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Cyclic connections

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Theorem Proving with Analytic Tableaux and Related Methods (TABLEAUX 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1071))

Abstract

We present a way to build-in the linear order theory into the connection method. The approach is an instance of the method developed by U. Petermann for building-in open theories into connection calculi. Connections with linear ordering as background theory are characterized and called cyclic connections. A query language Q and a complete set of such connections with respect to Q are defined and the associated unification problem is proved to be a simultaneous rigid E-unification problem. Although this problem is undecidable, we recall how methods like the equational matings method of J. Gallier et al. or the present cyclic connections method can be used owing to an enumeration procedure of rigid E-unifiers due to B. Beckert.

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References

  1. P. Andrews. Theorem Proving via General Matings. J.ACM, 28(2):193–214, 1981.

    Google Scholar 

  2. L. Bachmair and H. Ganzinger. Rewrite techniques for transitive relations. Technical Report MPI-I-93-249, Max-Planck-Institut für Informatik, 1993.

    Google Scholar 

  3. G. Becher. Démonstration Automatique en Logique Temporelle et Algorithmes d'E-Unification Rigide. PhD thesis, Université de Caen, 1995.

    Google Scholar 

  4. G. Becher and U. Petermann. Rigid Unification by Completion and Rigid Paramodulation. In B. Nebel and L. Dreschler-Fischer, editors, KI-94: Advances in Artificial Intelligence, volume 861 of Lecture Notes in Computer Science, pages 319–330. Springer-Verlag, 1994.

    Google Scholar 

  5. B. Beckert. Ein vervollständigungsbasiertes Verfahren zur Behandlung von Gleichheit im Tableaukalkül mit freien Variablen. Master's thesis, Universität Karlsruhe (TH), 1993.

    Google Scholar 

  6. W. Bibel. Automated Theorem Proving. Vieweg, 1st edition, 1982.

    Google Scholar 

  7. W. Bledsoe and L. Hines. Variable Elimination and Chaining in a Resolutionbased Prover for Inequalities. In S. Verlag, editor, Proc. 5th Conference on Automated Deduction, pages 70–87, Les Arcs, France, 1980.

    Google Scholar 

  8. A. Degtyarev and A. Voronkov. Simultaneous Rigid E-Unification is Undecidable. Technical report, Tech. Report No. 105. Computing Science Department, Uppsala University, May 1995.

    Google Scholar 

  9. J. Gallier, P. Narendran, S. Raatz, and W. Snyder. Theorem Proving with Equational Matings and Rigid E-Unification. Journal of ACM, 39(2):377–429, April 1992.

    Google Scholar 

  10. J. H. Gallier. Unification Procedures in Automated Deduction Methods Based on Matings: a Survey. In M. Nivat and A. Podelski, editors, Tree Automata and Languages, pages 439–485. North-Holland Publishing Company, 1992.

    Google Scholar 

  11. J. Goubault. A Rule-Based Algorithm for Rigid E-Unification. In G. Gottlob, A. Leitsch, and D. Mundici, editors, 3rd Kurt Gödel Colloquium '93, volume 713 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

    Google Scholar 

  12. L. M. Hines. Completeness of a Prover for Dense Linear Orders. Journal of Automated Reasoning, 8:45–75, 1992.

    Google Scholar 

  13. G. Nelson and D. C. Oppen. Fast Decision Procedures Based on Congruence Closure. Journal of Association for Computer Machinery, 27(2):356–364, April 1980.

    Google Scholar 

  14. U. Petermann. How to build in an open theory into connection calculi. J. on Computer and Artificial Intelligence, 11(2):105–142, 1992.

    Google Scholar 

  15. U. Petermann. A complete equational connection calculus with rigid E-unification. NTZ-Report 26/1993, Naturwissenschaftlich-Theoretisches Zentrum der Universität Leipzig, 1993.

    Google Scholar 

  16. M. E. Stickel. Automated deduction by theory resolution. Journal of Automated Reasoning, pages 333–356, 1985.

    Google Scholar 

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Authors and Affiliations

  1. GREYC - CNRS URA 1526, Université de Caen, F-14032, Caen Cedex, France

    Gérard Becher

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  1. Gérard Becher
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Editor information

P. Miglioli U. Moscato D. Mundici M. Ornaghi

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© 1996 Springer-Verlag Berlin Heidelberg

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Becher, G. (1996). Cyclic connections. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_6

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  • DOI: https://doi.org/10.1007/3-540-61208-4_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61208-7

  • Online ISBN: 978-3-540-68368-1

  • eBook Packages: Springer Book Archive

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