Abstract
The Constraint Logic Programming systems which have been implemented include various higher-order predicates for optimization. In CLP(FD) systems, optimization predicates such as min(G(X),f(X)), or min-max(G(X), [f1(X),..., fn(X)]), are implemented by using branch and bound algorithms. In CLP(R) systems, the Simplex algorithm used for satisfiability checks can also be used for linear optimization through the predicate rmin(f (X)) which adds to the constraints on X the ones defining the space where the linear term f(X) is minimized. These optimization constructs do not belong however to the formal CLP scheme of Jaffar and Lassez, and they lack a declarative semantics. In this paper we propose a general definition for optimization predicates, for which one can provide both a logical and a fixpoint semantics based on KunenFitting's semantics of negation. We show that the branch and bound algorithm can be derived as a specialized version of CSLDNF-resolution procedures, and that the branch and bound algorithm can be lifted to a full first-order setting with constructive negation.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S. Ganguly, S. Greco, C. Zaniolo, “Minimum and maximum predicates in logic programming”. Proc. of PODS'91, Denver, pp. 154–163. 1991.
D.B. Kemp, P.J. Stuckey, “Semantics of logic programs with aggregates”, Proc. of ILPS'91, San Diego, pp.387–401. 1991.
K. Kunen, “Negation in logic programming”, Journal of Logic Programming, 4(3), pp.289–308, 1987.
K. Kunen, “Signed data dependencies in logic programming”, Journal of Logic Programming, 7(3), pp.231–245, 1989.
J. Jaffar, J.L. Lassez, “Constraint Logic Programming”, Proc. of POPL'87, Munich. 1987.
J.W. Lloyd, “Foundations of Logic Programming”, Springer Verlag. 1987.
P. Stuckey, “Constructive negation for constraint logic programming”, Proc. LICS'91, 1991.
P. Van Hentenryck: ”Constraint Satisfaction in Logic Programming”, MIT Press 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fages, F. (1993). On the semantics of optimization predicates in CLP languages. In: Shyamasundar, R.K. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1993. Lecture Notes in Computer Science, vol 761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57529-4_53
Download citation
DOI: https://doi.org/10.1007/3-540-57529-4_53
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57529-0
Online ISBN: 978-3-540-48211-6
eBook Packages: Springer Book Archive