Skip to main content
SpringerLink
Log in
Book cover

International Joint Conference on Automated Reasoning

IJCAR 2014: Automated Reasoning pp 192–207Cite as

Locality Transfer: From Constrained Axiomatizations to Reachability Predicates

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

Abstract

In this paper, we build upon our previous work in which we used constrained clauses in order to finitely represent infinite sets of clauses and proved that constrained axiomatizations are local if they are saturated under a version of resolution. We extend this result by identifying situations in which locality of saturated axiomatizations is maintained if we enrich the base theory by introducing new predicates (often reachability predicates) instead of using constraints for these properties.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. of Logic and Computation 4(3), 217–247 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Basin, D., Ganzinger, H.: Complexity analysis based on ordered resolution. In: Proc. LICS 1996, pp. 456–465. IEEE Computer Society Press (1996)

    Google Scholar 

  3. Basin, D., Ganzinger, H.: Automated complexity analysis based on ordered resolution. Journal of the ACM 48(1), 70–109 (2001)

    Article  MathSciNet  Google Scholar 

  4. Ganzinger, H.: Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems. In: Proc. LICS 2001, pp. 81–92. IEEE Computer Society Press (2001)

    Google Scholar 

  5. Givan, R., McAllester, D.: New results on local inference relations. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR 1992), pp. 403–412. Morgan Kaufmann Press (1992)

    Google Scholar 

  6. Horbach, M., Sofronie-Stokkermans, V.: Obtaining finite local theory axiomatizations via saturation. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 198–213. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Horbach, M., Weidenbach, C.: Deciding the inductive validity of ∀ ∃ * queries. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 332–347. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Horbach, M., Weidenbach, C.: Superposition for Fixed Domains. ACM Transactions on Computational Logic 11(4), 27:1–27:35 (2010)

    Google Scholar 

  9. Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On local reasoning in verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Ihlemann, C., Sofronie-Stokkermans, V.: On hierarchical reasoning in combinations of theories. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 30–45. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Lev-Ami, T., Immerman, N., Reps, T.W., Sagiv, M., Srivastava, S., Yorsh, G.: Simulating reachability using first-order logic with applications to verification of linked data structures. Logical Methods in Computer Science 5(2) (2009)

    Google Scholar 

  12. Klaessen, K.: Expressing transitive closure for finite domains in pure first-order logic. Unpublished manuscript

    Google Scholar 

  13. 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 

  14. Sofronie-Stokkermans, V.: Locality results for certain extensions of theories with bridging functions. In: Schmidt, R.A. (ed.) CADE-22. LNCS (LNAI), vol. 5663, pp. 67–83. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Wies, T., Muñiz, M., Kuncak, V.: An efficient decision procedure for imperative tree data structures. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 476–491. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Wies, T., Muñiz, M., Kuncak, V.: Deciding functional lists with sublist sets. In: Joshi, R., Müller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol. 7152, pp. 66–81. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Koblenz-Landau, Koblenz, Germany

    Matthias Horbach & Viorica Sofronie-Stokkermans

  2. Max-Planck-Institut für Informatik Saarbrücken, Germany

    Matthias Horbach & Viorica Sofronie-Stokkermans

Authors
  1. Matthias Horbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Viorica Sofronie-Stokkermans
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Horbach, M., Sofronie-Stokkermans, V. (2014). Locality Transfer: From Constrained Axiomatizations to Reachability Predicates. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08587-6_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation