Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Connection Tableaux with Lazy Paramodulation

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

It is well known that the connection refinement of clause tableaux with paramodulation is incomplete (even with weak connections). In this paper, we present a new connection tableau calculus for logic with equality. This calculus is based on a lazy form of paramodulation where parts of the unification step become auxiliary subgoals in a tableau and may be subjected to subsequent paramodulations. Our calculus uses ordering constraints and a certain form of the basicness restriction.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Bachmair, L., Ganzinger, H., Lynch, C., Snyder, W.: Basic paramodulation. Inf. Comput. 121(2), 172–192 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bachmair, L., Ganzinger, H., Voronkov, A.: Elimination of equality via transformation with ordering constraints. In: Kirchner, C., Kirchner, H. (eds.) Automated Deduction: 15th International Conference, CADE-15. Lecture Notes in Computer Science, vol. 1421, pp. 175–190 (1998)

  3. Brand, D.: Proving theorems with the modification method. SIAM J. Comput. 4, 412–430 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  4. Degtyarev, A., Voronkov, A.: What you always wanted to know about rigid E-unification. J. Autom. Reason. 20(1), 47–80 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dougherty, D.J., Johann, P.: An improved general E-unification method. In: Stickel, M.E. (ed.) Automated Deduction: 10th International Conference, CADE-10. Lecture Notes in Computer Science, vol. 449, pp. 261–275 (1990)

  6. Gallier, J., Snyder, W.: Complete sets of transformations for general E-unification. Theor. Comp. Sci. 67, 203–260 (1989)

    Article  MathSciNet  Google Scholar 

  7. Giese, M.: A model generation style completeness proof for constraint tableaux with superposition. In: Egly, U., Fermüller, C.G. (eds.) Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2002. Lecture Notes in Computer Science, vol. 2381, pp. 130–144 (2002)

  8. Letz, R., Schumann, J., Bayerl, S., Bibel, W.: SETHEO: a high-performance theorem prover. J. Autom. Reason. 8(2), 183–212 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Letz, R., Stenz, G.: Model elimination and connection tableau procedures. In: Robinson, A., Voronkov, A. (eds.) Handbook for Automated Reasoning, vol. II, Chapt. 28, pp. 2017–2116. Elsevier Science (2001)

  10. Loveland, D.W.: Mechanical theorem proving by model elimination. J. ACM 16(3), 349–363 (1968)

    Article  Google Scholar 

  11. Loveland, D.W.: Automated Theorem Proving: A Logical Basis. Fundamental Studies in Computer Science, vol. 6. North-Holland (1978)

  12. Moser, M.: Improving transformation systems for general E-unification. In: Kirchner, C. (ed.) Rewriting Techniques and Applications: 5th International Conference, RTA 1993. Lecture Notes in Computer Science, vol. 690, pp. 92–105 (1993)

  13. Moser, M., Ibens, O., Letz, R., Steinbach, J., Goller, C., Schumann, J., Mayr, K.: SETHEO and E-SETHEO – the CADE-13 systems. J. Autom. Reason. 18(2), 237–246 (1997)

    Article  Google Scholar 

  14. Moser, M., Lynch, C., Steinbach, J.: Model elimination with basic ordered paramodulation. Technical Report AR-95-11, Fakultät für Informatik, Technische Universität München, München (1995)

  15. Moser, M., Steinbach, J.: STE-modification revisited. Technical Report AR-97-03, Fakultät für Informatik, Technische Universität München, München (1997)

  16. Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook for Automated Reasoning, vol. I, Chapt. 7, pp. 371–443. Elsevier Science (2001)

  17. Paskevich, A.: Connection tableaux with lazy paramodulation. In: Furbach, U., Shankar, N. (eds.) Automated Reasoning, 3rd International Joint Conference IJCAR 2006. Lecture Notes in Computer Science, vol. 4130, pp. 112–124. Seattle WA, USA (2006)

  18. Snyder, W., Lynch, C.: Goal directed strategies for paramodulation. In: Book, R. (ed.) Rewriting Techniques and Applications: 4th International Conference, RTA 1991. Lecture Notes in Computer Science, vol. 488, pp. 150–161 (1991)

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Algorithmique, Complexité et Logique, Université Paris 12, 94010, Créteil Cedex, France

    Andrei Paskevich

Authors
  1. Andrei Paskevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrei Paskevich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paskevich, A. Connection Tableaux with Lazy Paramodulation. J Autom Reasoning 40, 179–194 (2008). https://doi.org/10.1007/s10817-007-9089-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-007-9089-7

Keywords

Search

Navigation