Partial semantics for truth maintenance

A compositional approach
  • Cees Witteveen
Selected Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 478)


To generalize the 2-valued stable model semantics for truth maintenance, we introduce a partial semantics. This semantics can be given compositional properties and in particular, the well-founded model can be derived as a composition of partial interpretations.

Since the well-founded model is not a straightforward generalization of the 2-valued stable model semantics, we introduce the notion of an immune interpretation and show that it can be used to derive both the well-founded model as a minimal immune model and a uniquely characterized maximal immune model, the latter reducing to the unique 2-valued stable model if it exists.


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  1. [1]
    Dowling, W. and Gallier, J., Linear Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae, Journal of Logic Programming 3 (1984), 267–284.Google Scholar
  2. [2]
    Elkan, Ch., Logical Characterizations of Nonmonotonic TMSs, in: Kreczmar, A. and G. Mirkowska, (eds) Mathematical Foundations of Computer Science 1989, Springer Heidelberg, 1989, pp. 218–224.Google Scholar
  3. [3]
    Gelfond, M., and Lifschitz, V., The Stable Model Semantics for Logic Programming. In: Fifth International Conference Symposium on Logic Programming, pp. 1070–1080, 1988.Google Scholar
  4. [4]
    Goodwin, J., An Improved Algorithm for Non-Monotonic Dependency Net Update. LITH-MAT-R-82-23, Linkoeping University 1982.Google Scholar
  5. [5]
    Kleene, S., Introduction of metamathematics, Van Nostrand, 1952.Google Scholar
  6. [6]
    Kunen, K., Signed Data Dependencies in Logic Programs, Journal of Logic Programming, 7,(1989),231–245.Google Scholar
  7. [7]
    Lloyd, J.W., Foundations of Logic Programming, Springer Verlag, Heidelberg, 1987Google Scholar
  8. [8]
    Przymusinska, H., and Przymusinski, T., Semantic Issues in Deductive Databases and Logic Programs, in: Formal Techniques in Artificial Intelligence, A Sourcebook R.B. Banerji (ed.), Elsevier, Amsterdam, 1990, pp 321–367.Google Scholar
  9. [9]
    Reinfrank, M., Fundamentals and Logical Foundations of Truth Maintenance, Linköping Studies in Science and Technology. Dissertations no. 221, Linköping University, 1989.Google Scholar
  10. [10]
    Turner, R., Logics for Artificial Intelligence, Ellis Horwood Ltd, Chichester, 1987.Google Scholar
  11. [11]
    Van Gelder, A., Ross, K. and Schlipf, P., Unfounded Sets and Well-founded Semantics for General Logic Programs. In: Proceedings of the Symposium on Principles of Database Systems, ACM SIGACT-SIGMOD-SIGART, 1988.Google Scholar
  12. [12]
    Van Gelder, A., The Alternating Fixpoint of Logic Programs with Negation. In: Proceedings of the Eighth Symposium on Principles of Database Systems, ACM SIGACT-SIGMOD-SIGART, 1989.Google Scholar
  13. [13]
    Witteveen, C., Partial Semantics for Truth Maintenance, to appear as TWI-Report, Department of Mathematics and Computer Science, Delft University of Technology, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Cees Witteveen
    • 1
  1. 1.Department of Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands

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