Obtaining Finite Local Theory Axiomatizations via Saturation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8152)


In this paper we present a method for obtaining local sets of clauses from possibly non-local ones. For this, we follow the work of Basin and Ganzinger and use saturation under a version of ordered resolution. In order to address the fact that saturation can generate infinite sets of clauses, we use constrained clauses and show that a link can be established between saturation and locality also for constrained clauses: This often allows us to give a finite representation of possibly infinite saturated sets of clauses.


Function Symbol Predicate Symbol Horn Clause Ground Term Ground Instance 
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  1. 1.
    Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. ACM Trans. Comput. Log. 10(1) (2009)Google Scholar
  2. 2.
    Armando, A., Ranise, S., Rusinowitch, M.: A rewriting approach to satisfiability procedures. Inf. Comput. 183(2), 140–164 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. of Logic and Computation 4(3), 217–247 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Basin, D., Ganzinger, H.: Complexity analysis based on ordered resolution. In: Proc. 11th IEEE Symposium on Logic in Computer Science (LICS 1996), pp. 456–465. IEEE Computer Society Press (1996)Google Scholar
  5. 5.
    Basin, D.A., Ganzinger, H.: Automated complexity analysis based on ordered resolution. Journal of the ACM 48(1), 70–109 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ganzinger, H.: Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems. In: Proc. 16th IEEE Symposium on Logic in Computer Science (LICS 2001), pp. 81–92. IEEE Computer Society Press (2001)Google Scholar
  7. 7.
    Horbach, M.: Superposition-based Decision Procedures for Fixed Domain and Minimal Model Semantics. PhD thesis, Max Planck Institute for Computer Science and Saarland University (2010)Google Scholar
  8. 8.
    Horbach, M., Sofronie-Stokkermans, V.: Obtaining finite local theory axiomatizations via saturation. Technical Report ATR 93, Sonderforschungsbereich/Transregio 14 AVACS (2013)Google Scholar
  9. 9.
    Horbach, M., Weidenbach, C.: Superposition for fixed domains. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 293–307. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Horbach, M., Weidenbach, C.: Decidability results for saturation-based model building. In: Schmidt, R.A. (ed.) CADE 2009. LNCS (LNAI), vol. 5663, pp. 404–420. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Ihlemann, C., Sofronie-Stokkermans, V.: On hierarchical reasoning in combinations of theories. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 30–45. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Kirchner, H., Ranise, S., Ringeissen, C., Tran, D.-K.: On superposition-based satisfiability procedures and their combination. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 594–608. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Lynch, C., Morawska, B.: Automatic decidability. In: 17th IEEE Symposium on Logic in Computer Science (LICS 2002), pp. 7–16. IEEE Comp. Soc. (2002)Google Scholar
  16. 16.
    Lynch, C., Ranise, S., Ringeissen, C., Tran, D.-K.: Automatic decidability and combinability. Inf. Comput. 209(7), 1026–1047 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Nieuwenhuis, R., Rubio, A.: Theorem proving with ordering constrained clauses. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 477–491. Springer, Heidelberg (1992)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Tushkanova, E., Ringeissen, C., Giorgetti, A., Kouchnarenko, O.: Automatic decidability: A schematic calculus for theories with counting operators. In: Proceedings the RTA 2013 (to appear, 2013)Google Scholar
  21. 21.
    Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, ch. 27, pp. 1965–2012. Elsevier (2001)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University Koblenz-Landau and Max-Planck-Institut für InformatikSaarbrückenGermany

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