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Inference and verification in Medical Appropriateness Criteria using Gröbner Bases

  • L. M. Laita
  • E. Roanes-Lozano
  • V. Maojo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1476)

Abstract

In this article techniques borrowed from Computer Algebra (Gröbner Bases) are applied to deal with Medical Appropriateness Criteria including uncertainty. The knowledge was provided in the format of a table. A previous translation of the table into the format of a “Rule Based System≓ (denoted RBS) based on a three-valued logic is required before-hand to apply these techniques. Once the RBS has been obtained, we apply a Computer Algebra based inference engine, both to detect anomalies and to infer new knowledge. A specific set of criteria for coronary artery surgery (originally presented in the form of a table) is analyzed in detail.

Keywords

Verification Inference Engines RBSs in Medicine Gröbner Bases 

Topics

Integration of Logical Reasoning and Computer Algebra Symbolic Computation for Expert Systems and Machine Learning 

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References

  1. 1.
    V. Adams, P. Loustanau, An Introduction to Gröbner Bases. Graduate Studies in Mathematics 3, American Mathematical Society, Providence, RI, (1994).Google Scholar
  2. 2.
    J. A. Alonso and E. Briales, Lógicas Polivalentes y Bases de Gröbner. Procs. of the V Congress on Natural Languages and Formal Languages, Ed. M. Vide, Barcelona, (1989), 307–315.Google Scholar
  3. 3.
    B.G. Buchanan and E.H. Shortliffe, Rule Based Expert Systems: The MYCIN experiments of the Stanford Heuristic Programming Project. Addison-Wesley, Reading, MA. (1984).Google Scholar
  4. 4.
    S. Bernstein, J. Kahan, Personal communication. RAND Corporation (1993).Google Scholar
  5. 5.
    A. Capani and G. Niesi, CoCoA User’s Manual (v. 3.0b). Dept. of Mathematics, University of Genova (1996).Google Scholar
  6. 6.
    J. Chazarain, A. Riscos, J.A. Alonso, E. Briales, Multivalued Logic and Gröbner Bases with Applications to Modal Logic. Journal of Symbolic Computation, 11, 181–194 (1991).MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Field, M. Field, K. Lohr, (Eds). Guidelines for Clinical Practice. From Development to Use. National Academy Press, Washington D.C. (1992).Google Scholar
  8. 8.
    J. Hsiang, Refutationsl Theorem Proving using Term-rewriting Systems, Artificial Intelligence, 25 (1985), 255–300.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    D. Kapur and P. Narendran, An Equational Approach to Theorem Proving in First-Order Predicate Calculus. 84CRD296 General Electric Corporate Research and Development Report, Schenectady, NY, March 1984, rev. Dec. 1984. Also in, Proceedings of IJCAI-85 (1985), 1446–1156.Google Scholar
  10. 10.
    L.M. Laita, L. de Ledesma, Knowledge-Based Systems Verification, Encyclopedia of Computer Science and Technology, Eds. A Kent, J.G. Williams. Marcel Dekker, New York (1997), 253–280.Google Scholar
  11. 11.
    L.M. Laita, E. Roanes-Lozano, J.A. Alonso, L. de Ledesma, Automated Multi-Valued Logic reasoning in rule based Expert Systems. Preprint, AI Dept., Universidad Politécnica de Madrid, sent for tentative publication in Soft Computing (1998).Google Scholar
  12. 12.
    P. Lázaro, K. Fitch, Criterios de uso apropiado para by-pass coronario. Unpublished Report (1996).Google Scholar
  13. 13.
    G. C. Moisil, The Algebraic Theory of Switching Circuits. Pergamon Press, Oxford (1969).Google Scholar
  14. 14.
    E Roanes-Lozano, L.M. Laita, E. Roanes-Macías, A Polynomial Model for Multi-valued Logics with a Touch of Algebraic Geometry and Computer Algebra. Special Issue “Non-Standard Applications of CA≓, in Mathematics and Computers in Simulation, 45/1–2 (1998), 83–99.CrossRefGoogle Scholar
  15. 15.
    J.K. Slaney, Formal Logic and its application in medicine. Pillips CI. Logic in Medicine, British Medical journal (1988).Google Scholar
  16. 16.
    F. Winkler, Introduction to Computer Algebra. Lecture Notes WS 93/94, RISC-Linz (1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • L. M. Laita
    • 1
  • E. Roanes-Lozano
    • 2
  • V. Maojo
    • 1
  1. 1.Dept. I.A. (Fac. Informática) Campus de MontegancedoUniversidad Politécnica de MadridMadridSpain
  2. 2.Dept. Algebra Edificio “La Almudena≓Universidad Complutense de MadridMadridSpain

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