  Uncertain information is being taken into account in an increasing number of
application fields. In the meantime, abduction has been proved a powerful tool
for handling hypothetical reasoning and incomplete knowledge. Probabilistic
logical models are a suitable framework to handle uncertain information, and in
the last decade many probabilistic logical languages have been proposed, as
well as inference and learning systems for them. In the realm of Abductive
Logic Programming (ALP), a variety of proof procedures have been defined as
well. In this paper, we consider a richer logic language, coping with
probabilistic abduction with variables. In particular, we consider an ALP
program enriched with integrity constraints `a la IFF, possibly annotated with
a probability value. We first present the overall abductive language, and its
semantics according to the Distribution Semantics. We then introduce a proof
procedure, obtained by extending one previously presented, and prove its
soundness and completeness.
