Abstract
A commonplace in the expert system literature has been that the resolution principle is inapplicable as an inference rule for expert systems. This claim has been due to the fact that many expert system applications inevitably have to reason about uncertain knowledge, and that the resolution principle cannot handle that kind of information. Indeed, there have been only few attempts to extend the application of theorem proving techniques and full clausal logic to reasoning under uncertainty. These approaches have made semantic assumptions which resulted in limitations and inflexibilities of the proposed inference mechanisms.
However, starting with Zadeh's “fuzzy logic” an impressive logical machinery has been developed for reasoning revolving around the uncertainty phenomenon of vagueness. Fuzzy logic allows for statements to have truth-values falling within a range between true and false. In this essay we shall discuss a similar uncertainty phenmenon, namely the endorsement of a statement. We present a new approach to fuzzy logic and reasoning under uncertainty using the resolution principle based on a new operator, the fuzzy operator. We present the fuzzy resolution principle for this logic and show its completeness as an inference rule.
Since the uncertainty phenomenon of endorsements is quite central to expert system development, we will claim that the logic presented here provides an elegant inference mechanism for those occasions, where a well understood semantics of one's reasoning mechanism is required.
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References
J.B. Adams, “Probabilistic Reasoning and Certainty Factors”, Math. Bios., 32, 1976, pp.177–186.
R. Bellmann, M. Giertz, “On the Analytic Formalism of the Theory of Fuzzy Sets, Inf. Sciences, 5, 1973, pp.149–156.
P.P. Bonissone, K.S. Decker, “Selecting Uncertainty Calculi and Granularity”, L.N. Kanal, J.F. Lemmer, Uncertainty in Artificial Intelligence, North-Holland, Amsterdam, 1986, pp.217–247.
B. Buchanan, E.H. Shortliffe, Rule-Based Expert Systems—The Mycin Experts of the Stanford Heuristic Programming Project, Addison-Wesley, Reading, 1984.
C. Chang, R.C. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.
P. Cheeseman, “In Defense of Probability”, Proc. 9th IJCAI, Los Angeles, 1985, pp.1002–1009.
P. Cohen, Heuristic Reasoning about Uncertainty—An Artificial Intelligence Approach, Morgan Kaufmann, Los Altos, 1985.
D. Dubois, H. Prade, “A Class of Fuzzy Measures Based on Triangular Norms”, Int. J. General Systems, 8, 1, 1982.
D. Dubois, H. Prade, “Criteria Aggregation and Ranking of Alternatives in the Framework of Fuzzy Set Theory”, H. Zimmerman, L.A. Zadeh, B.R. Gaines, Stud. Management Sci., 20, 1984, pp.209–240.
R.O. Duda, J. Gaschnig, P.E. Hart, “Model Design in the Prospector Consultant System for Mineral Exploration”, D. Mitchie, Expert Systems in the Microelectronic Age, Edinburgh, Edinburgh Univ. Press, 1979.
M. Ishizuka, N. Kanai, “Prolog-Elf Incorporating Fuzzy Logic”, Proc. 9th IJCAI, Los Angeles, 1985, pp.701–704.
R. Lee, “Fuzzy Logic and the Resolution Principle”, JACM, 19, 1, 1972, pp.109–119.
X.H. Liu, J.P. Tsai, Th. Weigert, “A-resolution and the Interpretation of A-Implication in Fuzzy Operator Logic”, forthcoming in Information. Sci..
M. Mukaidono, “Fuzzy Inference of Resolution Style”, R. Yager, Fuzzy Set and Possibility Theory, Pergamon, New York, 1982, pp.224–231.
H. Prade, “A Combinatorial Approach to Approximate and Plausible Reasoning with Applications to Expert Systems”, IEEE Trans. Pattern Matching, 7, 3, 1985, pp.260–283.
G. Shafer, A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, 1976.
E.H. Shortliffe, “Mycin—A Rule-Based Computer Program for Advising Physicians Regarding Antimicrobial Therapy Selection”, Tech. Rep. CS-74-465, Stanford Univ., Palo Alto, 1974.
E.H. Shortliffe, B.G. Buchanan, “A Model of Inexact Reasoning in Medicine”, Math. Biosci., 23, 1975, pp.351–379.
E.H. Shortliffe, B.G. Buchanan, E.A. Feigenbaum, “Knowledge Engineering for Medical Decision Making—A Review of Computer-Based Clinical Decision Aids”, Proc. IEEE, 67, 9, 1979, pp.1207–1224.
P. Szlovits, S.G. Pauker, “Categorical and Probabilistic Reasoning in Medical Diagnosis”, Artificial Intelligence, 11, 1978, pp.115–144.
Th. Weigert, J.-P. Tsai, X.H. Liu, “Fuzzy Operator Logic and Fuzzy Resolution”, forthcoming in J. Autom. Reasoning.
L.A. Zadeh, “Fuzzy Logic and Approximate Reasoning”, Synthese, 30, 1975, pp.407–428.
L.A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility”, Fuzzy Sets and Systems, 1, 1, 1978, pp.3–28.
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© 1990 Springer-Verlag Berlin Heidelberg
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Weigert, T.J. (1990). Resolution-based reasoning for fuzzy logic. In: Gottlob, G., Nejdl, W. (eds) Expert Systems in Engineering Principles and Applications. ESE 1990. Lecture Notes in Computer Science, vol 462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53104-1_41
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DOI: https://doi.org/10.1007/3-540-53104-1_41
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