Abstract
An investigation is made into the ways proof planning can enhance the capability of a rule based prover for the theory of integration. The integrals are of the Riemann type and are defined in a way to maximize the theorem proving methods of predicate calculus. Approximately fifty theorems have been proved and several examples are discussed. A major shortcoming was found to be the inability of the system to work with or produce a proof plan. As a result, a planning scheme based on the idea of subgoals or milestones was considered. With user defined plans, there was a substantial increase in performance and capability of the system and, in some cases, proofs which were previously unsuccessful were completed.
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References
Baker, J. D., ‘Probability representations with right-cauchy integrals’, SIAM Journal of Applied Mathematics (December, 1970).
Baker, J. D., ‘The dipmeter advisor: an expert well log analysis system at Schlumberger’, in Winston, P. H. and Prendergas, K. A. (Eds.), A.I. Business, MIT Press (1984).
Bledsoe, W. W., ‘Some thoughts on proof discovery’, MCC Technical Report Number AI-208-86 (June, 1986).
Davis, P. J. and Hersh, R., The Mathematical Exprience, Houghton Mifflin, Boston (1981).
Pessin, I., Classical and Modern Integration Theories, Adademic Press, New York (1970).
Rosenlicht, M., Introduction to Analysis, Dover, New York (1968).
Schwartz, J., ‘Limits of artificial intelligence’, Encyclopedia of Artificial Intelligence, Vol. 1, Wiley Interscience Publishers, New York (1987).
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Baker, J.D., Zand-Biglari, S. An integral theorem prover and the role of proof planning. J Autom Reasoning 8, 275–295 (1992). https://doi.org/10.1007/BF00244284
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DOI: https://doi.org/10.1007/BF00244284