Abstract
In this paper we show how to syntactically represent the relation of cause and effect between a predicate name and the bodies of the clauses which define this predicate in a logic program. In so doing, we prove that we can logically express many properties about SLD-trees, especially the absence or the presence of an empty leaf and/or an infinite branch. This relation of cause and effect is linked to the execution of the program. Thus it is a temporal relation. Modal logics have shown in the past their ability to deal with temporal concepts and temporal properties of sequential or parallel programs. Consequently we naturally define in modal logic a completion formula of logic programs. This formula is a modal version of Clark's formula. It gives soundness and completeness results of two nononotonic inference rules : the negation as failure and the closed world assumption.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
5. references
Balbiani, P., Modal Logic and Negation as Failure, to appear in the Jour. of Logic and Computation.
Balbiani, P., A Promenade from Provability to Consistency, to appear in: L. Fariñas del Cerro et M. Penttonnen (eds.), Non-Classical Logic Programming, Oxford University Press.
P. Balbiani, Une Caractérisation Modale de la Sémantique des Programmes Logiques avec Négation, Thèse de l'Université Paul Sabatier, Toulouse, 1990.
Boolos, G., The Unprovability of Consistency, Cambridge University Press, 1979.
Clark, K.L., Negation as Failure, in: H. Gallaire et J. Minker (eds.), Logic and Databases, Plenum Press, New York, 1978, 293–322.
Cresswell and Hughes, A Companion to Modal Logic, Methuen, London, 1984.
van Emden, M.H. and Kowalski, R.A., The Semantics of Predicate Logic as a Programming Language, Jour. of the Assoc. for Computing Machinery, 1977, 23:733–742.
Fitting, M., A Kripke-Kleene Semantics for Logic Programs, Jour. of Logic Programming 1985:4:295–312.
Gabbay, D.M., Modal Provability Foundation for Negation by Failure, to appear in: P. Schroder Heister (ed.), Extensions of Logic Programming, Lecture Notes in Artificial Intelligence, Springer.
Jaffar, J., Lassez, J.-L. and Lloyd, J.W., Completeness of the Negation as Failure Rule, in: Proc. of the Eighth Int. Joint Conf. on Artificial Intelligence, Karlsruhe, 1983, 500–506.
Kunen, Negation in Logic Programming, Jour. of Logic Programming, 1987, 4:289–308.
Kunen, Signed Data Dependencies in Logic Programs, Jour. of Logic Programming, 1989, 7:231–245.
Lassez, J.-L. and Maher, M.J., Closure and Fairness in the Semantics of Programming Logic, Theoretical Computer Science, 1984, 29:167–184.
Lloyd, J., Foundations of Logic Programming, Springer, 2nd extended edition, 1987.
Reiter, R., On Closed World Data Bases, in: H. Gallaire et J. Minker (eds.), Logic and Databases, Plenum Press, New York, 1978, 55–76.
Shepherdson; J.C., Negation in Logic Programming, in: J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, Los Altos, 1988, 19–88.
Smorynski, C., Self Reference and Modal Logic, Springer Verlag, 1985.
Tärnlund, S.A., Horn Clause Computability, BIT, 1977, 17:215–216.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Balbiani, P. (1991). A modal semantics for the negation as failure and the closed world assumption rules. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020826
Download citation
DOI: https://doi.org/10.1007/BFb0020826
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53709-0
Online ISBN: 978-3-540-47002-1
eBook Packages: Springer Book Archive