Implication and axiomatization of functional and constant constraints

Abstract

Akhtar et al. introduced equality-generating constraints and functional constraints as a first step towards dependency-like integrity constraints for RDF data [3]. Here, we focus on functional constraints. Since the usefulness of functional constraints is not limited to the RDF data model, we study the functional constraints in the more general setting of relations with arbitrary arity. We further introduce constant constraints and study the functional and constant constraints combined. Our main results are sound and complete axiomatizations for the functional and constant constraints, both separately and combined. These axiomatizations are derived using the chase algorithm for equality-generating constraints. For derivations of constant constraints, we show how every chase step can be simulated by a bounded number of applications of inference rules. For derivations of functional constraints, we show that the chase algorithm can be normalized to a more specialized symmetry-preserving chase algorithm performing so-called symmetry-preserving steps. We then show how each symmetry-preserving step can be simulated by a bounded number of applications of inference rules. The axiomatization for functional constraints is in particular applicable to the RDF data model, solving a major open problem of Akhtar et al.