Advertisement

Simultaneous Rigid Sorted Unification

  • Pedro J. Martín
  • Antonio Gavilanes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1919)

Abstract

In this paper we integrate a sorted unification calculus into free variable tableau methods for logics with term declarations. The calculus we define is used to close a tableau at once, unifying a set of equations derived from pairs of potentially complementary literals occurring in its branches. Apart from making the deduction system sound and complete, the calculus is terminating and so, it can be used as a decision procedure. In this sense we have separated the complexity of sorts from the undecidability of first order logic.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. G. Cohn. A more expressive formulation of many sorted logic. Journal of Automated Reasoning 3, 113–200, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. G. Cohn. A many sorted logic with possibly empty sorts. CADE’11. LNCS 607, 633–647, 1992.Google Scholar
  3. 3.
    A. Degtyarev, A. Voronkov. What you always wanted to know about rigid Eunification. Journal of Automated Reasoning 20(1), 47–80, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Fitting. First-Order Logic and Automated Theorem Proving (2 edition). Springer, 1996.Google Scholar
  5. 5.
    A. M. Frisch. The substitutional framework for sorted deduction: fundamental results on hybrid reasoning. Artificial Intelligence 49, 161–198, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. Gavilanes, J. Leach, P. J. Martín, S. Nieva. Reasoning with preorders and dynamic sorts using free variable tableaux. AISMC-3. LNCS 1138, 365–379, 1996.Google Scholar
  7. 7.
    A. Gavilanes, J. Leach, P. J. Martín, S. Nieva. Semantic tableaux for a logic with preorders and dynamic declarations. TABLEAUX’97 (Position paper), CRIN 97-R-030, 7–12, 1997.Google Scholar
  8. 8.
    O. Herzog et al. LILOG-Linguistic and logic methods for the computational understanding of german. LILOG-Report 1b, IBM Germany, 1986.Google Scholar
  9. 9.
    P. J. Martín, A. Gavilanes. Simultaneous sorted unification for free variable tableaux: an elegant calculus. TR-SIP 86/98. 1998.Google Scholar
  10. 10.
    P. J. Martín, A. Gavilanes, J. Leach. Free variable tableaux for a logic with term declarations. TABLEAUX’98. LNAI 1397, 202–216. 1998.Google Scholar
  11. 11.
    P. J. Martín, A. Gavilanes, J. Leach. Tableau methods for a logic with term declarations. Journal of Symbolic Computation 29, 343–372, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    R. Nieuwenhuis, A. Rubio. Theorem proving with ordering and equality constrained clauses. Journal of Symbolic Computation 19, 321–351, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    M. Schmidt-Schauss. Computational Aspects of an Order Sorted Logic with Term Declarations. LNAI 395, Springer, 1989.Google Scholar
  14. 14.
    C. Walther. A Many-sorted Calculus based on Resolution and Paramodulation. Research Notes in Artificial Intelligence. Pitman, 1987.Google Scholar
  15. 15.
    C. Weidenbach. A sorted logic using dynamic sorts. MPI-I-91-218, 1991.Google Scholar
  16. 16.
    C. Weidenbach. First-order tableaux with sorts. Journal of the Interest Group in Pure and Applied Logics 3(6), 887–907, 1995.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pedro J. Martín
    • 1
  • Antonio Gavilanes
    • 1
  1. 1.Dep. de Sistemas Informáticos y ProgramaciónUniversidad Complutense de MadridSpain

Personalised recommendations