On the minimum number of logical clauses inferred from examples

Given two sets of positive and negative examples, the inductive inference problem is to infer a small set of logical clauses which appropriately classify the examples. A graph theoretic approach is used to establish a lower limit on the minimum number of required clauses. Furthermore, the findings of this paper reveal methods for partitioning the original data and thus solving efficiently large scale problems. _________________________________________________________________ + E. Triantaphyllou received a Dual Ph.D. in Industrial Engineering and Operations Research from the Pennsylvania State University in 1990. He also has an M.S. degree in Computer Science and a Dual M.S. degree in Environment and Operations Research from the same university. Currently, he is an Assistant Professor at Louisiana State University. His research interests include interfaces of artificial intelligence and operations research, mathematical programming, multi-criteria decision making, fuzzy sets, and machine learning. He is the author of more than 20 papers in the above areas which appeared in Decision Support Systems, Fuzzy Sets and Systems, Optimization Theory and Applications, ORSA Journal on Computing, Computers and OR, OR Letters, Global Optimization, IEEE Transactions on Fuzzy Systems, and Approximate Reasoning, among others. & Author for correspondence. ++ A.L. Soyster is a Professor & Head of Industrial & Management Systems Engineering at The Pennsylvania State University. He received his Ph.D. from Carnegie Mellon University, his M.S. from Cornell University and his B.S. from the Pennsylvania State University. His research expertise is in optimization of energy distribution systems and planning methods, modeling economic energy processes, and transportation; as well as artificial intelligence and expert systems application to Industrial Engineering. He is a member of IIE, ORSA, and TIMS. Dr. Soyster also served as Editor-in-Chief of IIE TRANSACTIONS, an international journal sponsored by IIE. He was awarded with the IIE Fellow Award in May 1988. Published in: Computers and Operations Research, Vol. 23, No. 8, pp. 783-799, 1996.