In dialogical argumentation, it is often assumed that the involved parties will always correctly identify the intended statements posited by each other and realize all of the associated relations, conform to the three acceptability states (accepted, rejected, undecided), adjust their views whenever new and correct information comes in, and that a framework handling only attack relations is sufficient to represent their opinions. Although it is natural to make these assumptions as a starting point for further research, dropping some of them has become quite challenging.Probabilistic argumentation is one of the approaches that can be harnessed for more accurate user modelling. The epistemic approach allows us to represent how much a given argument is believed or disbelieved by a given person, offering us the possibility to express more than just three agreement states. It comes equipped with a wide range of postulates, including those that do not make any restrictions concerning how initial arguments should be viewed. Thus, this approach is potentially more suitable for handling beliefs of the people that have not fully disclosed their opinions or counterarguments with respect to standard Dung's semantics. The constellation approach can be used to represent the views of different people concerning the structure of the framework we are dealing with, including situations in which not all relations are acknowledged or when they are seen differently than intended. Finally, bipolar argumentation frameworks can be used to express both positive and negative relations between arguments.In this paper we will describe the results of an experiment in which participants were asked to judge dialogues in terms of agreement and structure. We will compare our findings with the aforementioned assumptions as well as with the constellation and epistemic approaches to probabilistic argumentation and bipolar argumentation.

This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine-grained alternative to the standard Dung's approaches when it comes to determining the status of a given argument. Furthermore, the flexibility of the epistemic approach allows us to both model the rationale behind the existing semantics as well as completely deviate from them when required. Epistemic graphs can model both attack and support as well as relations that are neither support nor attack. The way other arguments influence a given argument is expressed by the epistemic constraints that can restrict the belief we have in an argument with a varying degree of specificity. The fact that we can specify the rules under which arguments should be evaluated and we can include constraints between unrelated arguments permits the framework to be more context-sensitive. It also allows for better modelling of imperfect agents, which can be important in multi-agent applications.Example 3 (Adapted from [23,24]). The work in [23] has investigated the problem of reinstatement in argumentation using an instantiated theory and preferences. We draw attention to two scenarios considered in the study, concerning weather forecast and car purchase, where each comes in the basic (without the last sentence) and extended (full text) version.The weather forecasting service of the broadcasting company AAA says that it will rain tomorrow. Meanwhile, the forecast service of the broadcasting company BBB says that it will be cloudy tomorrow but that it will not rain. It is also well known that the forecasting service of BBB is more accurate than the one of AAA. However, yesterday the trustworthy newspaper CCC published an article which said that BBB has cut the resources for its weather forecasting service in the past months, thus making it less reliable than in the past.You are planning to buy a second-hand car, and you go to a dealership with BBB, a mechanic whom has been recommended you by a friend. The salesperson AAA shows you a car and says that it needs very little work done to it. BBB says it will require quite a lot of work, because in the past he had to fix several issues in a car of the same model. While you are at the dealership, your friend calls you to tell you that he knows (beyond a shadow of a doubt) that BBB made unnecessary repairs to his car last month.The formal representation of the base (resp. extended) versions of these scenarios is equivalent (we refer to [23,24] for more details). However, the findings show that they are not judged in the same way and suggest that the domain dependent knowledge of the participants has affected their performance of the tasks. This shows the importance of modelling context-sensitivity and allowing an agent to evaluate structurally equivalent graphs differently.

Among the most general structures extending the framework by Dung are the abstract dialectical frameworks (ADFs). They come equipped with various types of semantics, with the most prominent -the labeling-based one -analyzed in the context of computational complexity, signatures, instantiations and software support. This makes the abstract dialectical frameworks valuable tools for argumentation. However, there are fewer results available concerning the relation between the ADFs and other argumentation frameworks. In this paper we would like to address this issue by introducing a number of translations from various formalisms into ADFs. The results of our study show the similarities and differences between them, thus promoting the use and understanding of ADFs. Moreover, our analysis also proves their capability to model many of the existing frameworks, including those that go beyond the attack relation. Finally, translations allow other structures to benefit from the research on ADFs in general and from the existing software in particular. * The author is a member of the Vienna PhD School of Informatics.Let us start with the famous Dung's framework [7], which is based on binary attack. Definition 1 A Dung's abstract argumentation framework (AF) is a pairDefinition 2 Let F = (A, R) be a Dung's framework and X ⊆ A a set of arguments.• the attacker set of X is X − = {a | ∃b ∈ X , aRb}• the discarded set of X is X + = {a | ∃b ∈ X , bRa}.

The aim of this paper is to study the concept of admissibility in abstract dialectical frameworks (ADFs). While admissibility is well-understood in Dung-style frameworks, a generalization to ADFs is not trivial. Indeed, the original proposal turned out to behave unintuitively at certain instances. A recent approach circumvented this problem by using a three-valued concept. In this paper, we propose a novel twovalued approach which more directly follows the original understanding of admissibility. We compare the two approaches and show that they behave differently on certain ADFs. Our results imply that for generalizations of Dung-style frameworks, establishing a precise correspondence between two-valued (i.e. extension-based) and three-value (i.e. labelingbased) characterizations of argumentation semantics is not easy and requires further investigations.

One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.