Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

TABLEAUX 1998: Automated Reasoning with Analytic Tableaux and Related Methods pp 202–216Cite as

Free Variable Tableaux for a Logic with Term Declarations

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1397))

Abstract

We study free variable tableau methods for logics with term declarations. We show how to define a substitutivity rule preserving the soundness of the tableaux and we prove that some other attempts lead to unsound systems. Based on this rule, we define a sound and complete free variable tableau system and we show how to restrict its application to close branches by defining a sorted unification calculus.

Research partially supported by the ESPRIT BR Working Group 6028 CCLII.

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   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. A. G. Cohn. A more expressive formulation of many sorted logic. Journal of Automated Reasoning 3, 113–200, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Fitting. First-Order Logic and Automated Theorem Proving. Second edition. Springer, 1996.

    Google Scholar 

  3. A. M. Frisch. The substitutional framework for sorted deduction: fundamental results on hybrid reasoning. Artificial Intelligence 49, 161–198, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Gavilanes, J. Leach, P. J. Martín, S. Nieva. Reasoning with preorders and dynamic sorts using free variable tableaux. Proc. AISMC-3. LNCS 1138, 365–379, 1996.

    Google Scholar 

  5. A. Gavilanes, J. Leach, P. J. Martín, S. Nieva. Ground semantic tableaux for a logic with preorders and dynamic declarations. TR DIA 50/97. 1997.

    Google Scholar 

  6. A. Gavilanes, J. Leach, P. J. Martín. Free variable tableaux for a logic with term declarations. TR DIA 69/97. 1997.

    Google Scholar 

  7. E. Kogel. Rigid E-unification simplified. Proc. 4th International Workshop TABLEAUX’95. LNCS 918, 17–30, 1995.

    Google Scholar 

  8. M. Schmidt-Schauss. Computational Aspects of an Order Sorted Logic with Term Declarations. LNAI 395. Springer, 1989.

    Google Scholar 

  9. C. Walther. A Many-sorted Calculus based on Resolution and Paramodulation. Research Notes in Artificial Intelligence. Pitman, 1987.

    Google Scholar 

  10. C. Weidenbach. A sorted logic using dynamic sorts. MPI-I-91-218, 1991.

    Google Scholar 

  11. C. Weidenbach. First-order tableaux with sorts. J. of the Interest Group in Pure and Applied Logics 3(6), 887–907, 1995.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep. de Sistemas Informáticos y Programación, Universidad Complutense de Madrid, Madrid

    P. J. Martín, A. Gavilanes & J. Leach

Authors
  1. P. J. Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Gavilanes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Leach
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Harrie de Swart

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martín, P.J., Gavilanes, A., Leach, J. (1998). Free Variable Tableaux for a Logic with Term Declarations. In: de Swart, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1998. Lecture Notes in Computer Science(), vol 1397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69778-0_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-69778-0_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64406-4

  • Online ISBN: 978-3-540-69778-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation