Abstract
Recently, several different sound and complete tableau calculi were introduced, all sharing the idea to use a selection function and so-called restart clauses: A-ordered tableaux, tableaux with selection function, and strict restart model elimination. We present two new sound and complete abstract tableau calculi which generalize these on the ground level. This makes differences and similarities between the calculi clearer and, in addition, gives insight into how properties of the calculi can be transferred among them. In particular, a precise borderline separating proof confluent from non-proof confluent variants is exhibited.
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P. Baumgartner and U. Furbach. Model Elimination without Contrapositives and its Application to PTTP. Journal of Automated Reasoning, 13:339–359, 1994.
H. de Nivelle. Resolution Games and Non-Liftable Resolution Orderings. In Collegium Logicum. Annals of the Kurt-Gödel-Society, volume 2, pages 1–20. Springer-Verlag, Wien New York, 1996.
E. Eder. A Comparison of the Resolution Calculus and the Connection Method, and a new Calculus Generalizing both Methods. In E. Bërger, H. K. Büning, and M. M. Richter, editors, Proceedings of the 2nd Workshop on Computer Science Logic, volume 385 of LNCS, pages 80–98, Berlin, Oct. 1989. Springer.
R. Hähnle and S. Klingenbeck. A-Ordered Tableaux. Journal of Logic and Computation, 6(6):819–834, 1996.
R. Hähnle and C. Pape. Ordered Tableaux: Extensions and Applications.In D. Galmiche, editor, Proc. International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Pont-á-Mousson, France, volume 1227 of LNAI, pages 173–187. Springer, 1997.
R. Letz, J. Schumann, S. Bayerl, and W. Bibel. SETHEO: A High-Perfomance Theorem Prover. Journal of Automated Reasoning, 8(2):183–212, 1992.
D. Loveland. Mechanical Theorem Proving by Model Elimination. Journal of the ACM, 15(2), 1968.
D. W. Loveland. Near-Horn Prolog and Beyond. Journal of Automated Reasoning, 7(1):1–26, Mar. 1991.
C. Pape. Vergleich und Analyse von Ordnungseinschränkungen für freie Variablen Tableau. Diplomarbeit, Fakultät für Informatik, Universität Karlsruhe, May 1996. In German. Available via anonymous ftp to ftp.ira.uka.de under pub/uni-karlsruhe/papers/techreports/1996/1996-30.ps.gz.
D. A. Plaisted. A Simplified Problem Reduction Format. Artificial Intelligence, 18:227–261, 1982.
M. E. Stickel. A Prolog Technology Theorem Prover. In E. Lusk and R. Overbeek, editors, 9th International Conference on Automated Deduction (CADE), LNCS, pages 752–753, Argonne, 111, 1988. Springer.
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Pape, C., Hähnle, R. (1997). Restart tableaux with selection function. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_45
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DOI: https://doi.org/10.1007/3-540-63385-5_45
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