%0 Generic
%D 2005
%T Category Theory in Ontology Research: Concrete Gain from an Abstract Approach
%A Markus Krotzsch
%A Marc Ehrig
%A York Sure
%X The focus of research on representing and reasoning with knowledge traditionally has been on single speciÃ¯Â¬Âcations and appropriate inference paradigms to draw conclusions from such data. Accordingly, this is also an essential aspect of ontology research which has received much attention in recent years. But ontologies introduce another new challenge based on the distributed nature of most of their applications, which requires to relate heterogeneous ontological speciÃ¯Â¬Âcations and to integrate information from multiple sources. These problems have of course been recognized, but many current approaches still lack the deep formal backgrounds on which todays reasoning paradigms are already founded. Here we propose category theory as a well-explored and very extensive mathematical foundation for modelling distributed knowledge. A particular prospect is to derive conclusions from the structure of those distributed knowledge bases, as it is for example needed when merging ontologies.
%G eng
%0 Conference Paper
%D 2005
%T What Is Ontology Merging? - A Category-Theoretical Perspective Using Pushouts
%A York Sure
%A Markus Krotzsch
%A Marc Ehrig
%A Pascal Hitzler
%X In this paper we explain how merging of ontologies is captured by the pushout construction from category theory, and argue that this is a very natural approach to the problem. We study this independent of a specific choice of ontology representation language, and thus provide a sort of blueprint for the development of algorithms applicable in practice. For this purpose, we view category theory as a universal 'meta specification language' that enables us to specify properties of ontological relationships and constructions in a way that does not depend on any particular implementation. This can be achieved since the basic objects of study in category theory are the relationships between multiple ontological specifications, not the internal structure of a single knowledge representation. Categorical pushouts are already considered in some approaches to ontology research (Jannink et al. 1998; Schorlemmer, Potter, & Robertson 2002; Goguen 2005; Kent 2005) and we do not claim our treatment to be entirely original. Still we have the impression that the potential of category theoretic approaches is by far not exhausted in todays ontology research. For our particular case the treatment will focus on the ontology merging, for which we will give both intuitive explanations and precise definitions. This reflects our belief that, at the current stage of research, it is not desirable to fade out the mathematical details of the categorical approach completely, since the interfaces to current techniques in ontology research are not yet available to their full extent. We will also keep this treatment rather general, not narrowing the discussion to specific formalisms - this added generality is one of the strengths of category theory. A long version of this paper with a tutorial character is available from the first author's homepage.
%I 20th National Conference on Artificial Intelligence, AAAI-05
%G eng