Syntactical characterization of a subset of domain-independent formulas

Abstract

A domain-independent formula of first-order predicate calculus is a formula whose evaluation in a given interpretation does not change when we add a new constant to the interpretation domain. The formulas used to express queries, integrity constraints or deductive rules in the database field that have an intuitive meaning are domain independent. That is the reason why this class is of great interest in practice. Unfortunately, this class is not decidable, and the problem is to characterize new subclasses, as large as possible, which are decidable. A syntactic characterization of a class of formulas, the Evaluable formulas, which are proved to be domain independent are provided. This class is defined only for function-free formulas. It is also proved that the class of evaluable formulas contains the other classes of syntactically characterized domain-independent formulas usually found in the literature, namely, range-separable formulas and range-restricted formulas. Finally, it is shown that the expressive power of evaluable formulas is the same as that of domain-independent formulas. That is, each domain-independent formula admits an equivalent evaluable one. An important advantage of this characterization is that, to check if a formula is evaluable, it is not necessary to transform it to a normal form, as is the case for range-restricted formulas.