Reasing about equations and functional dependencies on complex objects

Abstract

Virtually all semantic or object-oriented data models assume objects have an identity separate from any of their parts, and allows users to define complex object types in which part values may be any other object. This often results in a choice of query language in which a user can express navigating from one object to another by following a property value path.

In this paper, we consider a constraint language in which one may express equations and functional dependencies over complex object types. The language is novel in the sense that component attributes of individual constraints may correspond to property paths. The kind of equations we consider are also important since they are a natural abstraction of the class of conjunctive queries for query languages which support property value navigation. In our introductory comments, we give an example of such a query, and outline two applications of the constraint theory to problems relating to a choice of access plan for the query.

We present a sound and complete axiomatization of the constraint language for the case in which interpretations are permitted to be infinite, where interpretations themselves correspond to a form of directed labeled graph. Although the implication problem for our form of equational constraint alone over arbitrary schema is undecidable, we present decision procedures for the implication problem for both kinds of constraints when the problem scheme satisfies a stratification condition, and when all input functional dependencies are keys.