dialectical frameworks have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for (...) ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: whether a given interpretation is a strongly admissible interpretation of a given ADF, and whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs. (shrink)

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)

In informal argument, an essential step is to ask what will “resonate” with a particular audience and hence persuade. Marketers, for example, may recommend a certain colour for a new soda can becau...

In this work, we question the ability of existing ranking-based semantics to capture persuasion settings, emphasising in particular the phenomena of procatalepsis and of fading. Some widely accepted principles of ranking-based semantics are incompatible with a faithful treatment of these phenomena, which means that no existing ranking-based semantics can capture these two principles together. This motivates us to introduce a new parametrized ranking-based semantics based on the notion of propagation which extends the existing propagation semantics 139–150) by adding an additional (...) parameter allowing us to gradually decrease the impact of arguments when the length of the path between two arguments increases. We show that this parameter gives the possibility of choosing if one wants to satisfy the property Void Precedence or not and to control the scope of the impact of the arguments. We also propose an experiment to show that the new semantics remains stable when this parameter varies and an axiomatic evaluation to compare it with existing ranking-based semantics in the literature. (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)

In this work, we question the ability of existing ranking-based semantics to capture persuasion settings, emphasising in particular the phenomena of procatalepsis (the fact that it is often efficient to anticipate the counter-arguments of the audience) and of fading (the fact that long lines of argumentation become ineffective). Some widely accepted principles of ranking-based semantics (like Void Precedence) are incompatible with a faithful treatment of these phenomena, which means that no existing ranking-based semantics can capture these two principles together. This (...) motivates us to introduce a new parametrized ranking-based semantics based on the notion of propagation which extends the existing propagation semantics (In Proceedings of the 6th International Conference on Computational Models of Argument (COMMA’16) (2016) 139–150) by adding an additional parameter allowing us to gradually decrease the impact of arguments when the length of the path between two arguments increases. We show that this parameter gives the possibility of choosing if one wants to satisfy the property Void Precedence or not (and then capture procatalepsis) and to control the scope of the impact of the arguments (and then to capture fading principle). We also propose an experiment to show that the new semantics remains stable when this parameter varies and an axiomatic evaluation to compare it with existing ranking-based semantics in the literature. (shrink)