Combining description and similarity logics M. Sheremet, 1 D. Tishkovsky, 2 F. Wolter, 2 and M. Zakharyaschev 1 1 School of Computer Science and 2 Department of Computer Science Information Systems, Birkbeck College University of Liverpool Malet Street, London WC1E 7HX, U.K. Liverpool L69 3BX, U.K. {mikhail,michael}@dcs.bbk.ac.uk {dmitry,frank}@csc.liv.ac.uk Abstract Categorisation of objects into classes is currently supported by (at least) two ‘ortho- gonal’ methods. In logic-based approaches, classifications are defined through ontologies or knowledge bases which describe the existing relationships among terms. Description logic (DL) has become one of the most successful formalisms for representing such know- ledge bases, in particular because theoretically well-founded and efficient reasoning tools have been readily available. In numerical approaches, classifications are obtained by first computing similarity (or proximity) measures between objects and then categorising them into classes by means of Voronoi tessellations, clustering algorithms or nearest neighbour computations, etc. In many areas such as bioinformatics, computational linguistics or medical informatics, these two methods have been used independently of each other: although both of them are often applied to the same domain (and even by the same researcher), up to now no formal interaction mechanism has been developed. In this paper, we propose a DL-based integration of the two classification methods. Our formalism, called SL + ALCQIO, extends the expressive DL ALCQIO by means of constructors which allow definitions of concepts in terms of both comparative and absolute similarity. In the combined knowledge base the user should declare the similarity spaces where the new operators are interpreted. Of course, SL + ALCQIO can only be useful if classifications with this logic are sup- ported by automated reasoning tools. We lay theoretical foundations for the development of such tools by showing that reasoning problems for SL + ALCQIO can be decomposed into the corresponding problems for its DL-part ALCQIO and similarity part SL. Using our new theorem stating that reasoning in SL is ExpTime-complete and a recent complex- ity result of Pratt-Hartmann for ALCQIO, we prove that reasoning in SL + ALCQIO is NExpTime-complete. 1 Introduction Classification — “the actual or ideal arrangement together of those which are like, and the separation of those which are unlike” (see [22, 18] and references therein) — is said to be one of the main objectives of science, the Linnaean taxonomy and the Mendeleev periodic table being probably the best known witnesses. Modern classification and conceptualisation problems in bioinformatics, linguistics or the World Wide Web are characterised by huge numbers of objects to be categorised and/or their very complex structures. Building adequate ‘ontologies’ for such areas and developing powerful tools for dealing with them have been recognised among 1