A MODEL FOR HISTORICAL DATABASES

Abstract

It is becoming increasingly apparent that we are on the verge of several new technologies that will offer virtually unlimited secondary storage at affordable prices. Database applications can be expected to take advantage of this expanded storage capacity, and a particularly promising area in this regard is the use of so-called "non-deletion" or "historical" databases. It is therefore appropriate to begin exploring formal models f o r these historical databases -- models that are intrinsically oriented toward the storage of data over the course of time, and that provide a formal semantics for the interaction between time and the other stored data items. We present such a model, the Historical Database Model (HDBM), and define its semantics in terms of an underlying logical model. For this purpose we use the language IL-s and its model theory, a simplified version of Richard Montague's higher-order lambda calculus with intensions. The HDBM is defined as an extension of the relational database model, incorporating a distinguished STATE attribute that " time-stamps" the facts recorded in the database. Intuitively such a database can be viewed as a set of three-dimensional relations in the ordinary sense. The formal semantics is defined in terms of objects (the values of keys), which are identified with non-varying or constant entities, and the properties of these objects (the values of non-key attributes), which are identified with individual concepts is the intensional model. Two possible encodings of the database into the logical model are presented and discussed. It is a widely accepted view that first-order logic provides a formalization of the semantics of the relational database model that has helped to clarify many of the issues in relational database theory. We argue that the richer logic IL-s, with its built-in notion of "denotation with respect to a moment of time” and with its capability for naming higher-order objects, is an appropriate vehicle for providing an analogous formal theory of the semantics of an HDB. Finally, we briefly discuss our work using IL-s as a target language for interpreting a natural-language query fragment which we have defined as a Montague Grammar, and point to some interesting topics for further research in the general area of time and databases.