Constraints

, Volume 21, Issue 1, pp 59–76 | Cite as

Projection, consistency, and George Boole

Article

Abstract

Although best known for his work in symbolic logic, George Boole made seminal contributions in the logic of probabilities. He solved the probabilistic inference problem with a projection method, leading to the insight that inference (as well as optimization) is essentially a projection problem. This unifying perspective has applications in constraint programming, because consistency maintenance is likewise a form of inference that can be conceived as projection. Viewing consistency in this light suggests a concept of J-consistency, which is achieved by projection onto a subset J of variables. We show how this projection problem can be solved for the satisfiability problem by logic-based Benders decomposition. We also solve it for among, sequence, regular, and all-different constraints. Maintaining J-consistency for global constraints can be more effective than maintaining traditional domain and bounds consistency when propagating through a richer structure than a domain store, such as a relaxed decision diagram. This paper is written in recognition of Boole’s 200th birthday.

Keywords

Projection Consistency Optimization Inference Satisfiability Logic-based Benders decomposition Boole 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

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