Chance Constraint as a Basis for Probabilistic Query Model

We consider basic principles of probabilistic queries. Decomposition of a generic probabilistic query with conditioning in SQL-like syntax shows that data comparison operators are the only difference to the deterministic case. Any relational algebra operators presume comparison of attribute values. Probabilistic relational algebra operators are not comparable to deterministic ones due to uncertainty factor – they process distribution functions instead of unit values. We argue that chance constraint is a useful principle to build the basic set of binary probabilistic comparison operators (BPCO), the respective probabilistic relational algebra operators and their query syntax for query language implementations. We argue that these BPCO should be based on principles of probability theory. We suggest generic expressions for the BPCO as counterparts for deterministic ones. Comparison of two random variables and a random variable to a scalar are considered. We give examples of BPCO application to uniformly distributed random variables and show how to build more complex probabilistic aggregation operators. One of the main concerns is compatibility of uncertain query processing with query processing in modern deterministic relational databases. The advantage is knowledge continuity for developers and users of uncertain relational databases. With our approach, only addition of a probabilistic threshold to parameters of relational query operations is required for implementation. We demonstrate that the BPCO based on chance constraints maintain consistency of probabilistic query operators with the syntax of deterministic query operators that are common in today’s database industrial query languages like SQL.