Publication
Carnap, Goguen, and the Hyperontologies - Logical Pluralism and Heterogeneous Structuring in Ontology Design
Oliver Kutz; Till Mossakowski; Dominik Lücke
In: Jean-Yves Béziau (Hrsg.). Logica Universalis, Vol. 4, No. 2, Pages 255-333, Birkäuser, Basel, 2010.
Abstract
We present a general framework for the design of formal ontologies, resting on two main principles: firstly, we endorse Rudolf Carnap's principle of logical tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall.
The theoretical foundation in institution theory establishes a close link to algebraic specification theory. We explore this link by systematically applying tools and techniques from this area to corresponding ontology structuring and design tasks, in particular employ the structuring mechanisms of the heterogeneous algebraic specification language HetCASL for defining an abstract notion of structured heterogeneous ontology, leading to the idea of a hyperontology, a heterogeneous, distributed, highly modular and structured ontology. This approach enables the designer to split up a heterogeneous ontology into semantically meaningful parts and employ dedicated reasoning tools to them.
Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. The notion of heterogeneous refinement can, in particular, be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies.
Finally, we sketch how different modes of reasoning over ontologies are related to these different structuring aspects.