  We introduce SMProbLog, a generalization of the probabilistic logic
programming language ProbLog. A ProbLog program defines a distribution over
logic programs by specifying for each clause the probability that it belongs to
a randomly sampled program, and these probabilities are mutually independent.
The semantics of ProbLog is given by the success probability of a query, which
corresponds to the probability that the query succeeds in a randomly sampled
program. It is well-defined when each random sample uniquely determines the
truth values of all logical atoms. Argumentation problems, however, represent
an interesting practical application where this is not always the case.
SMProbLog generalizes the semantics of ProbLog to the setting where multiple
truth assignments are possible for a randomly sampled program, and implements
the corresponding algorithms for both inference and learning tasks. We then
show how this novel framework can be used to reason about probabilistic
argumentation problems. Therefore, the key contribution of this paper are: a
more general semantics for ProbLog programs, its implementation into a
probabilistic programming framework for both inference and parameter learning,
and a novel approach to probabilistic argumentation problems based on such
framework.
