Class Algebra for Ontology Reasoning
This work addresses the challenge of ontology integration for users handling heterogeneous data from relational, object-oriented, and XML sources, offering a novel approach to avoid negotiation and standardization.
The paper tackles the problem of integrating diverse data sources into a unified ontology without requiring prior standardization, by introducing class algebra, which enables sharing of ISA hierarchies and provides a functional link between class definitions and their instances. This framework facilitates example retrieval and supports theorem proving, while also enabling probabilistic classification through derived Boolean algebras.
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be unioned into one distributed ontology, sharable by all users without the need for prior negotiation or the development of a "standard" ontology for each field. Moreover, class algebra produces a functional correspondence between a class's class algebraic definition (i.e. its "intent") and the set of all instances which satisfy the expression (i.e. its "extent"). The framework thus provides assistance in quickly locating examples and counterexamples of various definitions. This kind of information is very valuable when developing models of the real world, and serves as an invaluable tool assisting in the proof of theorems concerning these class algebra expressions. Finally, the relative frequencies of objects in the ISA hierarchy can produce a useful Boolean algebra of probabilities. The probabilities can be used by traditional information-theoretic classification methodologies to obtain optimal ways of classifying objects in the database.