Inference of monotonicity constraints in Datalog programs

Abstract

Datalog (i.e., function-free logic) programs with monotonicity constraints on extensional predicates are considered. A monotonicity constraint states that one argument of a predicate or a constant is always less than another argument or a constant, according to some strict partial order. Relations of an extensional database are required to satisfy the monotonicity constraints imposed on their predicates. More specifically, a strict partial order is defined on the domain (i.e., set of constants) of the database, and every tuple of each relation satisfies the monotonicity constraints imposed on its predicate. This paper focuses on the problem of entailment of monotonicity constraints in the intensional database from monotonicity constraints in the extensional database. The entailment problem is proven to be decidable, based on a suggested algorithm for computing sound and complete disjunctions of monotonicity and equality constraints that hold in the intentional database. It is also shown that the entailment of monotonicity constraints in programs is a complete problem for exponential time. For linear programs, this problem is complete for polynomial space.