Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Dowling, W. and Gallier, J., Linear Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae, Journal of Logic Programming 3 (1984), 267–284.
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.
Gelfond, M., and Lifschitz, V., The Stable Model Semantics for Logic Programming. In: Fifth International Conference Symposium on Logic Programming, pp. 1070–1080, 1988.
Goodwin, J., An Improved Algorithm for Non-Monotonic Dependency Net Update. LITH-MAT-R-82-23, Linkoeping University 1982.
Kleene, S., Introduction of metamathematics, Van Nostrand, 1952.
Kunen, K., Signed Data Dependencies in Logic Programs, Journal of Logic Programming, 7,(1989),231–245.
Lloyd, J.W., Foundations of Logic Programming, Springer Verlag, Heidelberg, 1987
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.
Reinfrank, M., Fundamentals and Logical Foundations of Truth Maintenance, Linköping Studies in Science and Technology. Dissertations no. 221, Linköping University, 1989.
Turner, R., Logics for Artificial Intelligence, Ellis Horwood Ltd, Chichester, 1987.
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.
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.
Witteveen, C., Partial Semantics for Truth Maintenance, to appear as TWI-Report, Department of Mathematics and Computer Science, Delft University of Technology, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Witteveen, C. (1991). Partial semantics for truth maintenance. In: van Eijck, J. (eds) Logics in AI. JELIA 1990. Lecture Notes in Computer Science, vol 478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018465
Download citation
DOI: https://doi.org/10.1007/BFb0018465
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53686-4
Online ISBN: 978-3-540-46982-7
eBook Packages: Springer Book Archive