Extension of the Relational Algebra to Probabilistic Complex Values

We present a probabilistic data model for complex values. More precisely, we introduce probabilistic complex value relations, which combine the concept of probabilistic relations with the idea of complex values in a uniform framework. We then define an algebra for querying database instances, which comprises the operations of selection, projection, renaming, join, Cartesian product, union, intersection, and difference. We finally show that most of the query equivalences of classical relational algebra carry over to our algebra on probabilistic complex value relations. Hence, query optimization techniques for classical relational algebra can easily be applied to optimize queries on probabilistic complex value relations.