of the semantics of first-order logic (with equality) formulas, addressing the current shortage.

This volume contains revised versions of the papers selected for the third volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

Argumentation is a human-like reasoning mechanism contributing to the formalization of commonsense reasoning. In the last decade, several argument-based formalisms have emerged, with application in many areas, such as legal reasoning, autonomous agents and multi-agent systems; many are based on Dung's seminal work characterizing Abstract Argumentation Frameworks (AF). Recent research in the area has led to Temporal Argumentation Frameworks (TAF) that extend Dung's by considering the temporal availability of arguments. In this work we introduce a novel framework, called Extended Temporal Argumentation Framework (E-TAF), extending TAF with the capability of modeling availability of attacks among arguments, which allows for instance to model reliability of arguments varying over time. We show how E-TAF can be enriched by considering Structured Abstract Argumentation, adding compositional elements to the abstract arguments involved based on a simplified version of the recently introduced Dynamic Argumentation Frameworks.

This volume contains revised versions of the papers selected for the first volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

The Agile Robotics for Industrial Automation Competition (ARIAC) is an annual simulation-based competition initiated in 2017. The competition challenges teams to design industrial robotic system control code to function in a dynamic environment. Each team’s system is faced with challenges such as dropped parts, and must address these challenges and continue to function without operator intervention.

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.

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 Dung's 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.

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been pro- posed independently, often associated with some desirable properties. However, there is no comparative study which takes a broader perspective. This is what we propose in this work. We provide a general comparison of all these semantics with respect to the proposed proper- ties. That allows to underline the differences of behavior between the existing semantics.

The adoption of a generic contrariness notion in ASPIC+ substantially enhances its expressiveness with respect to other formalisms for structured argumentation. In particular, it opens the way to novel investigation directions, like the use of multivalued logics in the construction of arguments. This paper points out however that in the current version of ASPIC+ a serious technical difficulty related with generic contrariness is present. With the aim of preserving the same level of generality, the paper provides a solution based on a novel notion of closure of the contrariness relation at the level of sets of formulas and an abstract representation of conflicts between sets of arguments. The proposed solution is shown to satisfy the same rationality postulates as ASPIC+ and represents a starting point for further technical and conceptual developments in structured argumentation.