Strong Admissibility Revisited

Preprin

Some Supplementaries to The Counting Semantics for Abstract Argumentation

Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and non-extensions. In order to reason with a specific semantics, one needs to take a credulous or skeptical approach, i.e. an argument is eventually accepted, if it is accepted in one or all extensions, respectively. In our previous work \cite{ref-pu2015counting}, we have proposed a novel semantics, called \emph{counting semantics}, which allows for a more fine-grained assessment to arguments by counting the number of their respective attackers and defenders based on argument graph and argument game. In this paper, we continue our previous work by presenting some supplementaries about how to choose the damaging factor for the counting semantics, and what relationships with some existing approaches, such as Dung's classical semantics, generic gradual valuations. Lastly, an axiomatic perspective on the ranking semantics induced by our counting semantics are presented.Comment: 8 pages, 3 figures, ICTAI 201

A Two-Phase Dialogue Game for Skeptical Preferred Semantics

Postprin

Games and Argumentation: Time for a Family Reunion!

The rule "defeated(X) $\leftarrow$ attacks(Y,X), $\neg$ defeated(Y)" states that an argument is defeated if it is attacked by an argument that is not defeated. The rule "win(X) $\leftarrow$ move(X,Y), $\neg$ win(Y)" states that in a game a position is won if there is a move to a position that is not won. Both logic rules can be seen as close relatives (even identical twins) and both rules have been at the center of attention at various times in different communities: The first rule lies at the core of argumentation frameworks and has spawned a large family of models and semantics of abstract argumentation. The second rule has played a key role in the quest to find the "right" semantics for logic programs with recursion through negation, and has given rise to the stable and well-founded semantics. Both semantics have been widely studied by the logic programming and nonmonotonic reasoning community. The second rule has also received much attention by the database and finite model theory community, e.g., when studying the expressive power of query languages and fixpoint logics. Although close connections between argumentation frameworks, logic programming, and dialogue games have been known for a long time, the overlap and cross-fertilization between the communities appears to be smaller than one might expect. To this end, we recall some of the key results from database theory in which the win-move query has played a central role, e.g., on normal forms and expressive power of query languages. We introduce some notions that naturally emerge from games and that may provide new perspectives and research opportunities for argumentation frameworks. We discuss how solved query evaluation games reveal how- and why-not provenance of query answers. These techniques can be used to explain how results were derived via the given query, game, or argumentation framework.Comment: Fourth Workshop on Explainable Logic-Based Knowledge Representation (XLoKR), Sept 2, 2023. Rhodes, Greec

Explaining the outcome of knowledge-based systems; a discussion-based approach

Many inferences made in everyday life are only valid in the absence of explicit counter information. This has led to the development of nonmonotonic logics. The kind of reasoning performed by these logics can be difficult to explain to the average end-user of a knowledge based system that implements them. Although the system can still give advice, it is hard for the user to assess the rationale be- hind this advice. In this paper we propose an argumentation approach that enables the advice to be assessed through an interactive dialogue with the system much like the discussion one might have with a col- league. The aim of thie dialogue is for the system to convince the user that the advice is well-founded