© 1990 by British Computer Society
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The Nested Relation Type Model: An Application of Domain Theory to Databases
Department of Computer Science, Birkbeck College, University of London, Malet Street, London WC1E 7HX
To date most previous approaches to incomplete information within the relational model depend on the specific semantics of the null types incorporated into this model. Herein we propose a model for incomplete information in nested relational databases which is independent of the semantics of the null types pertaining to incomplete information. Thus, the proposed model, called the nested relation type (NRT) model, allows, in addition to system-defined null types, user-defined null types. The NRT model extends the nested relational model by incorporating a form of built-in inheritance. This allows us to define a partial order between nester-relations types and a partial order between the data values of these types. By utilizing these partial orders, we define an instance, over a NRT, to be incomplete when its information content may increase. In addition, we define an algebra for the NRT model, called the NRT algebra, which is shown to supersede known algebras for relations with nulls and for nested relations by showing faithfulness to these algebras. We then investigate the monotonicity of the operators of the NRT algebra, which allows us to predict how increasing or decreasing the information content of the instances in the database affects the information content of the user's view, which is constructed from an algebraic expression over the instances in the database. Finally, we enhance the expressive power of the NRT-algebra with a least fixpoint operator in order to allow users to pose recursive queries.
Received April 1989. revised September 1989.
* Department of Computer Science, Birkbeck College, University of London, Malet Street, London WC1E 7HX