An automatic learning capability has been developed and implemented for use with the MULTIPLE (MULTIpurpose Program that LEarns) heuristic tree-searching program, which is presently being applied to resolution theorem-proving in predicate calculus. MULTIPLE's proving program (PP) uses two evaluation functions to guide its search for a proof of whether or not a particular goal is achievable. Thirteen general features of predicate calculus clauses were created for use in the automatic learning of better evaluation functions for PP. A multiple regression program was used to produce optimal coefficients for linear polynomial functions in terms of the features. Also, automatic data-handling routines were written for passing data between the learning program and the proving program, and for analyzing and summarizing results. Data was generally collected for learning (regression analysis) from the experience of PP.
A number of experiments were performed to test the effectiveness and generality of the learning program. Results showed that the learning produced dramatic improvements in the solutions to problems which were in the same domain as those used for collecting learning data. Learning was also shown to generalize successfully to domains other than those used for data collection. Another experiment demonstrated that the learning program could simultaneously improve performance on problems in a specific domain and on problems in a variety of domains. Some variations of the learning program were also tested.
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