A Model for Historical Databases
54 Pages Posted: 31 Oct 2008
Date Written: November 1982
Abstract
It is becoming increasingly apparent that we are on the verge ofseveral new technologies that will offer virtually unlimitedsecondary storage at affordable prices. Database applicationscan be expected to take advantage of this expanded storagecapacity, and a particularly promising area in this regard isthe use of so-called "non-deletion" or "historical" databases.It is therefore appropriate to begin exploring formal models f o rthese historical databases -- models that are intrinsicallyoriented toward the storage of data over the course of time, andthat provide a formal semantics for the interaction between timeand the other stored data items.We present such a model, the Historical Database Model (HDBM),and define its semantics in terms of an underlying logicalmodel. For this purpose we use the language IL-s and its modeltheory, a simplified version of Richard Montague's higher-orderlambda calculus with intensions. The HDBM is defined as anextension of the relational database model, incorporating adistinguished STATE attribute that " time-stamps" the factsrecorded in the database. Intuitively such a database can beviewed as a set of three-dimensional relations in the ordinary sense. The formal semantics is defined in terms of objects (thevalues of keys), which are identified with non-varying orconstant entities, and the properties of these objects (thevalues of non-key attributes), which are identified withindividual concepts is the intensional model. Two possibleencodings of the database into the logical model are presentedand discussed.It is a widely accepted view that first-order logic provides aformalization of the semantics of the relational database modelthat has helped to clarify many of the issues in relationaldatabase theory. We argue that the richer logic IL-s, with itsbuilt-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.
Keywords: Relational database, entity-relationship model, intensional logic, historical databases, temporal semantics
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