Probabilistic Abstract Argumentation Research Articles

Credulous and skeptical acceptability in probabilistic abstract argumentation: complexity results

Credulous and skeptical acceptability in probabilistic abstract argumentation: complexity results

Complexity of fundamental problems in probabilistic abstract argumentation: Beyond independence

The complexity of the probabilistic counterparts of the classical verification and acceptance problems is investigated over probabilistic Abstract Argumentation Frameworks (prAAFs), in a setting more general than that considered in the current literature, where the complexity has been characterized only under the assumption of independence between arguments/defeats. The complexity of the problems is shown to range from FP to FP#P-complete, with FP‖NP-complete cases, depending on the semantics of the extensions, the representation paradigm used for encoding the prAAF, and the imposed correlations between arguments/defeats, thus providing a thorough analysis of the sensitivity to several aspects. In this regard, in order to allow the study of the impact of different forms of correlations between arguments/defeats on the complexity, a new form of prAAF is introduced, called gen. It is based on the well-known paradigm of world-set descriptors and world-set sets for representing probabilities, and it allows the correlations to be easily and explicitly expressed. Interestingly, the introduction of gen is shown to be also a standalone contribution as a powerful representation paradigm for prAAFs, owing to its high expressiveness, compactness, and the possibility to support user-friendly mechanisms for defining correlations.

On the Complexity of Probabilistic Abstract Argumentation Frameworks

Probabilistic abstract argumentation combines Dung’s abstract argumentation framework with probability theory in order to model uncertainty in argumentation. In this setting, we address the fundamental problem of computing the probability that a set of arguments is an extension according to a given semantics. We focus on the most popular semantics (i.e., admissible , stable , complete , grounded , preferred , ideal-set , ideal , stage , and semistable ) and show the following dichotomy result: computing the probability that a set of arguments is an extension is either FP or FP # P -complete depending on the semantics adopted. Our polynomial-time results are particularly interesting, as they hold for some semantics for which no polynomial-time technique was known so far.

Probabilistic abstract argumentation: an investigation with Boltzmann machines

Probabilistic argumentation and neuro-argumentative systems offer new computational perspectives for the theory and applications of argumentation, but their principled construction involves two entangled problems. On the one hand, probabilistic argumentation aims at combining the quantitative uncertainty addressed by probability theory with the qualitative uncertainty of argumentation, but probabilistic dependences amongst arguments as well as learning are usually neglected. On the other hand, neuro-argumentative systems offer the opportunity to couple the computational advantages of learning and massive parallel computation from neural networks with argumentative reasoning and explanatory abilities, but the relation of probabilistic argumentation frameworks with these systems has been ignored so far. Towards the construction of neuro-argumentative systems based on probabilistic argumentation, we associate a model of abstract argumentation and the graphical model of Boltzmann machines (BMs) in order to (i...