Logical Relevance in Ontologies

Most ontology development environments (ODEs) are term oriented and take a frame-based view of the information in an ontology about a given term. Even tools, such as Protégé 4, designed for axiom oriented development preserve the frame-based view as the central mode of interaction with the ontology. The frame-based approach has a number of advantages—most prominently that it is comfortable to people familiar with object oriented programming languages. However, in expressive languages the frame-based views suffer from being only sensitive to syntactic relations between axioms and terms, thus possibly missing key logical relations. In this paper, we first introduce a semantic notion of relevance between a term and axioms in an ontology, and we investigate the relation of this concept with the inseparability relation based on model Conservative Extensions. Unfortunately, we cannot use model conservativity to detect relevance since it is hard, or even impossible, to decide. Hence, we approximate model conservativity using two notions of modules based on locality, that can be efficiently computed, and provide logical guarantees, e.g. they preserve entailments over a given signature. In particular, we define relevance via Atomic Decomposition, that is a dependency graph showing the logical relations enforced by the two notions of modules between the axioms. We define a suitable labelling that allows us to locate axioms that are relevant for a term in the AD dependency structure. Finally, we describe an interesting consequence of such a view in terms of the models of an ontology.