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Well-founded and stable semantics of logic programs with aggregates

Published online by Cambridge University Press:  01 May 2007

NIKOLAY PELOV ,
MARC DENECKER  and
MAURICE BRUYNOOGHE
NIKOLAY PELOV
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Belgium (e-mail: pelov@cs.keleuven.be, marcd@cs.keleuven.be, maurice@cs.keleuven.be)
MARC DENECKER
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Belgium (e-mail: pelov@cs.keleuven.be, marcd@cs.keleuven.be, maurice@cs.keleuven.be)
MAURICE BRUYNOOGHE
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Belgium (e-mail: pelov@cs.keleuven.be, marcd@cs.keleuven.be, maurice@cs.keleuven.be)
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Abstract

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valued immediate consequence operator of an aggregate program. Such an operator approximates the standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs between precision and tractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

Keywords

logic programmingaggregates
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 7 , Issue 3 , May 2007 , pp. 301 - 353
Copyright
Copyright © Cambridge University Press 2007

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