1. Argumentation, by considering arguments and their interactions, is a way of reasoning that has proven successful in many contexts, for instance, in multi-agent applications (Carrera & Iglesias,...

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 \rho occurring in Δ, an extension E for Δ containing \rho, 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. (shrink)

solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have...

dialectical frameworks constitute a recent and powerful generalisation of Dung's argumentation frameworks, where the relationship between the arguments can be specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas thus are suitable engines to be (...) employed. In this paper we give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning. (shrink)

Persuasion is an activity that involves one party trying to induce another party to believe something or to do something. It is an important and multifaceted human facility. Obviously, sales and ma...