Class Algebra for Ontology Reasoning
  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.
