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Ontological Constitutions for Classes and Properties

  • Jørgen Fischer Nilsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4068)

Abstract

Formal ontologies model classes and their properties and relationships. This paper considers various choices for modelling of classes and properties, and the interrelationship of these within a formal logical framework. Unlike predicate logical usage with quantification over individuals only, in the applied metalogic classes and properties appear as first class non-extensional objects. Using this framework miscellaneous classification structures are examined ranging from mere partial orders to distributive lattices. Moreover, we seek to capture notions such as intensionality of classes and properties ascribed to individuals and classes in an coherent ontological framework. In this analytic framework we further present generative ontologies in which novel classes can be produced systematically by means of given classes and properties.

Keywords

Generative Ontology Distributive Lattice Noun Phrase Description Logic Predicate Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Andreasen, T., Nilsson, J.F.: Grammatical Specification of Domain Ontologies. Data & Knowledge Engineering 48 (2004)Google Scholar
  2. 2.
    Baader, F., et al.: Description Logic Handbook. Cambridge U.P., New York (2002)Google Scholar
  3. 3.
    Bealer, G.: Quality and Concept. Clarendon press, Oxford (1982)Google Scholar
  4. 4.
    Benthem, J.v., Doets, K.: Higher-Order Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 1. Reidel, Dordrecht (1983)Google Scholar
  5. 5.
    Bittner, T., Donnelly, M., Smith, B.: Individuals, Universals, Collections: On the Foundational Relations of Ontology. In: [36]Google Scholar
  6. 6.
    Bodenreider, O., Smith, B., Burgun, A.: The Ontology-Epistemology Divide: A Case Study in Medical Terminology. In: [36]Google Scholar
  7. 7.
    Brink, C., Britz, K., Schmidt, R.A.: Peirce Algebras. Formal Aspects of Computing 6, 339–358 (1994)MATHCrossRefGoogle Scholar
  8. 8.
    Bruun, H., Gehrke, M.: Distributive lattice structured ontologies (in preparation)Google Scholar
  9. 9.
    Bruun, H., Gehrke, M., Nilsson, J.F.: Lattice Structured Ontologies: An Ontological Account (in preparation)Google Scholar
  10. 10.
    Cappelli, A., Mazzeranghi, D.: An intensional semantics for a hybrid language. Data Knowledge Engineering 12, 31–62 (1994)MATHCrossRefGoogle Scholar
  11. 11.
    Carnap, R.: Introduction to Symbolic Logic and its Applications. Dover (1958)Google Scholar
  12. 12.
    Chen, P.P.-S.: The entity-relationship model: toward a unified view of data. ACM Trans. on Database Systems 1(1), 9–36 (1976)CrossRefGoogle Scholar
  13. 13.
    Cocchiarella, N.: Properties as Individuals in Formal Ontology. Noûs 6 (1972)Google Scholar
  14. 14.
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  15. 15.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1997)Google Scholar
  16. 16.
    Guarino, N., Welty, C.: Supporting ontological analysis of taxonomic relationships. Data & Knowledge Engineering 39, 51–74 (2001)MATHCrossRefGoogle Scholar
  17. 17.
    Gärdenfors, P.: Conceptual Spaces, The Geometry of Thought. MIT Press, Cambridge (2004)Google Scholar
  18. 18.
    Hamfelt, A., Nilsson, J.F., Oldager, N.: Logic Program Synthesis as Problem Reduction using Combining Forms. Automated Software Engineering 8, 167–193 (2001)MATHCrossRefGoogle Scholar
  19. 19.
    Jensen, P.A., Nilsson, J.F.: Ontology-based Semantics for Prepositions. In: Saint-Dizier, P. (ed.) Syntax and Semantics of Prepositions, Text, Speach & Language Technology, vol. 29, pp. 229–244. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Loux, M.J.: Metaphysics, a contemporary introduction. Routledge, London (1998, 2002)Google Scholar
  21. 21.
    Madsen, B.: Nistrup: Terminologi, principper og metoder. Gads forlag (1999)Google Scholar
  22. 22.
    Motik, B.: On the Properties of Metamodeling in OWL. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, pp. 548–562. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  23. 23.
    Neuhaus, F., Grenon, P., Smith, B.: A Formal Theory of Substances, Qualities, and Universals. In: [36]Google Scholar
  24. 24.
    Nilsson, J.F.: A Conceptual Space Logic. In: Kawaguchi, E. (ed.) Information Modelling and Knowledge bases XI, pp. 26–40. IOS Press, Amsterdam (2000)Google Scholar
  25. 25.
    Nilsson, J.F., Palomäki, J.: Towards Computing with Extensions and Intensions of Concepts. In: Charrel, P.-J., et al. (eds.) Information Modelling and Knowledge bases IX. IOS Press, Amsterdam (1998)Google Scholar
  26. 26.
    Oldager, N.: Conceptual Knowledge Representation and Reasoning. PhD thesis, Informatics and Mathematical Modelling, Technical University of Denmark (2003)Google Scholar
  27. 27.
    Oldager, N.: Intensional formalization of conceptual structures. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  28. 28.
    OntoQuery project net site: http://www.ontoquery.dk
  29. 29.
    Prior, A.N.: Intentionality and Intensionality. In: Geach, P.T., Kenny, A.J.P. (eds.) Papers in Logic and Ethics. University of Massachusetts Press (1976)Google Scholar
  30. 30.
    Quine, W.V.: Natural Kinds. In: Quine, W.V. (ed.) Ontological Relativity and other essays, Columbia U.P., New York (1969)Google Scholar
  31. 31.
    Smith, B.: Beyond Concepts: Ontology as Reality Representation. In: [36]Google Scholar
  32. 32.
    Smith, B.: Ontology and Information Systems, draft 11.12.01Google Scholar
  33. 33.
    Smith, B., Rosse, C.: The Role of Foundational Relations in the Alignment of Biomedical Ontologies. In: Proceedings MedInfo 2004, San Francisco, CA (2004)Google Scholar
  34. 34.
    Sowa, J.F.: Knowledge Representation, Logical, Philosophical, and Computational Foundations, Brooks/Cole Thomson Learning (2000)Google Scholar
  35. 35.
    Thomasson, A.L.: Methods of categorization. In: [36]Google Scholar
  36. 36.
    Varzi, A.C., Vieu, L. (eds.): Formal Ontology in Information Systems. IOS Press, Amsterdam (2004)Google Scholar
  37. 37.
    Weingartner, P.: On the Characterization of Entities by means of Individuals and Properties. Journal of Philosophical Logic 3, 323–336 (1974)MATHMathSciNetGoogle Scholar
  38. 38.
    Øhrstrøm, P., Andersen, J., Schärfe, H.: What has happened to Ontology. In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS 2005. LNCS (LNAI), vol. 3596, pp. 425–438. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jørgen Fischer Nilsson
    • 1
  1. 1.Informatics and Mathematical ModellingTechnical University of Denmark 

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