First-order logic characterization of program properties

Abstract

A program is first-order reducible (FO-reducible) w.r.t. a set IC of integrity constraints if there exists a first-order theory T such that the set of models for T is exactly the set of intended models for the program w.r.t. all possible EDB's. In this case, we say that P is FO-reducible to T w.r.t. IC. For FO-reducible programs, it is possible to characterize, using first-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 w.r.t. 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 nonstandard logic can be dealt with by using the rich reservoir of first-order theorem-proving tools, provided that the program is FO-reducible. The following classes of programs are shown to be FO-reducible. (1) A stratified acyclic program P is FO-reducible to comp(P)qqIC w.r.t. IC for any set IC of constraints; (2) a general chained program P is FO-reducible to comp(P)qqIC w.r.t. certain acyclicity constraints IC; (3) a bounded program P is FO-reducible to comp(P′)qqIC w.r.t. any set IC of constraints, where P′ is a nonrecursive program equivalent to P. Some heuristics for constructing FO-reducible programs are described.