  Knowledge graphs (KG) that model the relationships between entities as labeled edges (or facts) in a graph are mostly constructed using a suite of automated extractors, thereby inherently leading to uncertainty in the extracted facts. Modeling the uncertainty as probabilistic confidence scores results in a probabilistic knowledge graph. Graph queries over such probabilistic KGs require answer computation along with the computation of those result probabilities, aka, probabilistic inference. We propose a system, HAPPI (How Provenance of Probabilistic Inference), to handle such query processing. Complying with the standard provenance semiring model, we propose a novel commutative semiring to symbolically compute the probability of the result of a query. These provenance-polynomiallike symbolic expressions encode fine-grained information about the probability computation process. We leverage this encoding to efficiently compute as well as maintain the probability of results as the underlying KG changes. Focusing on a popular class of conjunctive basic graph pattern queries on the KG, we compare the performance of HAPPI against a possible-world model of computation and a knowledge compilation tool over two large datasets. We also propose an adaptive system that leverages the strengths of both HAPPI and compilation based techniques. Since existing systems for probabilistic databases mostly focus on query computation, they default to re-computation when facts in the KG are updated. HAPPI, on the other hand, does not just perform probabilistic inference and maintain their provenance, but also provides a mechanism to incrementally maintain them as the KG changes. We extend this maintainability as part of our proposed adaptive system. 
Computing and Maintaining Provenance of Query Result Probabilities in   Uncertain Knowledge Graphs