Extending Modular Semantics for Bipolar Weighted Argumentation (Technical Report)

Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until recently, convergence of these iterative procedures was not very well understood in cyclic graphs. Mossakowski and Neuhaus recently introduced a unification of different approaches and proved first convergence and divergence results. We build up on this work, simplify and generalize convergence results and complement them with runtime guarantees. As it turns out, there is a tradeoff between semantics' convergence guarantees and their ability to move strength values away from the initial weights. We demonstrate that divergence problems can be avoided without this tradeoff by continuizing semantics. Semantically, we extend the framework with a Duality property that assures a symmetric impact of attack and support relations. We also present a Java implementation of modular semantics and explain the practical usefulness of the theoretical ideas

Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches

In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted, rejected, undecided), adjust their views when 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, removing them or even acknowledging that such removal should happen is more challenging for some of these concepts than for others. 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 by a given person, offering us the possibility to express more than just three agreement states. It is equipped with a wide range of postulates, including those that do not make any restrictions concerning how initial arguments should be viewed, thus potentially being more adequate for handling beliefs of the people that have not fully disclosed their opinions in comparison to 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 cases 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 describe the results of an experiment in which participants judged dialogues in terms of agreement and structure. We compare our findings with the aforementioned assumptions as well as with the constellation and epistemic approaches to probabilistic argumentation and bipolar argumentation