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Decision procedures using model building techniques

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Computer Science Logic (CSL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1092))

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Abstract

Few year ago we have developed an Automated Deduction approach to model building. The method, called RAMC looks simultaneously for inconsistencies and models for a given formula. The capabilities of RAMC have been extended both for model building and for unsatisfiability detection by including in it the use of semantic strategies. In the present work we go further in this direction and define more general and powerful semantic rules. These rules are an extension of Slagle's semantic resolution. The robustness of our approach is evidenced by proving that the method is also a decision procedure for a wide range of classes decidable by semantic resolution and in particular by hyper-resolution. Moreover, the method builds models for satisfiable formulae in these classes, in particular, for satisfiable formulae that do not have any finite model.

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References

  1. Egon BÖRGER. Decision problems in predicate logic. In G. Longo G. Lolli and A. Marcja, editors, Logic Colloquium'82, pages 263–301. North-Holland, 1984.

    Google Scholar 

  2. Ricardo CAFERRA and Nicolas PELTIER. Extending semantic resolution via automated model building: applications. In Proceeding of IJCAI'95. Morgan Kaufmann, 1995.

    Google Scholar 

  3. Ricardo CAFERRA and Nicolas PELTIER. Model building and interactive theory discovery. In Proceeding of Tableaux'95, LNAI 918, pages 154–168. Springer-Verlag, 1995.

    Google Scholar 

  4. Ricardo Caferra and Nicolas Zabel. A method for simultaneous search for refutations and models by equational constraint solving. Journal of Symbolic Computation, 13:613–641, 1992.

    Google Scholar 

  5. Burton DREBEN and Warren D. GOLDFARB. The Decision Problem, Solvable Classes of Quantificational Formulas. Addison-Wesley, 1979.

    Google Scholar 

  6. Christian FERMÜLLER and Alexander LEITSCH. Model building by resolution. In Computer Science Logic, CSL '92, pages 134–148. Springer-Verlag, LNCS 702, 1992.

    Google Scholar 

  7. Christian FERMÃœLLER and A. LEITSCH. Hyperresolution and automated model building. Journal of Logic and Computation, 1995. To appear.

    Google Scholar 

  8. C. FERMÃœLLER, A. LEITSCH, T. TAMMET, and N. ZAMOV. Resolution Methods for the Decision Problem. LNAI 679, Springer-Verlag, 1993.

    Google Scholar 

  9. W.H. Joyner. Resolution strategies as decision procedures. Journal of the ACM, 23:398–417, 1976.

    Google Scholar 

  10. Alexander Leitsch. Deciding clause classes by semantic clash resolution. Fundamenta Informaticae, 18:163–182, 1993.

    Google Scholar 

  11. Harry LEWIS. Unsolvable classes of quantificational formulas. Addison-Wesley, 1979.

    Google Scholar 

  12. William McCune and Lawrence Henschen. Experiments with semantic paramodulation. Journal of Automated Reasoning, 1:231–261, 1985.

    Google Scholar 

  13. Grigori E. Mints. Proof theory in the USSR 1925–1969. Journal of Symbolic Logic, 56(2):385–424, June 1991.

    Google Scholar 

  14. James R. Slagle. Automatic theorem proving with renamable and semantic resolution. Journal of the ACM, 14(4):687–697, October 1967.

    Google Scholar 

  15. Tanel Tammet. Using resolution for deciding solvable classes and building finite models. In Baltic Computer Science, pages 33–64. Springer-Verlag, LNCS 502, 1991.

    Google Scholar 

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Hans Kleine Büning

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© 1996 Springer-Verlag Berlin Heidelberg

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Caferra, R., Peltier, N. (1996). Decision procedures using model building techniques. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_35

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  • DOI: https://doi.org/10.1007/3-540-61377-3_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61377-0

  • Online ISBN: 978-3-540-68507-4

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