Class Algebra for Ontology Reasoning

TL;DR

This paper introduces class algebra as a framework for sharing and reasoning about ontologies across diverse data sources, enabling distributed, interoperable, and probabilistic ontology management.

Contribution

It presents a novel class algebra framework that unifies ontology sharing, reasoning, and probabilistic classification across heterogeneous data sources.

Findings

Supports sharing of ISA hierarchies without prior negotiation

Provides a functional link between class definitions and instances

Enables probabilistic reasoning for classification

Abstract

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.