Locally Constrained Ontologies

Abstract

In 2014, Barzdins, Rencis and Sostaks introduced granular ontologies as a specific organization of databases allowing for extremely fast processing of ad hoc queries, and proved the following Granularity Theorem: Consider an ontology represented by graphical means of a UML class diagram. Then, under certain restrictions on association multiplicity constraints, this ontology is granular, if and only if it is a tree ontology. (In a tree ontology, associations and classes form a tree, and have the multiplicity 1..1 in the direction to root class.) The possibility of removing the restrictions was formulated as as open problem. The present paper solves this problem. It appears that the principal cause of the “tree phenomenon” is the local character of ontology constraints expressed by graphical means of UML class diagrams (roughly, each of such constraints involves at most one association). In the paper, properties of locally constrained ontologies (“locality phenomena”) are explored, and Generalized Granularity Theorem is proved, showing that in the Granularity Theorem, all restrictions to multiplicity constraints can be removed.