Towards a Computational Analysis of Probabilistic Argumentation Frameworks

In this paper we analyze probabilistic argumentation frameworks (PAFs), defined as an extension of Dung abstract argumentation frameworks in which each argument n is asserted with a probability p(n). The debate around PAFs has so far centered on their theoretical definition and basic properties. This work contributes to their computational analysis by proposing a first recursive algorithm to compute the probability of acceptance of each argument under grounded and preferred semantics, and by studying the behavior of PAFs with respect to reinstatement, cycles and changes in argument structure. The computational tools proposed may provide strategic information for agents selecting the next step in an open argumentation process and they represent a contribution in the debate about gradualism in abstract argumentation

Graduality in Probabilistic Argumentation Frameworks

Gradual semantics are methods that evaluate overall strengths of individual arguments in graphs. In this paper, we investigate gradual semantics for extended frameworks in which probabilities are used to quantify the uncertainty about arguments and attacks belonging to the graph. We define the likelihoods of an argument’s possible strengths when facing uncertainty about the topology of the argumentation framework. We also define an approach to compare the strengths of arguments in this probabilistic setting. Finally, we propose a method to calculate the overall strength of each argument in the framework, and we evaluate this method against a set of principles

Computing the Grounded Semantics in all the Subgraphs of an Argumentation Framework: an Empirical Evaluation

Given an argumentation framework – with a finite set of arguments and the attack relation identifying the graph – we study how the grounded labelling of a generic argument a varies in all the subgraphs of . Since this is an intractable problem of above-polynomial complexity, we present two non-naïve algorithms to find the set of all the subgraphs where the grounded semantic assigns to argument a specific label . We report the results of a series of empirical tests over graphs of increasing complexity. The value of researching the above problem is two-fold. First, knowing how an argument behaves in all the subgraphs represents strategic information for arguing agents. Second, the algorithms can be applied to the computation of the recently introduced probabilistic argumentation frameworks

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

Gödel Fuzzy Argumentation Frameworks

Acknowledgements This work is supported by the Excellent Young Scholars Research Fund of Shandong Normal University. This research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF-06-3-0001.Publisher PD

A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature

Stratified Labelings for Abstract Argumentation

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions

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