Formalizing Graphical Modularization Approaches for Ontologies and the Knowledge Loss

This paper formalizes the graphical modularization technique view traversal for an ontology component of a Domain Information System (DIS). Our work is motivated by developing the ability to dynamically extract a module (called a view traversal module) based on an initial set of concepts. We show how the ability to quantify the knowledge that is preserved (or lost) in a view traversal module is significant for a multi-agent setting, which is a setting that requires provable privacy. To ensure partial knowledge preservation, we extend the view traversal module to a principal ideal subalgebra module. The cost of this extension is that the obtained knowledge is coarser, as the atoms of the associated lattice are composite yet considered atomic. The presented work constitutes a foundational step towards theories related to reasoning on partial domain knowledge.