Skip to main content

Automated Model Building: From Finite to Infinite Models

  • Conference paper
Intelligent Computer Mathematics (CICM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5144))

Included in the following conference series:

  • 761 Accesses

Abstract

We propose a method for using existing finite model builders for constructing infinite models of first-order formulae. The considered interpretations are represented by tree tuple automata. Our approach is based on formula transformation. It is proven to be sound (i.e. all the constructed interpretations are models of the original formula) and complete for the considered class of interpretations (i.e. a model is eventually built for any formula having a model representable by a tree automaton).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Audemard, G., Benhamou, B.: Reasoning by symmetry and function ordering in finite model generation. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 226–240. Springer, Heidelberg (2002)

    Google Scholar 

  2. de la Tour, T.B.: A note on symmetry heuristics in SEM. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 181–194. Springer, Heidelberg (2002)

    Google Scholar 

  3. Caferra, R., Leitsch, A., Peltier, N.: Automated Model Building. Applied Logic Series, vol. 31. Kluwer Academic Publishers, Dordrecht (2004)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Claessen, K., Sorensson, N.: New techniques that improve mace-style finite model finding. In: Proceedings of the CADE-19 Workshop: Model Computation - Principles, Algorithms, Applications (Miami, USA) (2003)

    Google Scholar 

  6. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (1997), http://www.grappa.univ-lille3.fr/tata

  7. Fermueller, C., Pichler, R.: Model representation via contexts and implicit generalizations. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 409–423. Springer, Heidelberg (2005)

    Google Scholar 

  8. Fitting, M.: First-Order Logic and Automated Theorem Proving. Texts and Monographs in Computer Science. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  9. Gottlob, G., Pichler, R.: Working with ARMs: Complexity results on atomic representations of Herbrand models. Information and Computation 165, 183–207 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. McCune, B.: MACE 2.0 reference Manual and Guide. Technical report, Argonne National Laboratory (2001)

    Google Scholar 

  11. Peltier, N.: A new method for automated finite model building exploiting failures and symmetries. Journal of Logic and Computation 8(4), 511–543 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Plaisted, D., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation 2, 293–304 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Slaney, J.: Finder (FINite Domain EnumeratoR): Notes and guides. Technical report, Australian National University Automated Reasoning Project, Canberra (1992)

    Google Scholar 

  14. Zhang, J., Zhang, H.: SEM: a system for enumerating models. In: Proc. IJCAI 1995, vol. 1, pp. 298–303. Morgan Kaufmann, San Francisco (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Serge Autexier John Campbell Julio Rubio Volker Sorge Masakazu Suzuki Freek Wiedijk

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peltier, N. (2008). Automated Model Building: From Finite to Infinite Models. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85110-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85109-7

  • Online ISBN: 978-3-540-85110-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics