Abstract
The different properties characterizing the operational behavior of logic programs can be organized in a hierarchy of fixpoint semantics related by Galois insertions, having the least Herbrand model as most abstract semantics, and the SLD operational semantics as most concrete semantics. The choice of a semantics in the hierarchy allows to model precisely the program properties of interest while getting rid of useless details of too concrete semantics, which is crucial for the development of efficient program analysis tools.
The aim of this paper is to push forward these methods by making them apply to normal (constraint) logic programs, that is full first-order (non Horn) programs. The fixpoint semantics defined by the first author for the rule of constructive negation by pruning is at the center of the hierarchy developed in this paper. We show that that semantics can be obtained by concretization of Kunen's semantics defined as a fixpoint, taken as the most abstract semantics of the hierarchy, and that by further concretization it leads to a new operational semantics for normal CLP programs. The different observable properties of the program, such as successful derivations, finite failure, set of computed answer constraints, etc. are modeled by precise semantics in the hierarchy.
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References
A. Bossi, M. Gabbrielli, G. Levi, M. Martelli, “The s-semantics approach: theory and applications”, Journal of Logic Programming, 19–20, pp.149–197, 1994.
P. Cousot, R. Cousot, “Systematic design of program analysis frameworks”, In Proc. 6th Annual Symposium on Principles of Programming Languages, pp.269–282, 1979.
P. Cousot, R. Cousot, “Abstract interpretation and application to logic programs”, Journal of Logic Programming, 13(2 and 3), pp.103–179, 1992.
D. Chan, “Constructive negation based on the completed database”, in: R.A. Kowalski and K.A. Bowen (eds), Proc. of the fifth International Conference on Logic Programming, MIT Press, Cambridge, MA, pp.11–125, 1988.
M. Comini, G. Levi, M.C. Meo, “Compositionality in SLD-derivations and their abstractions”, Proc. of International Symposium on Logic Programming, ILPS'95, Portland, MIT Press, pp.561–575, 1995.
K. Doets “From Logic to Logic Programming”, MIT Press, 1992.
W. Drabent, “What is failure? An approach to constructive negation”, Acta Informatica, 32:1, pp.27–59, 1995.
F. Fages, “Constructive negation by pruning”, LIENS technical report 94-14, revised 95-24. To appear in the Journal of Logic Programming, 1996.
M. Fitting, “A Kripke/Kleene semantics for logic programs”, Journal of Logic Programming, 2(4), pp.295–312, 1985.
M. Falaschi, G. Levi, M. Martelli, C. Palamidessi, “Declarative modeling of the operational behavior of logic programs”, Theoretical Computer Science, 69(3), pp.289–318, 1989.
M. Falaschi, G. Levi, M. Martelli, C. Palamidessi, “A model-theoretic reconstruction of the operational semantics of logic programs”, Information and Computation, 103, pp.86–113, 1993.
R. Giacobazzi, “”Optimal” collecting semantics for analysis in a hierarchy of logic program semantics”, Proc of 13th STACS'96, C. Puech and R Reischuk Ed., LNCS 1046, Springer Verlag, pp.503–514. 1996.
R. Gori, “A hierarchy of semantics for CLP({ie91-01}) general programs”, Report of DEA IMA, LIENS, École Normale Supérieure, Paris, 1995.
J. Jaffar, J.L. Lassez, “Constraint Logic Programming”, Proc. of POPL'87, Munich, pp.111–119, 1987.
R. Kemp, G. Ringwood, “Reynolds base, Clark models and Heyting semantics of logic programs”, Technical Report, Queen Mary and Westfield College, 1991, revised 1995.
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.
M. Maher, “Equivalences of logic programs”, in: J. Minker (ed.) Foundations of deductive databases and logic programming, Morgan Kaufmann, pp.627–658, Los Altos, CA, 1988.
P. Stuckey, “Constructive negation for constraint logic programming”, Proc. LICS'91, pp.328–339, 1991.
P. Stuckey “Negation and constraint logic programming”, Information and Computation 118(1), pp.12–33 (1995).
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Fages, F., Gori, R. (1996). A hierarchy of semantics for normal constraint logic programs. In: Hanus, M., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_5
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DOI: https://doi.org/10.1007/3-540-61735-3_5
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