Sure. Category Theory in Ontology Research Concrete Gain from an Abstract Approach.pdfVIP

Category Theory in Ontology Research: Concrete Gain from an Abstract Approach Markus Krotzsch ¨ Pascal Hitzler Marc Ehrig York Sure Institute AIFB, University of Karlsruhe, Germany; {mak,hitzler,ehrig,sure}@aifb.uni-karlsruhe.de Abstract The focus of research on representing and reasoning with knowl- edge traditionally has been on single specifications 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 specifications 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 knowl- edge. A particular prospect is to derive conclusions from the structure of those distributed knowledge bases, as it is for example needed when merging ontologies. 1 1 The challenge of distributed knowledge bases At first sight, the goals pursued in ontology research appear to be largely the same as in classical research on knowledge representation and reasoning. Indeed, the specification of knowledge and the possibility to automatically draw conclusions from such data is at the heart of many related investi- gations, and the well-known trade-off between semantic expressi