Abstract
We describe two uses of meta-level inference: to control the search for a proof; and to derive new control information, and illustrate them in the domain of algebraic equation solving. The derivation of control information is the main focus of the paper. It involves the proving of theorems in the Meta-Theory of Algebra. These proofs are guided by meta-meta-level inference. We are developing a meta-meta-language to describe formulae, and proof plans, and have built a program, IMPRESS, which uses these plans to build a proof. We describe one such proof plan in detail. IMPRESS will form part of a self-improving algebra system.
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References
Boyer, R. S. and Moore, J S., A Computational Logic, Academic Press, ACM monograph series (1979).
Bundy A., The Impress Proof Plan Revisited, Working paper 138, Dept. of Artificial Intelligence, Edinburgh (April, 1983).
Bundy A. and Welham B., ‘Using meta-level inference for selective application of multiple rewrite rules in algebraic manipulation’, Artificial Intelligence 16(2), 189–212 (1981). Also available as DAI Research Paper 121.
Bundy A., Silver B., and Plummer D., ‘An Analytical Comparison of some Rule Learning Programs’, Artificial Intelligence 27(2), 137–182 (1985). Also available from Edinburgh as DAI Research Paper no. 215. Earlier version in Procs. of Third Annual Technical Conference of the British Computer Society's Expert System Specialist Group (1983).
Constable, R. L. et al., Implementing Mathematics with the NuPrl Proof Development System, Prentice-Hall (1986).
Darlington J., ‘An Experimental Program Transformation and Synthesis System’, Artificial Intelligence 16(3), 1–46 (August, 1981).
Gordon, M. J., Milner, A. J., and Wadsworth, C. P., Lecture Notes in Computer Science, Volume 78: Edinburgh LCF-A mechanised logic of computation, Springer Verlag (1979).
Silver, B., ‘Precondition Analysis: Learning Control Information’, in: Michalski, R. S., Carbonell, J. G., and Mitchell, R. M. (eds.), Machine Learning 2, Tioga Publishing Company (1984).
Sterling L., IMPRESS — Meta-level concepts in theorem proving, Working Paper 119, Dept. of Artificial Intelligence, Edinburgh (August, 1982).
Sterling, L. and Bundy, A., ‘Meta-level Inference and Program Verification’, in: Loveland, D. W. (ed.), 6th Conference on Automated Deduction, pp. 144–150, Springer Verlag (1982). Lecture Notes in Computer Science No. 138. Also available from Edinburgh as Research Paper 168.
Sterling, L., Bundy, A., Byrd, L., O'Keefe, R., and Silver, B., ‘Solving Symbolic Equations with PRESS’, in: Calmet, J. (ed.), Computer Algebra, Lecture Notes in Computer Science No. 144, pp. 109–116, springer Verlag (1982).
Wallen L. A., Towards the Provision of a Natural Mechanism for Expressing Domain-Specific Global Strategies in General Purpose Theorem-Provers. Research Paper 202, Dept. of Artificial Intelligence, Edinburgh (September, 1983).
Winston, P., ‘Learning structural descriptions from examples’, in: Winston, P. H. (ed.), The Psychology of Computer Vision, McGraw-Hill (1975).
Young, R. M., Plotkin, G. D., and Linz, R. F., ‘Analysis of an extended concept-learning task’, in: Reddy, R. (ed.), Proceedings of IJCAI-77, International Joint Conference on Artificial Intelligence (1977).
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Bundy, A., Sterling, L. Meta-level inference: Two applications. J Autom Reasoning 4, 15–27 (1988). https://doi.org/10.1007/BF00244511
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DOI: https://doi.org/10.1007/BF00244511