The relational algebra and calculus do not take the semantics of terms into account when answering queries. As a consequence, not all tuples that should be returned in response to a query are always returned, leading to low recall. In this paper, we propose the novel notion of a constrained probabilistic ontology (CPO). We developed the concept of a CPO-enhanced relation in which each attribute of a relation has an associated CPO. These CPOs describe relationships between terms occurring in the domain of that attribute. We show that the relational algebra can be extended to handle CPO-enhanced relations. This allows queries to yield sets of tuples, each of which has a probability of being correct.