Observational Distinguishability of Databases With Object Identity

We will examine the problem of distinguishing between database instances and values in models which incorporate object-identities and recursive data-structures. We will show that the notion of observational distinguishability is intricately linked to the languages available for querying a database. In particular we will show that, given a simple query language incorporating a test for equality of object-identities, database instances are indistinguishable if they are isomorphic, and that, in a language without any operators on object-identities, database instances are indistinguishable if a bisimilarity relation holds between them. Further, such a bisimulation relation may be computed on values, but doing so requires the ability to recurse over all the object-identities in an instance. We will then show that systems of keys give rise to observational distinguishability relations which lie between these two extremes. We show that a system of keys satisfying certain restrictions provides us with an efficient means of comparing values, while avoiding the need to compare object identities directly.