Abstract
Knowledge compilation speeds inference by creating tractable approximations of a knowledge base, but this advantage is lost if the approximations are too large. We show how learning concept generalizations can allow for a more compact representation of the tractable theory. We also give a general induction rule for generating such concept generalizations. Finally, we prove that unless NP ⊂-non-uniform P, not all theories have small Horn least upper-bound approximations.
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References
Amarel, Saul: On representations of problems of reasoning about actions, in D. Michie, editor Machine Intelligence 3 (Edinburgh University Press, 1968) 131–171.
Boppana, R. B. and Sipser, M.: The complexity of finite functions, in J. Leeuwen, editor, Handbook of Theoretical Computer Science, Volume A: Algorithms and Compexity (MIT Press, Cambridge, MA, 1990) 757–804.
Bresina, J. L.; Marsella, S. C.; and Schmidt, C. F.: Reappr — improving planning efficience via local expertise and reformulation, Technical Report LCSR-TR-82, Rutgers University, New Brunswick (1986).
Cook, S. A.: The complexity of theorem-proving procedures, in Proceedings of the 3rd Annual ACM Symposium on the Theory of Computing (1971) 151–158.
Dowling, William F. and Gallier, Jean H.: Linear time algorithms for testing the satisfiability of propositional horn formula, Journal of Logic Programming 3 (1984) 267–284.
Greiner, Russ and Schuurmans, Dale: Learning useful horn approximations, in Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning (KR-92), Cambridge, MA (Morgan Kaufmann, Los Altos, CA, 1992) 383–392.
Karp, R. M. and Lipton, R.: Turing machines that take advice, Enseign. Math. 28 (1982) 191–209.
Kautz, Henry and Selman, Bart: A general framework for knowledge compilation, in Proceedings of the International Workshop on Processing Declarative Knowledge (PDK), Kaiserslautern, Germany (1991).
Kearns, Michael J.: The Computational Complexity of Machine Learning (MIT Press, Boston, MA, 1990).
Minton, Steve: Selectively generalizing plans for problem solving, in Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI-85), Los Angeles (Morgan Kaufmann, Los Altos, CA, 1985).
Minton, Steven: Learning Effective Search Control Knowledge: an Explanation-Based Approach, Ph.D. Dissertation, Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA (1988).
Muggleton, Stephen and Buntine, Wray: Machine invention of first-order predicates by inverting resolution, in J. Laird editor Proceedings of the Fifth International Conference on Machine Learning (Morgan Kaufmann, Los Altos, CA 1988) 339.
Pagallo, Giulia and Haussler, David: Boolean feature discovery in empirical learning, Machine Learning 5 (1990) 77–99.
Selman, Bart and Kautz, Henry: Knowledge compilation using Horn approximations, in Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI-91), Anaheim, CA (1991) 904–909.
Shoenfield, Joseph R.: Mathematical Logic (Addison-Wesley, Reading, MA 1967).
Subramanian, Devika and Genesereth, Michael R.: The relevance of irrelevance, in Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), Milan (Morgan Kaufmann, Los Altos, CA, 1987).
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© 1994 Springer-Verlag Berlin Heidelberg
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Kautz, H., Selman, B. (1994). Forming concepts for fast inference. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_12
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DOI: https://doi.org/10.1007/3-540-58107-3_12
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