Summary
The need for an algebra to manipulate ontologies is motivated by the impossibility of achieving a globally consistent ontology. Our approach is to integrate information from diverse sources by focusing on the intersection of their ontologies and articulating them accordingly. These articulations typically require rules to define semantic correspondences like synonymy, homonymy, hypernymy, overlapping semantics, and abstraction among the terms of interest. The algebra, needed to compose multiple articulations, has to manipulate the ontologies based on these articulation rules.
The properties of the operators depend upon those of the articulation generation function deployed. The necessary and sufficient conditions that must be satisfied by the articulation generating function in order for the algebraic operators to satisfy properties like commutativity, associativity and distributivity have been identified in this work. Based on whether these properties are satisfied, a task of composing multiple ontologies can be expressed as multiple equivalent algebraic expressions. Using a cost model, the most optimal algebraic expression can be chosen and executed to derive the composed ontology.
This is a preview of subscription content, log in via an institution to check access.
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
Wiederhold, G. (1994) An algebra for ontology composition. In: Monterey Workshop on Formal Methods., Naval Postgraduate School, 56–61
Melnik, S., Garcia-Molina, H., Rahm, E. (2002) Similarity flooding: A versatile graph matching algorithm and its application to schema matching. In: Proc. of the 12th Int. Conf. on Data Engineering, (ICDE), San Jose, California.
Doan, A., Domingos, P., Halevy, A.Y. (2001) Reconciling schemas of disparate data sources: A machine-learning approach. In: SIGMOD.
Madhavan, J., Bernstein, P.A., Rahm, E. (2001) Generic schema matching with cupid. In: 27th Intl. Conf. VLDB, Roma, Italy, 49–58.
Noy, N., Musen, M. (2000) Prompt: Algorithm and tool for automated ontology merging and alignment. In: 7th Natl. Conf. of AAAI-2000.
Brooks, F.P. (1995). The Mythical Man-Month, Addison Wesley, 1975, reprinted’95.
Chalupsky, H., Hove, E., and Russ, T. (1997) Presentation on Ontology Alignment at ad hoc group on ontology, NCITS.TC.T2 ANSI.
Gruber, T.R., (1993) A Translation Approach to Portable Ontology Specifications, Knowledge Acquisition, Vol. 5 No. 2, pp. 199–220.
Gruber, T. R. (1993) Toward principles for the design of ontologies used for knowledge sharing. Talk Padua workshop on Formal Ontology, March. Ed. Nicola Guarino.
Guha, R.V. (1991) Contexts: A formalization and some application, Ph.D. dissertation, Stanford University. Also Technical Report Number ACT-CYC-42391.
Humphreys, B. and Lindberg, D. (1993) The project: Making the conceptual connection between users and the information they need, Bulletin of the Medical Library Association, 1993, see also http://www.lexical.com
Lenat, D., and Guha R.V. (1990) Building Large Knowledge-Based Systems, Addison-Wesley.
Oliver D.E., Shahar, Y., Shortliffe E.H., and Musen, M.A. (1998) Representation of Change on Controlled Medical Terminologies, In Proc. AMIA Conference, October.
Teknowledge (1997) High-Performance Knowledge-Bases (HPKB), maintained by Teknowledge Corp. for the DARPA, http://www.teknowledge.com/HPKB.
Hendler J., Berners-Lee T, and Miller E. (2001) The Semantic Web“. In Scientific American. May. http://www.scientificamerican.com/2001/0501issue/0501berners- lee.html
Jones T.C. (1998) Estimating Software Costs; McGraw-Hill.
Lenat, D. B. (1995) Cyc: A Large-Scale Investment in Knowledge Infrastructure. Communications of the ACM 38, no. 11 (November).
Mitra P., Kersten M. and Wiederhold G. (2000) Graph-Oriented Model for Articulation of Ontology Interdependencies. Proc. 7th Extending Database Technology, EDBT.
Mitra P., Wiederhold G., and Jannink J. (1999) Semi-automatic Integration of Knowl edge Sources. In Proceedings of Fusion ‘89, Sunnyvale, USA, July.
Gysenns M., Paredaens J., Van den Bussche J., and van Gucht D. (1994) A graph-oriented object database model. In IEEE Trans. on KDE, Vol. 6, No. 4, pp. 572–586.
Mitra P., Wiederhold G., and Decker S. (2001) A Scalable Framework for Interoperation of Information Sources. 1st Int. Semantic Web Working Symp. (SWWS ‘01).
Mitra P., http://www-db.stanford.edu/ - prasen9
Boole, G. (1854) An investigation into the Laws of Thought, on Which are founded the Mathematical Theories of Logic and Probabilities.
McGuiness, D.L., Fikes R., Rice, J., and Wilder, S. (2000) The Chimaera Ontology Environment. Seventh National Conference on Artificial Intelligence (AAAI2000).
Camara, G., Fonseca, F., and Monteiro A.M. (2002) Algebraic Structures For Spatial Ontologies. Poster at GlScience 2002, Boulder, CO, USA, Annals, AAG, September 25–28, http://www.dpi. inpe.br/gilberto/papers/ontologiesjiscience2002.pdf
Bernstein, P.A. (2003) Applying Model Management to Classical Meta Data Problems, Proc. CIDR 2003 pp. 209–220
Bernstein, P.A., Levy, A.Y., and Pottinger, R.A., A Vision for Management of Complex Models, Microsoft Research Technical Report MSR-TR-2000–53, June.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mitra, P., Wiederhold, G. (2004). An Ontology-Composition Algebra. In: Staab, S., Studer, R. (eds) Handbook on Ontologies. International Handbooks on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24750-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-24750-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11957-0
Online ISBN: 978-3-540-24750-0
eBook Packages: Springer Book Archive