Skip to main content
SpringerLink
Log in

Ontological Constitutions for Classes and Properties

  • Conference paper
Conceptual Structures: Inspiration and Application (ICCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4068))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreasen, T., Nilsson, J.F.: Grammatical Specification of Domain Ontologies. Data & Knowledge Engineering 48 (2004)

    Google Scholar 

  2. Baader, F., et al.: Description Logic Handbook. Cambridge U.P., New York (2002)

    Google Scholar 

  3. Bealer, G.: Quality and Concept. Clarendon press, Oxford (1982)

    Google Scholar 

  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. Bittner, T., Donnelly, M., Smith, B.: Individuals, Universals, Collections: On the Foundational Relations of Ontology. In: [36]

    Google Scholar 

  6. Bodenreider, O., Smith, B., Burgun, A.: The Ontology-Epistemology Divide: A Case Study in Medical Terminology. In: [36]

    Google Scholar 

  7. Brink, C., Britz, K., Schmidt, R.A.: Peirce Algebras. Formal Aspects of Computing 6, 339–358 (1994)

    Article  MATH  Google Scholar 

  8. Bruun, H., Gehrke, M.: Distributive lattice structured ontologies (in preparation)

    Google Scholar 

  9. Bruun, H., Gehrke, M., Nilsson, J.F.: Lattice Structured Ontologies: An Ontological Account (in preparation)

    Google Scholar 

  10. Cappelli, A., Mazzeranghi, D.: An intensional semantics for a hybrid language. Data Knowledge Engineering 12, 31–62 (1994)

    Article  MATH  Google Scholar 

  11. Carnap, R.: Introduction to Symbolic Logic and its Applications. Dover (1958)

    Google Scholar 

  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)

    Article  Google Scholar 

  13. Cocchiarella, N.: Properties as Individuals in Formal Ontology. Noûs 6 (1972)

    Google Scholar 

  14. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  15. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1997)

    Google Scholar 

  16. Guarino, N., Welty, C.: Supporting ontological analysis of taxonomic relationships. Data & Knowledge Engineering 39, 51–74 (2001)

    Article  MATH  Google Scholar 

  17. Gärdenfors, P.: Conceptual Spaces, The Geometry of Thought. MIT Press, Cambridge (2004)

    Google Scholar 

  18. Hamfelt, A., Nilsson, J.F., Oldager, N.: Logic Program Synthesis as Problem Reduction using Combining Forms. Automated Software Engineering 8, 167–193 (2001)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  20. Loux, M.J.: Metaphysics, a contemporary introduction. Routledge, London (1998, 2002)

    Google Scholar 

  21. Madsen, B.: Nistrup: Terminologi, principper og metoder. Gads forlag (1999)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  23. Neuhaus, F., Grenon, P., Smith, B.: A Formal Theory of Substances, Qualities, and Universals. In: [36]

    Google Scholar 

  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. 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. Oldager, N.: Conceptual Knowledge Representation and Reasoning. PhD thesis, Informatics and Mathematical Modelling, Technical University of Denmark (2003)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  28. OntoQuery project net site: http://www.ontoquery.dk

  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. Quine, W.V.: Natural Kinds. In: Quine, W.V. (ed.) Ontological Relativity and other essays, Columbia U.P., New York (1969)

    Google Scholar 

  31. Smith, B.: Beyond Concepts: Ontology as Reality Representation. In: [36]

    Google Scholar 

  32. Smith, B.: Ontology and Information Systems, draft 11.12.01

    Google Scholar 

  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. Sowa, J.F.: Knowledge Representation, Logical, Philosophical, and Computational Foundations, Brooks/Cole Thomson Learning (2000)

    Google Scholar 

  35. Thomasson, A.L.: Methods of categorization. In: [36]

    Google Scholar 

  36. Varzi, A.C., Vieu, L. (eds.): Formal Ontology in Information Systems. IOS Press, Amsterdam (2004)

    Google Scholar 

  37. Weingartner, P.: On the Characterization of Entities by means of Individuals and Properties. Journal of Philosophical Logic 3, 323–336 (1974)

    MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Informatics and Mathematical Modelling, Technical University of Denmark,  

    Jørgen Fischer Nilsson

Authors
  1. Jørgen Fischer Nilsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Communication and Psychology, Aalborg University,  

    Henrik Schärfe

  2. AIFB Institute, Universität Karlsruhe (TH), D-76128, Karlsruhe, Germany

    Pascal Hitzler

  3. Department of Communication, Aalborg University, Kroghstraede 3, 9220, Aalborg, Denmark

    Peter Øhrstrøm

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nilsson, J.F. (2006). Ontological Constitutions for Classes and Properties. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds) Conceptual Structures: Inspiration and Application. ICCS 2006. Lecture Notes in Computer Science(), vol 4068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787181_4

Download citation

  • DOI: https://doi.org/10.1007/11787181_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35893-0

  • Online ISBN: 978-3-540-35902-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation