Discovering whether or not two URIs described in Linked Data—in the same or different RDF datasets—refer to the same real-world entity is crucial for building applications that exploit the cross-referencing of open data. A major challenge in data interlinking is to design tools that effectively deal with incomplete and noisy data, and exploit uncertain knowledge. In this paper, we model data interlinking as a reasoning problem with uncertainty. We introduce a probabilistic framework for modelling and reasoning over uncertain RDF facts and rules that is based on the semantics of probabilistic Datalog. We have designed an algorithm, ProbFR, based on this framework. Experiments on real-world datasets have shown the usefulness and effectiveness of our approach for data linkage and disambiguation.