An algebraic approach to knowledge-based modeling

  • Gerhard Schwärzler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 737)


In the presented approach the basic domain for modeling components of a system will be sets of first order formulas. The formation process of rules is iterated and leads to the notion of cumulative logic programs, which are identified with elements of a graph algebra. The appropriate definition of the application operation on cumulative logic programs is given. The structure of the modeled system is specified by equations, and qualitative modeling is related to the algebraic problem of solving system of equations in a graph algebra. Using the concepts of consistency and knowledge extension, an algorithm for approximating solutions to such equational systems is presented.


qualitative modeling model-based reasoning expert systems logic programming combinatory algebra 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Price, C., Lee M.: “Applications of deep knowledge”. Artificial Intelligence in engineering, 1988, Vol. 3, No. 1, pp.1–7.Google Scholar
  2. 2.
    de Kleer, J., and Brown, J.S.: “A Qualitative Physics Based on Confluences” Artificial Intelligence 24, (1984), p. 7–83.Google Scholar
  3. 3.
    Forbus, K.D.: “Qualitative Process Theory”. Artificial Intelligence 24, (1984), p. 85–168.Google Scholar
  4. 4.
    Kuipers, B.: “Qualitative Simulation” Artificial Intelligence 29, (1986), p. 289–338.Google Scholar
  5. 5.
    Struss, P.: “Mathematical aspects of qualitative modelling” Artificial Intelligence in Engineering (1988), pp. 156–169.Google Scholar
  6. 6.
    Bratko, I., Mosetic, I., Lavrac, N.: “Automatic Synthesis and Compression of Cardiological Knowledge” Machine Intelligence 11, (1988), pp. 435–454.Google Scholar
  7. 7.
    Schwärzler G.: “Knowledge-Based Modeling of Cooperative Processes” PhD Thesis, ETH Zürich, to appear 1992.Google Scholar
  8. 8.
    Engeler, E.: “Modelling of Cooperative Processes” Report No. 86-06, Math. Dept. ETH Zürich, 1986.Google Scholar
  9. 9.
    Engeler, E.: “Cumulative Logic Programs and Modelling” Logic Colloquium '86, Drake, F., Truss, J., (Editors), North Holland, 1988.Google Scholar
  10. 10.
    Engeler, E.: “Sketch of a New Discipline of Modelling” Report Math. Dept. ETH Zürich, 1988.Google Scholar
  11. 11.
    Engeler, E.: “Algebras and Combinators” Algebra Universalis, (1981), p 389–392.Google Scholar
  12. 12.
    Engeler, E.: “Equations in Combinatory Algebras”. Proceedings of ”Logic of Programs '83”, SLNCS 164, (1984).Google Scholar
  13. 13.
    Aberer K.: “Combinatory Differential Fields and Constructive Analysis” PhD Thesis No. 9357, ETH Zurich, (1991).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gerhard Schwärzler
    • 1
  1. 1.Zürich Department of Mathematics ETH-ZentrumSwiss Federal Institute of TechnologyZürich

Personalised recommendations