On the Acceptability Semantics of Argumentation Frameworks with Recursive Attack and Support

Credulous acceptance in high-order argumentation frameworks with necessities: An incremental approach

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.

We propose a logical encoding of extended abstract argumentation frameworks, that is frameworks with higher-order attacks (i.e. attacks whose targets are other attacks). Our purpose is to separate the logical expression of the meaning of an attack (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung's argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung's frameworks, enabling to recover standard extensions.

The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dung's argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user.

Argumentative reasoning and taxonomic analysis for the identification of medical errors

This paper reconsiders Modgil's Extended Argumentation Frameworks EAFs that extend Dung's abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative but equivalent characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.

An abstract framework for structured arguments is presented, which instantiates Dung's (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games’, Artificial Intelligence, 77, 321–357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog.

Argument-based reasoning offers promising interaction and computation mechanisms for multi-agent negotiation and deliberation. Arguments in this context are typically statements of beliefs or actions related to agents' subjective values, preferences and so on. Consequences of such arguments can and should be evaluated using various criteria, and therefore it is desirable that semantics supports these criteria as principles for accepting arguments. This article gives an instance of Dung's abstract argumentation framework to deal with Pareto optimality, i.e. a fundamental criterion for social welfare. We show that the instance allows Dung's acceptability semantics to interpret Pareto optimal arguments, without loss of generality. We discuss the prospects of justified Pareto optimal arguments and Pareto optimal extensions.

Value-based argumentation framework built from prioritized qualitative choice logic

In this paper we further progress the analysis of the recently introduced multi-valued argumentation frameworks (MVAFs). MVAFs are an extension of Dung's abstract argumentation, where arguments have a degree of truth associated with them. Here we describe a list of properties of MVAFs considering the major multi-valued logics such as those proposed by Gödel, Zadeh and Łukasiewicz. We then propose a computational framework that joins multi-valued and probabilistic argumentation frameworks to handle situations where arguments affected by vagueness and/or probabilities coexist. The findings are a contribution to the field of non-monotonic approximate reasoning and they also represent a well-grounded proposal towards the introduction of gradualism in argumentation systems.

In this paper, we investigate the revision issue for Dung argumentation frameworks. The main idea is that such frameworks can be translated into propositional formulae, allowing the use of propositional revision operators to perform a rational minimal change. Our translation-based approach to revising argumentation frameworks can take advantage of any propositional revision operator ∘. Via a translation, each propositional operator ∘ can be associated with some revision operators ⋆ suited to argumentation frameworks. Some rationality postulates for the ⋆ operators are presented. If the revision formulae are restricted to formulae about acceptance statuses, some ⋆ operators satisfy these postulates provided that the corresponding ∘ operator is AGM.

Claim-augmented argumentation frameworks (CAFs) constitute a generic formalism for conflict resolution of conclusion-oriented problems in argumentation. CAFs extend Dung argumentation frameworks (AFs) by assigning a claim to each argument. So far, semantics for CAFs are defined with respect to the underlying AF by interpreting the extensions of the respective AF semantics in terms of the claims of the accepted arguments; we refer to them as inherited semantics of CAFs.<br>A central concept of many argumentation semantics is maximization, which can be done with respect to arguments as in preferred semantics, or with respect to the range as in semi-stable semantics. However, common instantiations of argumentation frameworks require maximality on the claim-level and inherited semantics often fail to provide maximal claim-sets even if the underlying AF semantics yields maximal argument sets. To address this issue, we investigate a different approach and introduce claim-level semantics (cl-semantics) for CAFs where maximization is performed on the claim-level. We compare these two approaches for five prominent semantics (preferred, naive, stable, semi-stable, and stage) and relate in total eleven CAF semantics to each other. Moreover, we show that for a certain subclass of CAFs, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the remaining semantics. We furthermore investigate a recently established translation between well-formed CAFs and SETAFs and show that, in contrast to the inherited naive, semi-stable and stage semantics, the cl-semantics correspond to the respective SETAF semantics. Finally, we investigate the expressiveness of the considered semantics in terms of their signatures.

The paper presents a study of abstract argumentation theory from the point of view of modal logic. The key thesis upon which the paper builds is that argumentation frameworks can be studied as Kripke frames. This simple observation allows us to import a number of techniques and results from modal logic to argumentation theory, and opens up new interesting avenues for further research. The paper gives a glimpse of the sort of techniques that can be imported, discussing complete calculi for argumentation, adequate model-checking and bisimulation games, and sketches an agenda for future research at the interface of modal logic and argumentation theory.

In argumentation theory, some reasoning problems involve the enumeration of all extensions of an abstract argumentation framework. Abstractly speaking, extensions are simply subsets of a given domain having some special properties. The result of the enumeration is usually presented as a single text file with elements and sets separated by designated delimiters. Neither the elements within each set (a single extension), nor the extensions themselves are presented in any pre-defined order. Events such as the International Competition of Computational Models of Argumentation require the comparison of a large number of enumerations and thus performing the comparisons very efficiently has become very desirable. This paper presents and compares three different alternative representations of extensions, one of which is novel for the argumentation domain, and provides an empirical evaluation of their effectiveness in the comparison of large enumerations. We found that the newly proposed representation can perform the comparisons in a much more memory and time efficient manner than existing solutions.

In this paper we propose a labelling based dialogue game for determining whether a single argument within a Dung argumentation framework is skeptically preferred. Our game consists of two phases, and determines the membership of a single argument within the extension, assuming optimal play by dialogue participants. In the first phase, one player attempts to advance arguments to construct an extension not containing the argument under consideration, while the second phase verifies that the extension is indeed a preferred one. Correctness within this basic game requires perfect play by both players, and we therefore also introduce an overarching game to overcome this limitation.