Abstract
This paper describes an hierarchical deduction proof procedure. This procedure proves a theorem by searching for a proof acceptable to an hierarchical deduction structire; those derivations which are irrelevant to this proof are limited by means of a set of completeness-preserving refinements of the basic procedure, such as constraints on framed literals and on common tails, a proper reduction refinement, a global subsumption constraint, and a level subgoal reordering refinement, etc. In addition to this basic algorithm, we will present a partial set of support strategy and a semantically guided hierarchical deduction for the incorporation of semantics and human factors. The paper concludes with proofs concerning the completeness of the basic algorithm and the results of a computer implementation applied to some nontrivial problems.
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References
AndersonR. and BledsoeW. W., ‘A linear format for resolution with merging and a new technique for establishing completeness’, J. ACM, 17, 525–534, (1970).
BledsoeW. W., ‘Non-resolution theorem proving,’ Artificial Intelligence 9, 1–35 (1977).
Bledsoe, W. W. and Hines, L. M., ‘Variable elimination and chaining in a resolution-based prover for inequalities,’ Tech. Report, ATP-56A, University of Texas at Austin. 5th Conference on Automated Deduction.
Boyer, R. S. and Moore, J S., A Computational Logic, Academic Press, 1979.
Boyer, R. S., Locking: a restriction of resolution; Ph.D. Thesis, University of Texas at Austin.
Chang, C. and Lee, R. C., Symbol Logic and Mechanical Theorem Proving, Academic Press, 1973.
KowalskiR. and KuehnerD., ‘Linear resolution with selection function,’ AitArtifical Intelligence 2 227–260 (1971).
LovelandD. W., ‘Mechanical theorem-proving by model elimination,’ J. ACM 15, 236–251 (1968).
LovelandD. W., ‘A simplified format for the model-elimination theorem-proving procedure’, J. ACM 16, 349–363 (1969).
FleisingS., LovelandD., SmileyIIIA. K., and YarmushD. L., ‘An implementation of the model elimination proof procedure’, J. ACM 21, 124–139 (1974).
Loveland, D. W., Automated Theorem Proving; a Logical Basis, North-Holland, 1978.
McCharen, J. D., Overbeek, R. A., and Wos, L. A., ‘Problems and experiments for and with automated theorem-proving programs,’ IEEE Trans. on Compt. C-25, No. 8, 1976.
OverbeekR. A., ‘A new class of automatic theorem proving algorithms’, J. ACM 21, 191–200 (1974).
Tyson, W. M., ‘A priority-ordered agenda theorem prover’, Ph.D. dissertation, University of Texas at Austin (1981).
Walther, C., ‘A mechanical solution of Schubert's steamroller by many-sorted resolution’. Proc. 8th AAAI (1984) pp. 330–334.
Wang, T.-C. and Bledsoe, W. W., ‘Hierarchical deduction’, Tech. Report, ATP-78A, Univ. of Texas at Austin, March 1984.
Wang, T.-C., ‘Designing example for semantically guided hierarchical deduction’. Proc. 9th IJCAI (1985), pp. 1201–1207.
WosL. T., CarsonD. F., and RobinsonG. A., ‘Efficiency and completeness of the set of support strategy in theorem-proving’, J. ACM 12, 687–697 (1965).
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This work was supported in part by NSF grant MCS-8313499.
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Wang, TC., Bledsoe, W.W. Hierarchical deduction. J Autom Reasoning 3, 35–77 (1987). https://doi.org/10.1007/BF00381144
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DOI: https://doi.org/10.1007/BF00381144