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Weight constraints as nested expressions

Published online by Cambridge University Press:  10 January 2005

PAOLO FERRARIS  and
VLADIMIR LIFSCHITZ
PAOLO FERRARIS
Affiliation:
Department of Computer Sciences, University of Texas at Austin, Austin, TX 78712, USA (e-mail: otto@cs.utexas.edu, vl@cs.utexas.edu)
VLADIMIR LIFSCHITZ
Affiliation:
Department of Computer Sciences, University of Texas at Austin, Austin, TX 78712, USA (e-mail: otto@cs.utexas.edu, vl@cs.utexas.edu)
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Abstract

We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemelä and Simons, uses weight constraints. We show that there is a simple, modular translation from the language of weight constraints into the language of nested expressions that preserves the program's answer sets. Nested expressions can be eliminated from the result of this translation in favor of additional atoms. The translation makes it possible to compute answer sets for some programs with weight constraints using satisfiability solvers, and to prove the strong equivalence of programs with weight constraints using the logic of here-and-there.

Keywords

answer setscardinality constraintsSMODELSstable modelsweight constraints
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 5 , Issue 1-2 , January 2005 , pp. 45 - 74
Copyright
© 2005 Cambridge University Press

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