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)

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework, the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last (...) years. In this paper, we survey approaches that allow to express information like “There may be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future. (shrink)

It is often necessary and reasonable to justify preferences before reasoning from them. Moreover, justifying a preference ordering is reduced to justifying the criterion that produces the ordering. This paper builds on the well-known ASPIC+ formalism to develop a model that integrates justifying qualitative preferences with reasoning from the justified preferences. We first introduce a notion of preference criterion in order to model the way in which preferences are justified by an argumentation framework. We also adapt the notion of argumentation (...) theory to build a sequence of argumentation frameworks, in which an argumentation framework justifies preferences that are to underlie the next framework. That is, in our formalism, preferences become not only an input of an argumentation framework, but also an output of it. This kind of input-output process can be applied in the further steps of argumentation. We also explore some interesting properties of our formalism. (shrink)

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states of a (...) multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication. (shrink)

The principle-based approach is a methodology to classify and analyse argumentation semantics. In this paper we classify seven of the main alternatives for argumentation semantics using a set of new robustness principles. These principles complement Baroni and Giacomin’s original classification and deal with the behaviour of a semantics when the argumentation framework changes due to the addition or removal of an attack between two arguments. We distinguish so-called persistence principles and monotonicity principles, where the former deal with the question of (...) whether a labelling or extension of an argumentation framework under a given semantics persists after a change, and the latter with the question of whether new labellings or extensions are created after a change. We furthermore show in which sense labelling-based and extension-based semantics lead to subtly different principles and results. Our results can be used for choosing a semantics for a particular application, or to guide the search for new argumentation semantics, but they have been used also in the design of algorithms. (shrink)