Abstract
In this paper we have a closer look at one of the rules of the tableau calculus presented in [3], called the δ-rule, and the modification of this rule, that has been proved to be sound and complete in [6], called the δ +-rule, which uses fewer free variables. We show that, an even more liberalized version, the \(\delta ^{ + ^ + }\)-rule, that in addition reduces the number of different Skolem-function symbols that have to be used, is also sound and complete. Examples show the relevance of this modification for building tableau-based theorem provers.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Peter B. Andrews. An Introduction to Mathematical Logic and Type Theory. Academic Press, 1986.
Melvin C. Fitting. First-order modal tableaux. Journal of Automated Reasoning, 4:191–213, 1988.
Melvin C. Fitting. First-Order Logic and Automated Theorem Proving. Springer, New York, 1990.
Reiner Hähnle. Automated Theorem Proving in Multiple-Valued Logics. Oxford University Press, forthcoming, 1993.
Reiner Hähnle, Bernhard Beckert, Stefan Gerberding, and Werner Kernig. The Many-Valued Tableau-Based Theorem Prover 3TAP. IWBS Report 227, Wissenschaftliches Zentrum Heidelberg, IWBS, IBM Deutschland, July 1992.
Reiner Hähnle and Peter H. Schmitt. The liberalized δ-rule in free variable semantic tableaux. Journal of Automated Reasoning, to appear, 1993.
Steve V. Reeves. Semantic tableaux as a framework for automated theorem-proving. Department of Computer Science and Statistics, Queen Mary College, Univ. of London, 1987.
Raymond Smullyan. First-Order Logic. Springer, New York, 1968.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beckert, B., Hähnle, R., Schmitt, P.H. (1993). The even more liberalized δ-rule in free variable Semantic Tableaux. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022559
Download citation
DOI: https://doi.org/10.1007/BFb0022559
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57184-1
Online ISBN: 978-3-540-47943-7
eBook Packages: Springer Book Archive