ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of another well-known formalism combining symbolic reasoning and reasoning under uncertainty, i.e. probabilistic argumentation. Specifically, we show that ProbLog is an instance of a form of Probabilistic Abstract Argumentation (PAA) that builds upon Assumption-Based Argumentation (ABA). The connections pave the way towards equipping ProbLog with alternative semantics, inherited from PAA/PABA, as well as obtaining novel argumentation semantics for PAA/PABA, leveraging on prior connections between ProbLog and argumentation. Further, the connections pave the way towards novel forms of argumentative explanations for ProbLog's outputs.

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 retrieve (by derivation) multiple statements (sometimes assumed) or results from the literature.

In existing literature, while approximate approaches based on Monte-Carlo simulation technique have been proposed to compute the semantics of probabilistic argumentation, how to improve the efficiency of computation without using simulation technique is still an open problem. In this paper, we address this problem from the following two perspectives. First, conceptually, we define specific properties to characterize the subgraphs of a PrAG with respect to a given extension, such that the probability of a set of arguments E being an extension can be defined in terms of these properties, without (or with less) construction of subgraphs. Second, computationally, we take preferred semantics as an example, and develop algorithms to evaluate the efficiency of our approach. The results show that our approach not only dramatically decreases the time for computing p(E^\sigma), but also has an attractive property, which is contrary to that of existing approaches: the denser the edges of a PrAG are or the bigger the size of a given extension E is, the more efficient our approach computes p(E^\sigma). Meanwhile, it is shown that under complete and preferred semantics, the problems of determining p(E^\sigma) are fixed-parameter tractable.