Elementary formal system as a logic programming language

  • Akihiro Yamamoto
Logic Programming Language
Part of the Lecture Notes in Computer Science book series (LNCS, volume 485)


In this paper, we give a theoretical foundation of EFS (elementary formal system) as a logic programming language. We show that the set of all the unifiers of two atoms is finite and computable by restricting the form of axioms and goals without losing generality. The restriction makes the negation as failure rule complete. We give two conditions of EFS's such that the negation as failure rule is identical to the closed world assumption. We also give a subclass of EFS's where a procedure of CWA is given as bounding the length of derivations We compare these classes with the Chomsky hierarchy.


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  1. [1]
    Arikawa, S., Elementary Formal Systems and Formal Languages — Simple Formal Systems. Memoirs of Fac. Sci., Kyushu University Ser. A. Math. 24:47–75 (1970).Google Scholar
  2. [2]
    Arikawa, S., Shinohara, T., and Yamamoto, A., Elementary Formal System as a Unifying Framework for Language Learning, in Rivest, R., Haussler, D., and Warmuth, M. K. (eds.), Proc. COLT'89, 312–327, Morgan-Kaufmann, 1989.Google Scholar
  3. [3]
    Arimura, H., Completeness of Depth-Bounded Resolution in Logic Programming, Internal report, Research Institute of Fundamental Information Science, Kyushu University, 1989, to appear in 6th Conf. Proc. of JSSST.Google Scholar
  4. [4]
    Dershowitz, N. and Manna, Z., Proving Termination with Multiset Orderings. CACM 8(22):465–476 (1979).Google Scholar
  5. [5]
    Fitting, M., Computability Theory, Semantics, and Logic Programming, Oxford University Press, 1987.Google Scholar
  6. [6]
    Jaffar, J. and Lassez, J.-L., Constraint Logic Programming, in Proc. Conference on Principle of Programming Languages, 1987.Google Scholar
  7. [7]
    Jaffar, J., Lassez, J.-L., and Maher, M. J., Logic Programming Scheme, in DeGroot, D. and Lindstrom, G. (eds.), Logic Programming: Functions, Relations, and Equations, 211–233, Prentice-Hall, 1986.Google Scholar
  8. [8]
    Lloyd, J. W., Foundations of Logic Programming Second, Extended Edition, Springer-Verlag, 1987.Google Scholar
  9. [9]
    Makanin, G. S., The Problem of Solvability of Equations in a Free Semigroup. Soviet Math. Dokl. 18(2):330–335 (1977).Google Scholar
  10. [10]
    Plotkin, G. D., Building in Equational Theories, in Machine Intelligence 7, 132–147, Edinburgh University Press, 1972.Google Scholar
  11. [11]
    Reiter, R., On Closed World Data Bases, in Gallaire, H. and Minker, J. (eds.), Logic and Data Bases, 55–76, Plenum Press, 1978.Google Scholar
  12. [12]
    Shapiro, E. Y.. Inductive Inference of Theories From Facts. Research Report 192, Yale University, 1981.Google Scholar
  13. [13]
    Smullyan, R. M., Theory of Formal Systems, Princeton Univ. Press, 1961.Google Scholar
  14. [14]
    Yamamoto, A., A Theoretical Combination of SLD-Resolution and Narrowing, in Lassez, J.-L. (ed.), Proc. 4th ICLP, 470–487, The MIT Press, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Akihiro Yamamoto
    • 1
  1. 1.Department of Information SystemsKyushu University 39KasugaJapan

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