A Framework for Conditioning Uncertain Relational Data

Abstract

We propose a framework for representing conditioned probabilistic relational data. In this framework the existence of tuples in possible worlds is determined by Boolean expressions composed from elementary events. The probability of a possible world is computed from the probabilities associated with these elementary events. In addition, a set of global constraints conditions the database. Conditioning is the formalization of the process of adding knowledge to a database. Some worlds may be impossible given the constraints and the probabilities of possible worlds are accordingly re-defined. The new constraints can come from the observation of the existence or non-existence of a tuple, from the knowledge of a specific rule, such as the existence of an exclusive set of tuples, or from the knowledge of a general rule, such as a functional dependency. We are therefore interested in computing a concise representation of the possible worlds and their respective probabilities after the addition of new constraints, namely an equivalent probabilistic database instance without constraints after conditioning. We devise and present a general algorithm for this computation. Unfortunately, the general problem involves the simplification of general Boolean expressions and is NP-hard. We therefore identify specific practical families of constraints for which we devise and present efficient algorithms.