Conditioning Probabilistic Relational Data with Referential Constraints

A probabilistic relational database is a compact form of a set of deterministic relational databases (namely, possible worlds), each of which has a probability. In our framework, the existence of tuples is determined by associated Boolean formulae based on elementary events. An estimation, within such a setting, of the probabilities of possible worlds uses a prior probability distribution specified over the elementary events. Direct observations and general knowledge, in the form of constraints, help refining these probabilities, possibly ruling out some possible worlds. More precisely, new constraints can translate the observation of the existence or non-existence of a tuple, the knowledge of a well-defined rule, such as primary key constraint, foreign key constraint, referential constraint, etc. Informally, the process of enforcing knowledge on a probabilistic database, which consists of computing a new subset of valid possible worlds together with their new (conditional) probabilities, is called conditioning. In this paper, we are interested in finding a new probabilistic relational database after conditioning with referential constraints involved. In the most general case, conditioning is intractable. As a result, we restricted our study to probabilistic relational databases in which formulae of tuples are independent events in order to achieve some tractability results. We devise and present polynomial algorithms for conditioning probabilistic relational databases with referential constraints.