Topicality in Logic-Based Ontologies Chiara Del Vescovo, Bijan Parsia, and Uli Sattler The University of Manchester, Oxford Road, Manchester, M13 9PL, UK {delvescc,bparsia,sattler}@cs.man.ac.uk Abstract In this paper we examine several forms of modularity in logics as a basis for various conceptions of the topical structure of an ontology. Intuitively, a topic is a coherent fragment of the subject matter of the ontology. Different topics may play different roles: e.g., the main topic (or topics), side topics, or subtopics. If, at the lowest level, the subject matter of an ontology is characterized by the set of concepts of the on- tology, a topic is a “coherent” subset of those concepts. Different forms of modularity induce different, more or less cognitively helpful, notions of coherence and thus distinct topical structures. 1 Introduction When formalising a set of concepts in some logic we encounter a variety of structural issues. For example, we look for definitions of concepts in terms of categorizing attributes, that is, for the “internal” structure of our concepts. We also seek to discover “external” relations between concepts, e.g., of subsumption, equivalence, or disjointness. In a logic based knowledge representation system, we can hope that by giving the former, the system can discover the latter. Common such systems are those based on description logic ontologies. On- tologies are (decidable) logical theories describing a shared vocabulary about a domain in terms of a set of concepts plus the relationships between those con- cepts. In notable examples, as SNOMED CT 1 (Systematized Nomenclature of Medicine – Clinical Terms) that contains more than 300, 000 axioms, while the internal structure of any concept may well be intelligible, the large scale struc- ture is not. In particular, the subsumption hierarchy, as a whole, is not particular well suited to guide the interested reader toward a grasp of “what the ontology is about.” All concepts – relevant or irrelevant, well or cursorily described, cen- tral or peripheral – participate, at least vacuously, in the subsumption hierarchy. One could attempt to heuristically organise concepts in the subsumption hierar- chy in some larger grain way so that more strongly related terms were clustered together (e.g., as in [15]). With such a coarse grain structure, one might hope to discern the “main topics” of the ontology, various side topics, as well as topics that are neglected in the formalisation. Unfortunately, such heuristic organisa- tion, even if based on the prior, logic-derived structural aspects of concepts, is not, itself, derived from logical features of the representation. That is, it is not 1 http://www.ihtsdo.org/snomed-ct/