Building bridges between knowledge representation and algebraic specification

  • Jacques Calmet
  • Indra A. Tjandra
Communications Methodologies
Part of the Lecture Notes in Computer Science book series (LNCS, volume 869)


An approach to transforming the algebraic specification of a mathematical domain of computation into a knowledge base, preserving the semantics determined in the specification, is introduced. It involves the algebraic specification language Formal-⌆ and the hybrid knowledge representation system Mantra. In the framework of Formal-⌆ mathematical domains of computation are represented algebraically. The transformation aims at achieving the executability of a specification.


Methodology modeling mathematical domains of computation knowledge representation algebraic specification program transformation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Belnap]
    N.D. Belnap. A useful four-valued logic. In J.M. Dunn and G. Epstein, editors, Modern Use of Multiple-Valued Logics. D. Reidel, 1977.Google Scholar
  2. [Brachman et al.]
    R.J. Brachman, R.E. Fikes, and H.J. Levesque. Krypton: A functional approach to knowledge representation. IEEE Computer, 16(10), pp. 67–73, October 1983.Google Scholar
  3. [Bittencourt]
    G. Bittencourt. An Architecture for Hybrid Knowledge Representation. PhD thesis, Universität Karlsruhe, Institut für Algorithme und Kognitive Systeme, 1990.Google Scholar
  4. [Calmet-Tjandra]
    J. Calmet and I.A. Tjandra. A unified-algebra-based specification language for symbolic computing. In A. Miola, editor, Design and Implementaion of Symbolic Computation Systems. Springer-Verlag, LNCS 722, pp. 122–133, 1993.Google Scholar
  5. [Calmet-Tjandra-Bittencourt]
    J. Calmet, I.A. Tjandra, and G. Bittencourt. Mantra: A shell for hybrid knowledge representation. In E. Lee, B. Wah, N.G. Bourbakis, and W.T. Tsai, editors, Tools for Artificial Intelligence, pp. 164–171. IEEE Computer Society Press, 1991.Google Scholar
  6. [Ehrig-Mahr]
    H. Ehrig and B. Mahr. Fundamental of Algebraic Specification 2. Monograph on Theoretical Computer Science, vol 21. Springer-Verlag, 1990.Google Scholar
  7. [Etherington]
    D.W. Etherington. Reasoning with Incomplete Information: Investigation of Nonmonotonic Reasoning. PhD thesis, University of British Columbia, Vencouver, CS, 1986.Google Scholar
  8. [Fasel et al.]
    J.H. Fasel, P. Hudak, S.P. Jones, and P. Wadler. SIGPLAN notices special issue on the functional programming language Haskell. ACM Sigplan Notices, 27(5):1, 1992.Google Scholar
  9. [Mosses]
    P.D. Mosses. Unified algebras and institutions. In Logics in Computer Science, pp. 304–312. IEEE Press, 1989.Google Scholar
  10. [PatelSchneider84]
    P.F. Patel-Schneider. Small can be beautiful in knowledge representation. In Proceedings of Workshop on Principle of Knowldege-Based Systems, pages 11–19. IEEE, 1984.Google Scholar
  11. [PatelSchneider90]
    P.F. Patel-Schneider. A decidable first-order logic for knowledge representation. Journal of Automated Reasoning, 6, pp. 361–388, 1990.Google Scholar
  12. [Sanella]
    D Sanella. A set-theoretic semantics of Clear. Acta Informatica, 21(5), pp. 443–472, 1984.Google Scholar
  13. [Stroustrup]
    B. Stroustrup. The C++ Programming Language. Addison Wesley, 2nd edition, 1993.Google Scholar
  14. [Sutor]
    R.S. (Ed.) Sutor. Axiom User's Guide. The Numerical Algorithm Group Limited, 1991.Google Scholar
  15. [Thomason et al.]
    R.H. Thomason, J.F. Horty, and D.S. Touretzky. A calculus for inheritance in monotonic semantic nets. CMU-CS-86-138, Carnegie Mellon Univeristuy, Dept. of CS, 1986.Google Scholar
  16. [Tjandra]
    I.A. Tjandra. Algebraic Specification of Mathematical Domains of Computation and Type Polymorphisms in Symbolic Computing (in German). PhD thesis, University of Karlsruhe, Dept. of CS, 1993.Google Scholar
  17. [Vilain]
    M. Vilain. The restriction language architecture of a hybrid representation system. In Proceeding of 9th IJCAI, pp. 547–551, 1985.Google Scholar
  18. [VanEmden-Yukawa]
    M.H. VanEmden and K. Yukawa. Logic programming with equations. The Journal of Logic Programming, 4, pp. 265–288, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jacques Calmet
    • 1
  • Indra A. Tjandra
    • 2
  1. 1.IAKSUniversität KarlsruheKarlsruheGermany
  2. 2.Dept. of CS PQConcordia UniversityMontrealCanada

Personalised recommendations