Reasoning Under Uncertainty in Knowledge Graphs.

We provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), able to satisfy the requirements of ontological reasoning: full recursion, powerful existential quantification, and the ability to express inductive definitions. Vadalog is based on Warded Datalog+/−, an existential rule language that strikes a good balance between computational complexity: with tractable reasoning in data complexity, and expressive power covering SPARQL under set semantics and the entailment regime for OWL 2 QL. Vadalog and its logical core Warded Datalog+/− are not covered by existing probabilistic programming and statistical relational models for many reasons including weak support for existentials, recursion and the impossibility to express inductive definitions. We introduce Soft Vadalog, a probabilistic extension to Vadalog satisfying these desiderata. It defines a probability distribution over the nodes of a chase network, a structure induced by the grounding of a Soft Vadalog program with the chase procedure.