© The Author, 2005. Published by Oxford University Press. All rights reserved.
Original Articles |
A Theory of Local Set Queries
1 Massey University, Information Science Research Centre, Private Bag 11222, Palmerston North, New Zealand. Email: k.d.schewe{at}massey.ac.nz, 2 Massey University, Information Science Research Centre, Private Box 756, Wellington, New Zealand. Email: j.m.turull{at}massey.ac.nz
A relational database can be considered as a finite structure for a finite relational signature in first-order logic. This allows finite model theory to be used for investigating database theory. However, database research in the last decade has shifted its emphasis from the relational datamodel to higher-order datamodels including object oriented databases, object-relational databases, and most recently the model of semi-structured data and XML. A common characteristic of these new datamodels of interest is their richness in structure. In order to find a suitable generalisation of database theory that can cope with this structural richness a suitable logical ground is needed.
In this paper local set theory, which can be considered as a version of higher-order intuitionistic logic, is investigated for this purpose. The central notions of database schema and instance for a slighly restricted class of higher-order datamodels are re-defined in local languages using a finite set interpretation. Terms of "set type" define simple queries, which provide the analogue of relational calculus queries in the relational model.
Then the work on computable queries can be generalised as well. An analogue of the reflective relational machine model called LQ machine is defined and proven to be complete, i.e., able to express exactly the computable queries over local languages. Finally, fixed-point operators are added to simple queries. However, adding fixed-points will not increase expressiveness.
Received June 30, 2004.