Skip to main content

Redundancy-Free Lemmatization in the Automated Model-Elimination Theorem Prover AI-SETHEO

  • Conference paper
  • 963 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1847))

Abstract

Lemmatization is a promising way for solving “hard” problems with automated theorem provers. However, valuable results can only be reached, if the employed lemmata are restricted to useful records. The automated model-elimination theorem prover AI-SETHEO was designed for using such a controlled lemmatization from the beginning. Mainly responsible for the success of the newest version of AI-SETHEO is the implementation of an algorithm for eliminating lemma redundancies. Here, a lemma f is called redundant to other lemmata f 1,...,f n , if f can be generated within very few inferences from f 1,...,f n . Conflicts between redundacies are resolved with an importance criterion. First experiments with AI-SETHEO give promising results.

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

Buying options

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. Astrachan, O., Stickel, M.: Caching and Lemmaizing in Model Elimination Theorem Provers. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, Springer. Heidelberg (1992)

    Google Scholar 

  2. Draeger, J.: Acquisition of Useful Lemma Knowledge in Automated Reasoning. In: Giunchiglia, F. (ed.) AIMSA 1998. LNCS (LNAI), vol. 1480, p. 230. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  3. Draeger, J.: Modularisierte Suche in Theorembeweisern. Ph.D. Dissertation, Technical University Munich (1998)

    Google Scholar 

  4. Draeger, J., Wolf, A.: Strategy Parallelism and Lemma Evaluation. In: FLAIRS 1999 (1999)

    Google Scholar 

  5. 5. Goller, C.: A Connectionist Approach for Learning Search-Control Heuristics for Automated Deduction Systems, Ph.D. Dissertation, Technical University Munich (1997)

    Google Scholar 

  6. Goller, C., Letz, R., Mayr, K., Schumann, J.: SETHEO V3.2: Recent Developments. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814. Springer, Heidelberg (1994)

    Google Scholar 

  7. Loveland, D.: Mechanical Theorem-Proving by Model Elimination. JACM 15(2) (1968)

    Google Scholar 

  8. Loveland, D.: Automated Theorem Proving: a Logical Basis. North-Holland, Amsterdam (1978)

    MATH  Google Scholar 

  9. Mitchell, T.: Learning and Problem Solving. In: IJCAI (1983)

    Google Scholar 

  10. Moser, M., et al.: SETHEO and E-SETHEO. The CADE-13 Systems. JAR 18(2), 237 (1997)

    Article  Google Scholar 

  11. Schumann, J.: DELTA A Bottom-up Preprocessor for Top-Down Theorem Provers. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814. Springer, Heidelberg (1994)

    Google Scholar 

  12. Sutcliffe, G., Suttner, C., Yemenis, T.: The TPTP Problem Library. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814. Springer, Heidelberg (1994)

    Google Scholar 

  13. Wolf, A., Draeger, J.: Strategy Parallelism and Lemma Evaluation. In: Murray, N.V. (ed.) TABLEAUX 1999. LNCS (LNAI), vol. 1617, pp. 319–323. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Draeger, J. (2000). Redundancy-Free Lemmatization in the Automated Model-Elimination Theorem Prover AI-SETHEO. In: Dyckhoff, R. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2000. Lecture Notes in Computer Science(), vol 1847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722086_33

Download citation

  • DOI: https://doi.org/10.1007/10722086_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67697-3

  • Online ISBN: 978-3-540-45008-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics