A query-based approach to ontologies using the theory of institutions

• Main Author: Pokrywczynski, Daniel
• Published: University of Liverpool 2010
• Subjects: 006.3
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.539530

In recent years we can observe an increasing interest in using ontologies in different branches of science and commerce. This includes disciplines like medicine, bio-informatics,the semantic web, artificial intelligence, and software engineering, to name a few. The need to use ontologies in new and evolving applications requires ontologies to evolve. Typical modifications of ontologies include extending an ontology with new axioms, extracting a module (by which we mean a self-sufficient part), and merging two ontologies together. While performing these operations one usually wants to know whether the semantics of the ontologies are, in some sense, preserved. As the number of ontology applications grew, so did the number of formalisms for ontology formulation. But this increasing number of ontology languages, while helping to develop ontologies and answering the various needs of users, turned out to be a potential source of problems as well. This becomes evident when one is working with multiple ontologies. For instance, when merging two ontologies one not only has to make sure that unwanted consequences are not entailed as a result of this operation but one may also have to solve the problem of these ontologies being given in different formalisms. Even within one formal language, different ontologies may use different vocabularies. Again, different vocabularies make ontologies difficult to use together. Similar problems arise when one wants to compare two ontologies or use an ontology to answer a query that may be given in different formalisms, or that may use different vocabularies. In the literature, modularity of ontologies, extending, merging and comparing ontologies have received a lot of attention, but usually these problems are considered within one formalism only. On the other hand the problem of comparing and combining ontologies formulated in distinct formalisms has not yet been deeply analysed. 'In our work we consider the issues of querying, merging and comparing ontologies in a more general way. In particular, we investigate how one can query an ontology if the query and the ontology are formulated in different formalisms and possibly different vocabularies. We research how to compare and how to merge ontologies if they are formulated in distinct formalisms and vocabularies. To make this possible we start by presenting an abstract view on ontologies; instead of focusing on the axioms inside the ontology, in our approach we lookat its consequences within certain query languages. Then we use the theory of institutions to define the consequence relation in a way that does not depend on a particular formal language. Thanks to that ontologies and queries do not have to be formulated in the same, formal language anymore; moreover, 'the ontology and the query may be formulated with the use of different vocabularies. This provides the first steps towards a formalism that allows us to compare and combine arbitrary ontologies. As the next step we introduce a structure which allows us to work with multiple ontologies, and we formulate the notions of entailment and inseparability of ontologies relative to a 'signature of interest in a way that does not depend on a particular formalism. This structure allows us to compare and combine arbitrary ontologies. Furthermore, we show how an abstract description logic can be extended to a description logic with individuals in a systematic and uniform way. We also investigate the relations between description logics and their counterparts with individuals. Thanks to that we areable to use ontologies together with sets of assertion (ABoxes) to answer queries about individuals. Again, we provide a structure allowing for answering queries about individuals originally formulated in a different formal language than the ontology and the ABox, we assume that ABoxes and ontologies are formulated in the same language. We also present a formulation of entailment and inseparability of ontologies based on instance checking as the one based on subsumption is not strong enough if we consider ontologies together with ABoxes. This formulation is also presented in a way that does not depend on a particular formal language. Finally, we investigate the problem of entailment with respect to some vocabulary E formulated in the lightweight description logic £GSf and prove that the corresponding decision problem is ExPTiME-complete. This extends the result presented by Lutz and Wolter [611 for description logic £G.