Skip to main content
Springer Nature Link
Log in

Interpolation in Local Theory Extensions

  • Conference paper
Automated Reasoning (IJCAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

Included in the following conference series:

  • 1110 Accesses

Abstract

In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the base theory as black-boxes. We present several examples of theory extensions in which interpolants can be computed this way, and discuss applications in verification, knowledge representation, and modular reasoning in combinations of local theories.

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

Access this chapter

Log in via an institution

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. Bacsich, P.D.: Amalgamation properties and interpolation theorem for equational theories. Algebra Universalis 5, 45–55 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Jónsson, B.: Extensions of relational structures. In: Addison, J.W., Henkin, L., Tarski, A. (eds.) The Theory of Models, Proc. of the 1963 Symposium at Berkeley, pp. 146–157. North-Holland, Amsterdam (1965)

    Google Scholar 

  3. McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. McMillan, K.L.: An interpolating theorem prover. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 16–30. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. McMillan, K.L.: Applications of Craig interpolants in model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. V. Sofronie-Stokkermans. On combinations of local theory extensions (Submitted)

    Google Scholar 

  7. Sofronie-Stokkermans, V.: Automated theorem proving by resolution in non-classical logics. In: 4th Int. Conf. Journees de l’Informatique Messine: Knowledge Discovery and Discrete Mathematics (JIM-03), pp. 151–167 (2003)

    Google Scholar 

  8. Sofronie-Stokkermans, V.: Hierarchic reasoning in local theory extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Wroński, A.: On a form of equational interpolation property. In: Foundations of logic and linguistics (Salzburg, 1983), Plenum, New York, pp. 23–29 (1985)

    Google Scholar 

  10. Yorsh, G., Musuvathi, M.: A combination method for generating interpolants. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 353–368. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

Authors
  1. Viorica Sofronie-Stokkermans
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Artificial Intelligence Research Group, University of Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz

    Ulrich Furbach

  2. SRI International, MS EL256,, 333 Ravenswood Avenue, 94025-3493, Menlo Park, CA, USA

    Natarajan Shankar

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sofronie-Stokkermans, V. (2006). Interpolation in Local Theory Extensions. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_21

Download citation

  • DOI: https://doi.org/10.1007/11814771_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation