article

Constraint programming viewed as rule-based programming

Authors:

Krzysztof R. Apt,

Eric MonfroyAuthors Info & Claims

Theory and Practice of Logic Programming, Volume 1, Issue 6

Pages 713 - 750

https://doi.org/10.1017/S1471068401000072

Published: 01 November 2001 Publication History

Abstract

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

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Cited By

Fertin GMonfroy EVasconcellos-Gaete C(2024)Best of Both Worlds: Solving the Cyclic Bandwidth Problem by Combining Pre-existing Knowledge and Constraint Programming TechniquesComputational Science – ICCS 202410.1007/978-3-031-63775-9_14(197-211)Online publication date: 2-Jul-2024
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Gent IJefferson CLinton SMiguel INightingale P(2014)Generating custom propagators for arbitrary constraintsArtificial Intelligence10.1016/j.artint.2014.03.001211:1(1-33)Online publication date: 1-Jun-2014
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Narboni G(2013)On rule systems whose consistency can be locally maintainedAI Communications10.5555/2594638.259464426:1(67-77)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.5555/2594638.2594644
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Constraint programming viewed as rule-based programming
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
2. Theory of computation
  1. Logic

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cover image Theory and Practice of Logic Programming

Theory and Practice of Logic Programming Volume 1, Issue 6

November 2001

96 pages

ISSN:1471-0684

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Cambridge University Press

United States

Publication History

Published: 01 November 2001

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Cited By

Fertin GMonfroy EVasconcellos-Gaete C(2024)Best of Both Worlds: Solving the Cyclic Bandwidth Problem by Combining Pre-existing Knowledge and Constraint Programming TechniquesComputational Science – ICCS 202410.1007/978-3-031-63775-9_14(197-211)Online publication date: 2-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63775-9_14
Gent IJefferson CLinton SMiguel INightingale P(2014)Generating custom propagators for arbitrary constraintsArtificial Intelligence10.1016/j.artint.2014.03.001211:1(1-33)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.1016/j.artint.2014.03.001
Narboni G(2013)On rule systems whose consistency can be locally maintainedAI Communications10.5555/2594638.259464426:1(67-77)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.5555/2594638.2594644
Chun A(2011)Optimizing Limousine Service with AIAI Magazine10.1609/aimag.v32i2.234632:2(27-41)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1609/aimag.v32i2.2346
Gent IJefferson CMiguel INightingale P(2010)Generating special-purpose stateless propagators for arbitrary constraintsProceedings of the 16th international conference on Principles and practice of constraint programming10.5555/1886008.1886030(206-220)Online publication date: 6-Sep-2010
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Chun A(2008)Using AI for olympic equestrian event preparationProceedings of the 20th national conference on Innovative applications of artificial intelligence - Volume 310.5555/1620138.1620141(1616-1623)Online publication date: 13-Jul-2008
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Choi CLee JStuckey P(2007)Removing propagation redundant constraints in redundant modelingACM Transactions on Computational Logic10.1145/1276920.12769258:4(23-es)Online publication date: 1-Aug-2007
https://dl.acm.org/doi/10.1145/1276920.1276925
Stéphan I(2006)Boolean Propagation Based on Literals for Quantified Boolean FormulaeProceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy10.5555/1567016.1567115(452-456)Online publication date: 22-May-2006
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Hawkins PStuckey P(2006)A hybrid BDD and SAT finite domain constraint solverProceedings of the 8th international conference on Practical Aspects of Declarative Languages10.1007/11603023_8(103-117)Online publication date: 9-Jan-2006
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Apt K(2005)Explaining constraint programmingProcesses, Terms and Cycles10.5555/2168279.2168285(55-69)Online publication date: 1-Jan-2005
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