How to use modalities and sorts in Prolog

  • Andreas Nonnengart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 838)


Standard logic programming languages like Prolog lack the possibility of dealing with modalities and/or sorts. A first idea how to overcome this problem (and that without changing anything on Prolog itself) would be to apply the well-known relational translation approaches from modal and sorted logic into first-order predicate logic and to feed this translation result into Prolog. This, however, leads into other problems: firstly, the transformed problem is usually of much bigger size (number of clauses) than the original one and, secondly, very often it is not even in Horn form anymore.

In this paper a translation approach is proposed which avoids both of these problems, i.e. the number of clauses after translation is exactly as big as it would have been if we simply ignored the modal operators and sort restrictions and, also, the result is in Horn form provided it was already before (modulo modal operators and sorts).


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  1. 1.
    Yves Auffray and Patrice Enjalbert. Modal theorem proving: An equational viewpoint. Journal of Logic and Computation, 2(3):247–295, 1992.Google Scholar
  2. 2.
    Luis Fariñas del Cerro and Andreas Herzig. Quantified modal logic and unification theory. Rapport LSI 293, Languages et Systèmes Informatique, Université Paul Sabatier, Toulouse, 1988.Google Scholar
  3. 3.
    Andr≸s Nonnengart. First-order modal logic theorem proving and standard PROLOG. Technical Report MPI-I-92-228, Max-Planck-Institute for Computer Science, Saarbrücken, Germany, July 1992.Google Scholar
  4. 4.
    Andreas Nonnengart. First-order modal logic theorem proving and functional simulation. In Ruzena Bajcsy, editor, Proceedings of the 13th IJCAI, volume 1, pages 80–85. Morgan Kaufmann Publishers, 1993.Google Scholar
  5. 5.
    Hans Jürgen Ohlbach. A resolution calculus for modal logics. In Ewing Lusk and Ross Overbeek, editors, Proc. of 9 th International Conference on Automated Deduction, CADE-88 Argonne, IL, volume 310 of LNCS, pages 500–516, Berlin, Heidelberg, New York, 1988. Springer-Verlag, extended version: SEKI Report SR-88-08, FB Informatik, Universität Kaiserslautern, 1988.Google Scholar
  6. 6.
    Hans Jürgen Ohlbach. A Resolution Calculus for Modal Logics. PhD thesis, University of Kaiserslautern, Germany, 1989.Google Scholar
  7. 7.
    Hans Jürgen Ohlbach. Semantics-based translation methods for modal logics. Journal of Logic and Computation, 1(5):691–746, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Andreas Nonnengart
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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