Skip to main content
SpringerLink
Log in

Relative and absolute order-of-magnitude models unified

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

The aim of this paper is to analyze under which conditions Absolute Order-of-Magnitude and Relative Order-of-Magnitude models may be concordant and to determine the constraints which guarantee concordance. A graphical interpretation of the constraints is provided, bridging the absolute qualitative labels of two quantities into their corresponding relative relation(s), and conversely. The relative order of magnitude relations are then characterized in the absolute order-of-magnitude world.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Agell, Estructures matemàtiques per al model qualitatiu de ordres de magnitud absoluts. PhD. diss. Universitat Politècnica de Catalunya (Barcelona, Spain, 1998).

  2. P. Dague, Numeric reasoning with relative orders of magnitude, in: Proc. of 11th National Conf. on Artificial Intelligence AAAI'93 (Washington, District of Columbia, USA, 1993) pp. 541–547.

  3. P. Dague, Symbolic reasoning with relative orders of magnitude, in: Proc. of the 13th Int. Joint Conf. on Artificial Intelligence IJCAI'93 (Chambéry, France, 1993) pp. 1509–1514.

  4. J.L. Dormoy, Nouvelles méthodes de calcul qualitatif, Revue d'Intelligence Artificielle 3(4) (1989) 39–53

    Google Scholar 

  5. R. Gasca, Razonamiento y simulación en sistemas que integran conocimiento cualitativo y cuantitativo. PhD diss. Universidad de Sevilla, Spain (1998).

  6. J. Kalagnanam, H.A. Simon and Y. Iwasaki, The mathematical bases for qualitative reasoning, IEEE Expert: Intelligent Systems and Their Applications (April 1991) 11–19.

  7. M.L. Mavrovouniotis and G. Stephanopoulos, Reasoning with orders of magnitude and approximate relations, in: Proc. of 6th National Conf. on Artificial Intelligence AAAI'87 (Seattle, USA, 1987) pp. 626–630.

  8. A. Missier, N. Piera and L. Travé, Order of magnitude algebras: A survey, Revue d'Intelligence Artificielle 3(4) (1989) 95–109.

    Google Scholar 

  9. A. Missier, Structures mathématiques pour le calcul qualitatif, contribution à la simulation qualitative. PhD. diss. INSA (Toulouse, France, 1991).

  10. N. Piera and L. Travé, About qualitative equality: Axioms and properties, in: Proc. of 9th International Conf. on Expert System and their Applications (Avignon, France, 1989) pp. 73–87.

    Google Scholar 

  11. N. Piera and L. Travé, Mathematical Foundations for Order of Magnitude Reasoning. Technical Report # 90252, L.A.A.S.-C.N.R.S. (Toulouse, France 1990).

  12. O. Raiman, Order of magnitude reasoning, Artificial Intelligence 24 (1986) 11–38.

    Google Scholar 

  13. M. Sánchez, F. Prats and N. Piera, Una formalización de relaciones de comparabilidad en modelos cualitativos. Boletín AEPIA n.6 Madrid (1996) pp. 15–22.

  14. P. Struss, Mathematical aspects of qualitative reasoning, AI in Engineering 3(3) (1988) 156–169.

    Google Scholar 

  15. L. Travé and N. Piera, The orders of magnitude models as qualitative algebras, in: Proc. of the 11th Int. Joint Conf. on Artificial Intelligence IJCAI'89 (Detroit, USA, 1989) pp. 1261–1266.

  16. L. Travé-Massuyès and P. Dague, Modéles et raisonnements qualitatifs. Ed. Hermès, (Paris, 2003) p. 363

  17. L. Travé-Massuyès, P. Dague and L. Ironi, Mathematical foundations of qualitative reasoning, AI Magazine 24/4 (2003) 91–106.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LAAS-CNRS, 7, Avenue du Colonel Roche, 31077, Toulouse, Cedex, France

    Louise Travé-Massuyès

  2. MA2-UPC, Jordi Girona, 1-3, 08034, Barcelona, Spain

    Francesc Prats & Mónica Sánchez

  3. ESADE-URL, Av. Pedralbes, 62, 08034, Barcelona, Spain

    Núria Agell

Authors
  1. Louise Travé-Massuyès
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesc Prats
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mónica Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Núria Agell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Louise Travé-Massuyès.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Travé-Massuyès, L., Prats, F., Sánchez, M. et al. Relative and absolute order-of-magnitude models unified. Ann Math Artif Intell 45, 323–341 (2005). https://doi.org/10.1007/s10472-005-9002-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-005-9002-1

Keywords

Search

Navigation