First-Order Logic Characterization of Program Properties

A program is rst-order reducible (FO-reducible) with respect to (wrt) a set of integrity constraints if there exists a rst-order theory T such that the set of models for T is exactly the set of intended models for the program wrt all possible EDB's. In this case, we say that P is FO-reducible to T wrt IC. For FO-reducible programs, it is possible to characterize, using rst-order logic implications, properties of programs that are related to all possible EDB's as in the database context. These properties include, among others, containment of programs, independence of updates wrt queries and integrity constraints, and characterization and implication of integrity constraints in programs, all of which have no known proof procedures. Therefore, many important problems formalized in a non-standard logic can be dealt with using the rich reservoir of rst-order theorem-proving tools, provided that the program is FO-reducible. The following classes of programs are shown to be FO-reducible. (1) A stratiied acyclic program P is FO-reducible to comp(P) IC wrt IC for any set IC of constraints; (2) a general chained program P is FO-reducible to comp(P) IC wrt certain acyclicity constraints IC; (3) a bounded program P is FO-reducible to comp(P 0)IC wrt any set IC of constraints, where P 0 is a non-recursive program equivalent to P. Some heuristics for constructing FO-reducible programs are described.