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.
Partially supported by projects FIS 95/1952 and DGES PB96-0098-C04 (Spain).
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References
V. Adams, P. Loustanau, An Introduction to Gröbner Bases. Graduate Studies in Mathematics 3, American Mathematical Society, Providence, RI, (1994).
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.
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).
S. Bernstein, J. Kahan, Personal communication. RAND Corporation (1993).
A. Capani and G. Niesi, CoCoA User’s Manual (v. 3.0b). Dept. of Mathematics, University of Genova (1996).
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).
M. Field, M. Field, K. Lohr, (Eds). Guidelines for Clinical Practice. From Development to Use. National Academy Press, Washington D.C. (1992).
J. Hsiang, Refutationsl Theorem Proving using Term-rewriting Systems, Artificial Intelligence, 25 (1985), 255–300.
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.
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.
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).
P. Lázaro, K. Fitch, Criterios de uso apropiado para by-pass coronario. Unpublished Report (1996).
G. C. Moisil, The Algebraic Theory of Switching Circuits. Pergamon Press, Oxford (1969).
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.
J.K. Slaney, Formal Logic and its application in medicine. Pillips CI. Logic in Medicine, British Medical journal (1988).
F. Winkler, Introduction to Computer Algebra. Lecture Notes WS 93/94, RISC-Linz (1994).
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Laita, L.M., Roanes-Lozano, E., Maojo, V. (1998). Inference and verification in Medical Appropriateness Criteria using Gröbner Bases. In: Calmet, J., Plaza, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 1998. Lecture Notes in Computer Science, vol 1476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055912
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DOI: https://doi.org/10.1007/BFb0055912
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