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Theory Instantiation

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4246))

Abstract

In this paper we present a method of integrating theory reasoning into the instantiation framework. This integration is done in the black-box style, which allows us to integrate different theories in a uniform way. We prove completeness of the resulting calculus, provided that the theory reasoner is answer-complete and complete for reasoning with ground clauses. One of the distinctive features of our approach is that it allows us to employ off-the-shelf satisfiability solvers for ground clauses modulo theories, as a part of general first-order reasoning. As an application of this approach, we show how it is possible to combine the instantiation calculus with other calculi, such as ordered resolution and paramodulation.

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References

  1. Armando, A., Ranise, S., Rusinowitch, M.: A Rewriting Approach to Satisfiability Procedures. Info. and Comp. 183(2), 140–164 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baader, F., Snyder, W.: Unification theory. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 445–532. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  3. Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 19–100. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  4. Bachmair, L., Ganzinger, H., Waldmann, U.: Refutational Theorem Proving for Hierarchic First-Order Theories. Applicable Algebra in Engineering, Communication and Computing 5(3/4), 193–212 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barrett, C., de Moura, L., Stump, A.: Design and results for the 1st satisfiability modulo theories competition. Journal of Automated Reasoning (to appear, 2006)

    Google Scholar 

  6. Baumgartner, P.: FDPLL – a first-order Davis-Putnam-Logeman-Loveland Procedure. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 200–219. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 350–364. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Baumgartner, P., Tinelli, C.: The model evolution calculus with equality. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 392–408. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Baumgartner, P.: An order theory resolution calculus. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 119–130. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  10. Gallier, J., Snyder, W.: Complete sets of transformations for general E-unification. Theoretical Computer Science 67(2,3), 203–260 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Ganzinger, H., Hillenbrand, T., Waldmann, U.: Superposition modulo a shostak theory. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 182–196. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: Proc. 18th IEEE Symposium on LICS, pp. 55–64. IEEE, Los Alamitos (2003)

    Google Scholar 

  14. Ganzinger, H., Korovin, K.: Integrating equational reasoning into instantiation-based theorem proving. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 71–84. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Ganzinger, H., Korovin, K.: Theory Instantiation (2006), Full version, Available at: http://www.cs.man.ac.uk/~korovink/

  16. Hooker, J., Rago, G., Chandru, V., Shrivastava, A.: Partial instantiation methods for inference in first order logic. J. of Automated Reasoning 28, 371–396 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hustadt, U., Motik, B., Sattler, U.: Reasoning in description logics with a concrete domain in the framework of resolution. In: ECAI, pp. 353–357 (2004)

    Google Scholar 

  18. Letz, R., Stenz, G.: Proof and model generation with disconnection tableaux. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS, vol. 2250, pp. 142–156. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Letz, R., Stenz, G.: Integration of equality reasoning into the disconnection calculus. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS, vol. 2381, pp. 176–190. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Lynch, C., Morawska, B.: Goal-directed E-unification. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 231–245. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Nieuwenhuis, R.: On narrowing, refutation proofs and constraints. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 56–70. Springer, Heidelberg (1995)

    Google Scholar 

  22. Nieuwenhuis, R., Oliveras, A.: Decision Procedures for SAT, SAT Modulo Theories and Beyond. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS, vol. 3835, pp. 23–46. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 371–443. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  24. Plaisted, D., Zhu, Y.: Ordered semantic hyper-linking. J. of Automated Reasoning 25(3), 167–217 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. Stickel, M.: Automated deduction by theory resolution. J. Autom. Reasoning 1(4), 333–355 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  26. Tinelli, C.: A DPLL-based calculus for ground satisfiability modulo theories. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 308–319. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. MPI für Informatik,  

    Harald Ganzinger

  2. University of Manchester,  

    Konstantin Korovin

Authors
  1. Harald Ganzinger
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  2. Konstantin Korovin
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Editor information

Editors and Affiliations

  1. LIX (CNRS, UMR 7161), École Polytechnique, 91128, Palaiseau, France

    Miki Hermann

  2. University of Manchester, UK

    Andrei Voronkov

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Ganzinger, H., Korovin, K. (2006). Theory Instantiation. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_34

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  • DOI: https://doi.org/10.1007/11916277_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48281-9

  • Online ISBN: 978-3-540-48282-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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