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Proof Development with Ωmega

  • Jörg Siekmann
  • Christoph Benzmüller
  • Vladimir Brezhnev
  • Lassaad Cheikhrouhou
  • Armin Fiedler
  • Andreas Franke
  • Helmut Horacek
  • Michael Kohlhase
  • Andreas Meier
  • Erica Melis
  • Markus Moschner
  • Immanuel Normann
  • Martin Pollet
  • Volker Sorge
  • Carsten Ullrich
  • Claus-Peter Wirth
  • Jürgen Zimmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2392)

Abstract

The Ωmega proof development system [2] is the core of several related and well integrated research projects of the Ωmega research group.

Keywords

Residue Class Natural Deduction Constraint Solver Proof Assistant Proof Tree 
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.

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References

  1. 1.
    S. Allen, R. Constable, R. Eaton, C. Kreitz, and L. Lorigo. The Nuprl open logical environment. In Proc. of CADE-17, LNAI 1831. Springer, 2000.Google Scholar
  2. 2.
    C. Benzmüller et al. Ωmega: Towards a mathematical assistant. In Proc. of CADE-14, LNAI 1249. Springer, 1997.Google Scholar
  3. 3.
    C. Benzmüller and V. Sorge. Ω-Ants-An open Approach at Combining Interactive and Automated Theorem Proving. In Proc. of Calculemus-2000. AK Peters, 2001.Google Scholar
  4. 4.
    W.W. Bledsoe. Challenge problems in elementary analysis. Journal of Automated Reasoning, 6:341–359, 1990.zbMATHCrossRefGoogle Scholar
  5. 5.
    A. Bundy. The Use of Explicit Plans to Guide Inductive Proofs. In Proc. of CADE-9, LNCS 310. Springer, 1988.Google Scholar
  6. 6.
    A. Bundy, F. van Harmelen, J. Hesketh, and A. Smaill. Experiments with proof plans for induction. Journal of Automated Reasoning, 7:303–324, 1991. Earlier version available from Edinburgh as DAI Research Paper No 413.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    L. Cheikhrouhou and V. Sorge. PDS — A Three-Dimensional Data Structure for Proof Plans. In Proc. of ACIDCA’2000, 2000.Google Scholar
  8. 8.
    A. Church. A Formulation of the Simple Theory of Types. The Journal of Symbolic Logic, 5:56–68, 1940.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    S. Owre et al. PVS: Combining specification, proof checking and model checking. In Proc. of CAV-96, LNCS 1102. Springer, 1996.Google Scholar
  10. 10.
    A. Fiedler. P.rex: An interactive proof explainer. In Proc. of IJCAR 2001, LNAI 2083. Springer, 2001.Google Scholar
  11. 11.
    M. Kohlhase and J. Zimmer. System description: The MathWeb Software Bus for Distributed Mathmatical Reasoning. In Proc. of CADE-18, LNAI. Springer, 2002.Google Scholar
  12. 12.
    A. Franke and M. Kohlhase. System description: MBase, an open mathematical knowledge base. In Proc. of CADE-17, LNAI 1831. Springer, 2000.Google Scholar
  13. 13.
    M. Gordon and T. Melham. Introduction to HOL-A theorem proving environment for higher order logic. Cambridge University Press, 1993.Google Scholar
  14. 14.
    W. McCune. Otter 3.0 reference manual and guide. Technical Report ANL-94-6, Argonne National Laboratory, Argonne, Illinois 60439, USA, 1994.Google Scholar
  15. 15.
    A. Meier. TRAMP: Transformation of Machine-Found Proofs into Natural Deduction Proofs at the Assertion Level. In Proc. of CADE-17, LNAI 1831. Springer, 2000.Google Scholar
  16. 16.
    A. Meier, M. Pollet, and V. Sorge. Comparing Approaches to Explore the Domain of Residue Classes. Journal of Symbolic Computations, 2002. forthcoming.Google Scholar
  17. 17.
    E. Melis and A. Meier. Proof Planning with Multiple Strategies. In Proc. of CL-2000, LNAI 1861. Springer, 2000.Google Scholar
  18. 18.
    E. Melis and J. Siekmann. Knowledge-Based Proof Planning. Artificial Intelligence, 115(1):65–105, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    E. Melis, J. Zimmer, and T. Müller. Integrating constraint solving into proof planning. In Proc. of FroCoS 2000, LNAI 1794. Springer, 2000.Google Scholar
  20. 20.
    J.D.C Richardson, A. Smaill, and I.M. Green. System description: Proof planning in higher-order logic with λ-CLAM. In Proc. of CADE-15, LNAI 1421, Springer, 1998.Google Scholar
  21. 21.
    J. Siekmann et al. \( \mathcal{L}\mathcal{O}\mathcal{U}\mathcal{I}{\text{: }}\mathcal{L}{\text{ovely}} \) Ωmega \( \mathcal{U}{\text{ser }}\mathcal{I}{\text{nterface}} \). Formal Aspects of Computing, 11:326–342, 1999.CrossRefGoogle Scholar
  22. 22.
    V. Sorge. Non-Trivial Computations in Proof Planning. In Proc. of FroCoS 2000, LNAI 1794. Springer, 2000.Google Scholar
  23. 23.
    Coq Development Team. The Coq Proof Assistant Reference Manual. INRIA. see http://coq.inria.fr/doc/main.html.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jörg Siekmann
    • 1
  • Christoph Benzmüller
    • 1
  • Vladimir Brezhnev
    • 1
  • Lassaad Cheikhrouhou
    • 1
  • Armin Fiedler
    • 1
  • Andreas Franke
    • 1
  • Helmut Horacek
    • 1
  • Michael Kohlhase
    • 1
  • Andreas Meier
    • 1
  • Erica Melis
    • 1
  • Markus Moschner
    • 1
  • Immanuel Normann
    • 1
  • Martin Pollet
    • 1
  • Volker Sorge
    • 1
  • Carsten Ullrich
    • 1
  • Claus-Peter Wirth
    • 1
  • Jürgen Zimmer
    • 1
  1. 1.FR 6.2 InformatikUniversität des SaarlandesSaarbrückenGermany

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