Abstract
In this paper we present a variant of paramodulation, called s-paramodulation, that simultaneously replaces certain subterms that unify with the “into-term” by an instance of the “from-term”. We show that in contrast to ordinary paramodulation, the lifting lemma holds for s-paramodulation. We also show that s-paramodulation in conjunction with resolution is refutationally complete in the ground case. Completeness in the general case follows easily from the lifting lemma and the ground case.
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References
D. Benanav. Recognizing Unnecessary Inference. PhD thesis, Rensselaer Polytechnic Institute, 1989.
D. S. Lankford. Some approaches to equality for computational logic: A survey and assessment. Memo ATP-36, Automatic Theorem Proving Project, University of Texas, Austin, 1977.
W. McCune. Otter 1.0 users' guide. Technical Report ANL-88-44, Argonne National Laboratory, Argonne, IL, January 1989.
G. Peterson. A technique for establishing completeness results in theorem proving with equality. SIAM J. Computing, 12(1):82–99, February 1983.
G. Peterson and M. Stickel. Complete sets of reductions for some equational theories. Journal of the Association for Computing Machinery, 28(2):231–264, April 1981.
G. Robinson and L. Wos. Paramodulation and theorem-proving in first-order theories with equality. In B. Meltzer and D. Michie, editors, Machine Intelligence 4. Edinburgh University Press, 1969.
H. Zhang. Reduction, Superposition & Induction:, Automated Reasoning in an Equational Logic. PhD thesis, Rensselaer Polytechnic Institute, August 198
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© 1990 Springer-Verlag Berlin Heidelberg
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Benanav, D. (1990). Simultaneous paramodulation. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_106
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DOI: https://doi.org/10.1007/3-540-52885-7_106
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Online ISBN: 978-3-540-47171-4
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