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 anextensionaccording to a given semantics. We focus on the most popular semantics (i.e.,admissible,stable,complete,grounded,preferred,ideal-set,ideal,stage, andsemistable) and show the following dichotomy result: computing the probability that a set of arguments is an extension is eitherFPorFP^#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.

The problem of extracting consistent information from relational databases violating integrity constraints on numerical data is addressed. In particular, aggregate constraints defined as linear inequalities on aggregate-sum queries on input data are considered. The notion of repair as consistent set of updates at attribute-value level is exploited, and the characterization of several data-complexity issues related to repairing data and computing consistent query answers is provided. Moreover, a method for computing “reasonable” repairs of inconsistent numerical databases is provided, for a restricted but expressive class of aggregate constraints. Several experiments are presented which assess the effectiveness of the proposed approach in real-life application scenarios.

Recently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework Δ can be translated into a logic program P_Δ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of P_Δ. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.

A probabilistic framework for cleaning the data collected by Radio-Frequency IDentification (RFID) tracking systems is introduced. What has to be cleaned is the set of trajectories that are the possible interpretations of the readings: a trajectory in this set is a sequence whose generic element is a location covered by the reader(s) that made the detection at the corresponding time point. The cleaning is guided by integrity constraints and consists of discarding the inconsistent trajectories and assigning to the others a suitable probability of being the actual one. The probabilities are evaluated by adopting probabilistic conditioning that logically consists of the following steps. First, the trajectories are assigned a priori probabilities that rely on the independence assumption between the time points. Then, these probabilities are revised according to the spatio-temporal correlations encoded by the constraints. This is done by conditioning the a priori probability of each trajectory to the event that the constraints are satisfied: this means taking the ratio of this a priori probability to the sum of the a priori probabilities of all the consistent trajectories. Instead of performing these steps by materializing all the trajectories and their a priori probabilities (which is infeasible, owing to the typically huge number of trajectories), our approach exploits a data structure called conditioned trajectory graph (ct-graph) that compactly represents the trajectories and their conditioned probabilities, and an algorithm for efficiently constructing the ct-graph, which progressively builds it while avoiding the construction of components encoding inconsistent trajectories.