Argumentation is an important research area in the field of AI. There is a substantial amount of work on different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are: i) extending the framework to account for recursive attacks and supports, and ii) considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on High-Order Argumentation Frameworks with Necessities (HOAFNs) which allow for attack and support relations (interpreted as necessity) not only between arguments but also targeting attacks and supports at any level. We propose an approach for the incremental evaluation of the credulous acceptance problem in HOAFNs, by “incrementally” computing an extension (a set of accepted arguments, attacks and supports), if it exists, containing a given goal element in an updated HOAFN. In particular, we are interested in monitoring the credulous acceptance of a given argument, attack or support (goal) in an evolving HOAFN. Thus, our approach assumes to have a HOAFN Δ, a goal ϱ occurring in Δ, an extension E for Δ containing ϱ, and an update u establishing some changes in the original HOAFN, and uses the extension for first checking whether the update is relevant; for relevant updates, an extension of the updated HOAFN containing the goal is computed by translating the problem to the AF domain and leveraging on AF solvers. We provide formal results for our incremental approach and empirically show that it outperforms the evaluation from scratch of the credulous acceptance problem for an updated HOAFN.

In enthymeme-based dialogues, involved participants create assumptions in order to decode arguments from the exchanged enthymemes. This work introduces the concept of assumptions operator, which formalizes the mechanism for generating these assumptions, and proposes a set of principles to guide the construction of these operators. Said principles are inspired by Grice’s Maxims of Conversation, as well as Govier’s ARG conditions for cogent arguments. Then, in order to analyze how the used operator influences the dialogue and how that dialogue differs from the one in which the original argument is sent, we propose a framework to compare both scenarios, the former being the enthymemic one and the latter the complete one. Finally, we formally show that if the used assumptions operator complies with a set of the aforementioned principles, then most arguments in the complete dialogue have their counterpart in the enthymemic one. Furthermore, we show that under certain conditions, the enthymemic dialogue preserves some semantic properties from the complete one, specifically: conflict-freeness, acceptability and admissibility.

Arguments in argumentation systems cannot always be considered as standalone entities, requiring the consideration of the pieces of evidence they rely on. This evidence might have to be retrieved from external sources such as databases or the web, and each attempt to retrieve a piece of evidence comes with an associated cost. Moreover, a piece of evidence may be available in a given scenario but not in others, and this is not known beforehand. As a result, the collection of active arguments (whose entire set of evidence is available) that can be used by the argumentation machinery of the system may vary from one scenario to another. In this work, we consider an Abstract Argumentation Framework with Fallible Evidence that accounts for these issues, and propose a heuristic measure used as part of the acceptability calculus (specifically, for building pruned dialectical trees) with the aim of minimizing the evidence retrieval cost of the arguments involved in the reasoning process. We provide an algorithmic solution that is empirically tested against two baselines and formally show the correctness of our approach.

Argumentation is an important topic in the field of AI. There is a substantial amount of work about different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are extending the framework to account for recursive attacks and supports, and considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on Attack-Support Argumentation Frameworks (ASAFs) which allow for attack and support relations not only between arguments but also targeting attacks and supports at any level, and propose an approach for the incremental computation of extensions (sets of accepted arguments, attacks and supports) of updated ASAFs. Our approach assumes that an initial ASAF extension is given and uses it for first checking whether updates are irrelevant; for relevant updates, an extension of an updated ASAF is computed by translating the problem to the AF domain and leveraging on AF solvers. We experimentally show our incremental approach outperforms the direct computation of extensions for updated ASAFs.

The Attack-Support Argumentation Framework (ASAF) is an abstract argumentation framework that provides a unified setting for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. Currently, the extensions of the ASAF are obtained by translating it into a Dung's Argumentation Framework (AF). In this work we provide the ASAF with the ability of determining its extensions without requiring such a translation. We follow an extension-based approach for characterizing the acceptability semantics directly on the ASAF, considering the complete, preferred, stable and grounded semantics. Finally, we show that the proposed characterization satisfies different results from Dung's argumentation theory.