An efficient constraint language for polymorphic order-sorted resolution

  • Christian Prehofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 633)


In recent years various sorted logics have been developed, mostly to facilitate knowledge representation and to speed up automated deduction. We present a polymorphic order-sorted logic that can be implemented efficiently. Because the polymorphism is almost unrestricted, it is possible for two terms to have an exponential number of maximally general unifiers. To guarantee a single most general unifier, we embed the sorted logic into a more general constraint logic and create a distinct constraint satisfaction search space. This separates the total search space into two orthogonal ones and facilitates many optimizations. The main complexity gains are that the unnecessary generation of unifiers can be avoided and that the primary resolution search space remains constant if the complexity of the unification grows.


Constraints Order-sorted Logic Polymorphism Resolution Unification 


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  1. [Aït-Kaci, 1989]
    H. Aït-Kaci, R. Boyer, P. Lincoln, and R. Nasr. Efficient lattice operations. ACM Transactions on Programming Languages and Systems, 11(1):115–146, January 1989.CrossRefGoogle Scholar
  2. [Beierle, 1991]
    C. Beierle, G. Meyer, and H. Semle. Extending the Warren abstract machine to polymorphic order-sorted resolution. In Logic Programming: Proceedings of the 1991 International Symposium, pages 272–286, October 1991.Google Scholar
  3. [Bürkert, 1991]
    Hans-Jürgen Bürkert. A Resolution Principle for a Logic with Restricted Quantifiers. Springer-LNAI 568, 1991.Google Scholar
  4. [Cohn, 1985]
    Anthony G. Cohn. On the solution of Schubert's Steamroller in many sorted logic. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 1169–1174, August 1985.Google Scholar
  5. [Cohn, 1989]
    Anthony G. Cohn. Taxonomic reasoning with many-sorted logics. Artificial Intelligence Review, 3:89–128, 1989.Google Scholar
  6. [Frisch and Scherl, 1991]
    Alan M. Frisch and Richard B. Scherl. A general framework for modal deduction. In Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, pages 196–207. Morgan Kaufman, San Mateo, CA, 1991.Google Scholar
  7. [Frisch, 1985]
    Alan M. Frisch. An investigation into inference with restricted quantification and a taxonomic representation. SIGART Newsletter, (91):28–31, 1985.Google Scholar
  8. [Frisch, 1991a]
    Alan M. Frisch. The substitutional framework for hybrid reasoning. Working Notes of the 1991 Fall Symposium on Principles of Hybrid Reasoning. Asilomar, CA., November 1991.Google Scholar
  9. [Frisch, 1991b]
    Alan M. Frisch. The substitutional framework for sorted deduction: Fundamental results on hybrid reasoning. Artificial Intelligence, 49:161–198, 1991.CrossRefGoogle Scholar
  10. [Hanus, 1989]
    Michael Hanus. Horn clause programs with polymorphic types: semantics and resolution. pages 225–240. TAPSOFT'89, Springer Verlag, 1989.Google Scholar
  11. [Huber and Varsek, 1987]
    H. Huber and L. Varsek. Extended Prolog for order-sorted resolution. In Proceedings of the 4th IEEE Symposium on Logic Programming, pages 34–45, 1987.Google Scholar
  12. [Martelli and Montanari, 1982]
    Alberto Martelli and Ugo Montanari. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems, 4(2):258–282, April 1982.CrossRefGoogle Scholar
  13. [Mycroft and O'Keefe, 1984]
    A. Mycroft and U. O'Keefe. A polymorphic type system for Prolog. Artificial Intelligence, (23):295–307, 1984.CrossRefMathSciNetGoogle Scholar
  14. [Prehofer, 1992]
    Christian F. Prehofer. A constraint language for order-sorted polymorphic resolution. Master's thesis, Univ. of Illinois at Urbana-Champaign, January 1992.Google Scholar
  15. [Schmidt-Schauß, 1989]
    Manfred Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations. Springer-LNAI 395, 1989.Google Scholar
  16. [Smolka, 1989]
    Gert Smolka. Logic programming over polymorphically order-sorted types. PhD thesis, Universität Kaiserslautern, May 1989.Google Scholar
  17. [Walther, 1985]
    Christoph Walther. A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217–224, 1985.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Christian Prehofer
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2Germany

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