Toward Measuring Knowledge Loss due to Ontology Modularization

Abstract

This paper formalizes the graphical modularization technique, View Traversal, for an ontology-based system represented using the Domain Information System (DIS). Our work is motivated by the need for autonomous agents, within an ontology-based system, to automatically create their own views of the ontology to address the problems of ontology evolution and data integration found in an enterprise setting. Through DIS, we explore specific ontologies that give Cartesian perspectives of the domain, which allows modularization to be a means for agents to extract views of specific combinations of data. The theory of ideals from Boolean algebra is used to formalize a module. Then, with the use of homomorphisms, the quantity of knowledge within the module can be measured. More specifically, through the first isomorphism theorem, we establish that the loss of information is quantified by the kernel of the homomorphism. This constitutes a foundational step towards theories related to reasoning on partial domain knowledge, and is important for applications where an agent needs to quickly extract a view that contains a specific set of knowledge.