Abstract
Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared sub-ontologies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Michael Barr and Charles Wells. Category Theory for Computing Science. Prentice Hall, 1990.
Trevor Bench-Capon and Grant Malcolm. Relating ontologies. Draft available at http://www.csc.liv.ac.uk/~grant/ps/, 1999.
Trevor Bench-Capon. The role of ontologies in the verification and validation of knowledge based systems. In R. Wagner, editor, Proceedings of the 9th International Workshop on Database and Expert Systems, pages 64–69. IEEE Press, Los Alamitos, 1998.
Jan A. Bergstra and John V. Tucker. Algebraic specifications of computable and semicomputable data types. Theoretical Computer Science, 50:137–181, 1987.
Rod Burstall and Joseph A. Goguen. The semantics of Clear, a specification language. In Dines Bjorner, editor, Proceedings, 1979 Copenhagen Winter School on Abstract Software Specification, pages 292–332. Springer, 1980. Lecture Notes in Computer Science, Volume 86.
Robert L. Carpenter. The Logic of Typed Feature Structures, volume 32 of Cambridge Tracts in Theoretical Computer Science. Cambridge, 1992.
Corina Cîrstea. A semantical study of the object paradigm. Transfer thesis, Oxford University Computing Laboratory, 1996.
Răzvan Diaconescu and Kokichi Futatsugi. CafeOBJ Report, volume 6 of AMAST Series in Computing. World Scientific, 1998.
Hartmut Ehrig and Bernd Mahr. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Springer, 1985.
Joseph A. Goguen and Rod Burstall. Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery, 39(1):95–146, 1992.
Joseph A. Goguen and Grant Malcolm. Algebraic Semantics of Imperative Programs. MIT Press, 1996.
Joseph A. Goguen and Grant Malcolm. A hidden agenda. Theoretical Computer Science, 1999. To appear.
Joseph A. Goguen and Grant Malcolm. Hidden coinduction: behavioral correctness proofs for objects. Mathematical Structures in Computer Science, 1999. To appear.
Joseph A. Goguen and José Meseguer. Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science, 105(2):217–273, 1992.
Joseph A. Goguen, James Thatcher, and Eric Wagner. An initial algebra approach to the specification, correctness and implementation of abstract data types. In Current Trends in Programming Methodology, IV, Raymond Yeh, editor, Prentice-Hall, 1978, pages 80–149.
Joseph A. Goguen, Timothy Winkler, José Meseguer, Kokichi Futatsugi, and Jean-Pierre Jouannaud. Introducing OBJ. In Joseph A. Goguen and Grant Malcolm, editors, Software Engineering with OBJ: Algebraic Specification in Practice. to appear. Also available as a technical report from SRI International.
Thomas R. Gruber. Towards Principles for the Design of Ontologies Used for Knowledge Sharing. In N. Guarino and R. Poli, editors, Formal Ontology in Conceptual Analysis and Knowledge Representation. Kluwer Academic Publishers, 1993.
Anne E. Haxthausen and Friederike Nickl. Pushouts of order-sorted algebraic specifications. In AMAST’ 96. Springer-Verlag Lecture Notes in Computer Science 1101, 1996.
Gertjan van Heijst, Guus Schreiber, and Bob J. Wielinga. Using explicit ontologies in KBS development. International Journal of Human Computer Interaction, 45:183–192, 1997.
Saunders Mac Lane. Categories for the Working Mathematician, volume 5 of Graduate Texts in Mathematics. Springer Verlag, 1971.
Grant Malcolm. Interconnection of object specifications. In Stephen Goldsack and Stuart Kent, editors, Formal Methods and Object Technology. Springer Workshops in Computing, 1996.
Karl Meinke and John V. Tucker. Universal algebra. In S. Abramsky, D. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 1, pages 189–411. Oxford University Press, 1993.
Mark A. Musen. Automated Generation of Model-Based Knowledge-Acquisition Tools. Research Notes in Artificial Intelligence. Pitman, 1989.
Donald Sannella and Andrzej Tarlecki. Toward formal development of programs from algebraic specifications. Acta Informatica, 25:233–281, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bench-Capon, T., Malcolm, G. (1999). Formalising Ontologies and Their Relations. In: Bench-Capon, T.J., Soda, G., Tjoa, A.M. (eds) Database and Expert Systems Applications. DEXA 1999. Lecture Notes in Computer Science, vol 1677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48309-8_23
Download citation
DOI: https://doi.org/10.1007/3-540-48309-8_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66448-2
Online ISBN: 978-3-540-48309-0
eBook Packages: Springer Book Archive