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International Conference on Formal Methods in Computer-Aided Design

FMCAD 1998: Formal Methods in Computer-Aided Design pp 82–99Cite as

A Tutorial on Stålmarck’s Proof Procedure for Propositional Logic

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1522))

Abstract

We explain Stålmarck’s proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions that have resulted in a system that copes well with the large formulas encountered in industrial-scale verification. We also discuss possible applications in Computer Aided Design of electronic circuits.

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References

  1. E.W. Beth: Semantic entailment and formal derivability. Mededelingen der Kon. Nederlandes Akademie van Wetenschappen. Afd. letterkunde, n.s., 18, 309–342, Amsterdam, 1955.

    MathSciNet  Google Scholar 

  2. P. Bjesse, K. Claessen, M. Sheeran and S. Singh: Lava: Hardware Design in Haskell. Proc. Int. Conf. on Functional Programming, ACM Press, 1998.

    Google Scholar 

  3. A. BorÄlv:The industrial success of verification tools based on Stålmarck’s method. Proc. 9th Int. Conf. on Computer Aided Verification, Springer-Verlag LNCS vol. 1254, 1997.

    Google Scholar 

  4. A. BorÄlv and G. Stålmarck. Prover Technology in Railways, In Industrial-Strength Formal Methods, Academic Press, 1998.

    Google Scholar 

  5. R. Bryant: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. Comp., vol. c-35, no. 8, 1986.

    Google Scholar 

  6. S.A. Cook: The complexity of theorem-proving procedures. In Proc. 3rd ACM Symp. on the Theory of Computing, 1971.

    Google Scholar 

  7. M. D’Agostino: Investigation into the complexity of some propositional calculi. D. Phil. Dissertation, Programming Research Group, Oxford University, 1990.

    Google Scholar 

  8. M. Davis, G. Logemann and D. Loveland: A machine program for theorem proving. Communications of the ACM, 5:34–397, 1962. Reprinted in [21].

    Article  MathSciNet  Google Scholar 

  9. M. Davis and H. Putnam: A computing procedure for quantification theory. Journal of the ACM, 7:201–215, 1960. Reprinted in [21].

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Gentzen: Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39, 176–210, 1935. English translation in The Collected Papers of Gerhard Gentzen, Szabo (ed.), North-Holland, Amsterdam, 1969.

    Article  MathSciNet  Google Scholar 

  11. J.F. Groote, J.W.C. Koorn and S.F.M. van Vlijmen: The Safety Guaranteeing System at Station Hoorn-Kersenboogerd. Technical Report 121, Logic Group Preprint Series, Utrecht Univ., 1994.

    Google Scholar 

  12. J. Harrison: The Stålmarck Method as a HOL Derived Rule. Theorem Proving in Higher Order Logics, Springer-Verlag LNCS vol. 1125, 1996.

    Google Scholar 

  13. J.K.J. Hintikka: Form and content in quantification theory. Acta Philosophica Fennica, VII, 1955.

    Google Scholar 

  14. S. Kanger: Provability in Logic. Acta Universitatis Stockholmiensis, Stockholm Studies in Philosopy, 1, 1957.

    Google Scholar 

  15. S. C. Kleene: Mathematical Logic. John Wiley and Sons Inc., New York, 1967.

    MATH  Google Scholar 

  16. W. Kunz and D.K. Pradhan: Recursive Learning: A New Implication Technique for Efficient Solutions to CAD-problems: Test, Verification and Optimization. IEEE Trans. CAD, vol. 13, no. 9, 1994.

    Google Scholar 

  17. M. Mondadori: An improvement of Jeffrey’s deductive trees. Annali dell’Universita di Ferrara; Sez III; Discussion paper 7, Universita di Ferrara, 1989.

    Google Scholar 

  18. K. Schütte: Proof Theory, Springer-Verlag, Berlin, 1977.

    Google Scholar 

  19. G. Stålmarck: A system for determining propositional logic theorems by applying values and rules to triplets that are generated from a formula, 1989. Swedish Patent No. 467 076 (approved 1992), U.S. Patent No. 5 276 897 (approved 1994), European Patent No. 0403 454 (approved 1995).

    Google Scholar 

  20. M. Sheeran and A. BorÄlv: How to prove properties of recursively defined circuits using Stålmarck’s method. Proc. Workshop on Formal Methods for Hardware and Hardware-like systems, Marstrand, June 1998.

    Google Scholar 

  21. J. Siekman and G. Wrightson (editors): Automation of Reasoning. Springer-Verlag, New York, 1983.

    Google Scholar 

  22. R.M. Smullyan: First Order Logic. Springer, Berlin, 1969.

    Google Scholar 

  23. M. Srivas and A. Camilleri (editors): Proc. Int. Conf. on Formal Methods in Computer-Aided Design. Springer-Verlag LNCS vol. 1146, 1996.

    Google Scholar 

  24. M. SÄflund: Modelling and formally verifying systems and software in industrial applications. Proc. second Int. Conf. on Reliability, Maintainability and Safety (ICRMS’ 94), Xu Ferong (ed.), 1994.

    Google Scholar 

  25. O. åkerlund, G. Stålmarck and M. Helander: Formal Safety and Reliability Analysis of Embedded Aerospace Systems at Saab. Proc. 7th IEEE Int. Symp. on Software Reliability Engineering (Industrial Track), IEEE Computer Society Press, 1996.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Prover Technology AB and Chalmers University of Technology, Sweden

    Mary Sheeran & Gunnar Stålmarck

Authors
  1. Mary Sheeran
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  2. Gunnar Stålmarck
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Utah, 50 S Central Campus, Salt Lake City, UT, 841112-9205, USA

    Ganesh Gopalakrishnan

  2. Department of Computer Science, Brigham Young University, 3361 TMCB, Provo, UT, 84602-6576, USA

    Phillip Windley

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© 1998 Springer-Verlag Berlin Heidelberg

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Sheeran, M., Stålmarck, G. (1998). A Tutorial on Stålmarck’s Proof Procedure for Propositional Logic. In: Gopalakrishnan, G., Windley, P. (eds) Formal Methods in Computer-Aided Design. FMCAD 1998. Lecture Notes in Computer Science, vol 1522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49519-3_7

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  • DOI: https://doi.org/10.1007/3-540-49519-3_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65191-8

  • Online ISBN: 978-3-540-49519-2

  • eBook Packages: Springer Book Archive

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