Abstract
We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of first-order clauses with equality. Technically proofs by consistency will be similar to proofs by case analysis over the term structure. As our method also allows to prove sufficient-completeness of function definitions in parallel with proving an inductive theorem we need not distinguish between constructors and defined functions. Our method is linear and refutationally complete with respect to the perfect model, it supports lemmas in a natural way, and it provides for powerful simplification and elimination techniques.
This research was funded by the German Ministry for Research and Technology (BMFT) under grant ITS 9103. The responsibility for the contents of this publication lies with the authors.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Leo Bachmair. Proof by consistency in equational theories. In Proc. 3rd IEEE Symp. on Logic in Computer Science, pages 228–233, Edinburgh, July 1988.
Leo Bachmair and Harald Ganzinger. On restrictions of ordered paramodulation with simplification. In Proc. 10th Int. Conf. on Automated Deduction, Kaiserslautern, July 1990. Springer LNCS 449.
Leo Bachmair and Harald Ganzinger. Completion of first-order clauses with equality by strict superposition. In Proc. 2nd Int. Workshop on Conditional and Typed Rewriting Systems, Montreal, June 1990. Springer LNCS 516.
Leo Bachmair and Harald Ganzinger. Perfect model semantics for logic programs with equality. In Proc. 8th Int. Conf. on Logic Programming. MIT Press, 1991.
Leo Bachmair and Harald Ganzinger. Rewrite-based equational theorem proving with selection and simplification. Technical Report MPI-I-91-208, Max-Planck-Institut für Informatik, Saarbrücken, August 1991.
Eddy Bevers and Johan Lewi. Proof by consistency in conditional equational theories. In Proc. 2nd Int. Workshop on Conditional and Typed Rewriting Systems, Montreal, June 1990. Springer LNCS 516.
Robert S. Boyer and J. Strother Moore. A Computational Logic. Academic Press, New York, 1979.
A. Bundy, F. van Harmelen, A. Smail, and A. Ireland. Extensions to the rippling-out tactic for guiding inductive proofs. In Proc. 10th Int. Conf. on Automated Deduction, pages 132–146, Kaiserslautern, July 1990. Springer LNCS 449.
Laurent Fribourg. A strong restriction of the inductive completion procedure. In Proc. 13th Int. Coll. on Automata, Languages and Programming, pages 105–115, Rennes, France, July 1986. Springer LNCS 226.
H. Ganzinger and R. Schäfers. System support for modular order-sorted Horn clause specifications. Proc. 12th Int. Conf. on Software Engineering, Nice, pages 150–163, 1990.
Stephen J. Garland and John V. Guttag. Inductive methods for reasoning about abstract data types. In Proc. 15th Annual ACM Symp. on Principles of Programming Languages, pages 219–228, San Diego, January 1988.
Gérard Huet and Jean-Marie Hullot. Proofs by induction in equational theories with constructors. Journal of Computer and System Sciences, 25:239–266, 1982.
Jean-Pierre Jouannaud and Emmanuel Kounalis. Proofs by induction in equational theories without constructors. In Proc. Symp. on Logic in Computer Science, pages 358–366, Cambridge, Mass., June 1986.
Stephane Kaplan and Marianne Choquer. On the decidability of quasi-reducibility. EATCS Bulletin, 28:32–34, 1986.
David R. Musser. On proving inductive properties of abstract data types. In Proc. 7th Annual ACM Symp. on Principles of Programming Languages, pages 154–162, Las Vegas, January 1980.
Fernando Orejas. Theorem proving in conditional-equational theories. Draft.
Peter Padawitz. Inductive expansion: A calculus for verifying and synthesizing functional and logic programs. Journal of Automated Reasoning, 7(1):27–103, March 1991.
David A. Plaisted. Semantic confluence tests and completion methods. Information and Control, 65:182–215, 1985.
T. C. Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Data Bases and Logic Programming, pages 193–216. Morgan Kaufmann Publishers, Los Altos, 1988.
Jürgen Stuber. Inductive theorem proving for horn clauses. Master's thesis, Universität Dortmund, April 1991.
Author information
Authors and Affiliations
Corresponding author
Editor information
Additional information
A full version of this paper appeared in: Informatik—Festschrift zum 60. Geburtstag von Günter Hotz, Teubner-Verlag, Stuttgart 1992
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ganzinger, H., Stuber, J. (1993). Inductive theorem proving by consistency for first-order clauses. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_17
Download citation
DOI: https://doi.org/10.1007/3-540-56393-8_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56393-8
Online ISBN: 978-3-540-47549-1
eBook Packages: Springer Book Archive