
From Constraints to Resolution Rules, Part II: chains, braids, confluence and T&E
In this Part II, we apply the general theory developed in Part I to a de...
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Some Remarks on Boolean Constraint Propagation
We study here the wellknown propagation rules for Boolean constraints. ...
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Automatic Generation of Constraint Propagation Algorithms for Small Finite Domains
We study here constraint satisfaction problems that are based on predefi...
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PatternBased Constraint Satisfaction and Logic Puzzles
PatternBased Constraint Satisfaction and Logic Puzzles develops a pure ...
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The Regularization of Small SubConstraint Satisfaction Problems
This paper describes a new approach on optimization of constraint satisf...
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Truth as Utility: A Conceptual Synthesis
This paper introduces conceptual relations that synthesize utilitarian a...
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Generating Significant Examples for Conceptual Schema Validation
This report bases itself on the idea of using concrete examples to verif...
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From Constraints to Resolution Rules, Part I: Conceptual Framework
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between variables (with the goal of reducing their sets of possible values) and some kind of structured search (depthfirst, breadthfirst,...). But when such blind search is not possible or not allowed or when one wants a 'constructive' or a 'patternbased' solution, one must devise more complex propagation rules instead. In this case, one can introduce the notion of a candidate (a 'still possible' value for a variable). Here, we give this intuitive notion a well defined logical status, from which we can define the concepts of a resolution rule and a resolution theory. In order to keep our analysis as concrete as possible, we illustrate each definition with the well known Sudoku example. Part I proposes a general conceptual framework based on first order logic; with the introduction of chains and braids, Part II will give much deeper results.
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