In this paper we introduce dialectical frameworks, a powerful generalization of Dung-style argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes within a single framework. We show that Dung’s standard semantics can be generalized to dialectical frameworks, in case of stable and preferred semantics to a slightly restricted class which we call bipolar frameworks. We show how acceptance conditions can be conveniently represented using weights respectively priorities on the links and demonstrate how some of the legal proof standards can be modeled based on this idea.

This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of con-flict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic ap-proaches to argumentation. We conclude by arguing that ASPIC+’s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung’s framework and its extensions to accommodate preferences.

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one storybased. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence of an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore a hybrid approach is proposed and formally developed, doing justice to both the argumentbased and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases.

Carneades is a recently proposed formalism for structured argumentation with varying proof standards. An open question is its relation with Dung’s seminal abstract approach to argumentation. this paper the two formalisms are formally related by translating Carneades into ASPIC +, another recently proposed formalism for structured argumentation. Since ASPIC + is defined to generate Dungstyle abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. It is proven that Carneades always induces a unique Dung extension, which is the same in all of Dung’s semantics. 1

Abstract. Equivalence between two argumentation systems means mainly that the two systems return the same outputs. It can be used for different purposes, namely in order to show whether two systems that are built over the same knowl-edge base but with distinct attack relations return the same outputs, and more importantly to check whether an infinite system can be reduced into a finite one. Recently, the equivalence between abstract argumentation systems was investi-gated. Two categories of equivalence criteria were particularly proposed. The first category compares directly the outputs of the two systems (e.g. their extensions) while the second compares the outputs of their extended versions (i.e. the sys-tems augmented by the same set of arguments). It was shown that only identical systems are equivalent w.r.t. those criteria. In this paper, we study when two logic-based argumentation systems are equiva-lent. We refine existing criteria by considering the internal structure of arguments and propose new ones. Then, we identify cases where two systems are equivalent. In particular, we show that under some reasonable conditions on the logic under-lying an argumentation system, the latter has an equivalent finite subsystem. This subsystem constitutes a threshold under which arguments of the system have not yet attained their final status and consequently adding a new argument may result in status change. From that threshold, the statuses of all arguments become stable. 1

In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [8] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming. We believe the results of this paper are not only relevant by themselves, but can also potentially be used for future work on the correspondence between argumentation and logic programming semantics.

The ASPIC+ framework is intermediate in abstraction between Dung’s argumentation framework and concrete instantiating logics. This paper generalises ASPIC+ to accommodate classical logic instantiations, and adopts a new proposal for evaluating extensions: attacks are used to define the notion of conflict-free sets, while the defeats obtained by applying preferences to attacks, are exclusively used to determine the acceptability of arguments. Key properties and rationality postulates are then shown to hold for the new framework.

Since the 1980s, computer science, especially artificial intelligence (AI) has developed formal models of many aspects of argumentation that since the work of Toulmin and Perelman were thought of as belonging to informal logic. Doug Walton is one of the argumentation theorists who has recognised the relevance of this body of work for argumentation

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In this paper we offer an account of reasoning with legal cases in terms of argumentation schemes. These schemes, and undercutting attacks associated with them, are expressed as defeasible rules of inference that will lend themselves to formalisation within the AS-PIC+ framework. We begin by modelling the style of reasoning with cases developed by Aleven and Ashley in the CATO project, which describes cases using factors, and then extend the account to accommodate the dimensions used in Rissland and Ashley’s earlier HYPO project. Some additional scope for argumentation is then identified and formalised. 1.