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In this paper, we present a general scheme for incremental constraint retraction algorithms that encompasses all existing algorithms. Moreover, we introduce some necessary conditions to ensure the correctness of any new incremental constraint retraction algorithms. This rather theoretical work is based on the notion of explanation for constraint programming… (More)

Solvers on finite domains use local consistency notions to remove values from the domains. This paper defines value withdrawal explanations. Domain reduction is formalized with chaotic iterations of monotonic operators. To each operator is associated its dual which will be described by a set of rules. For classical consistency notions, there exists a… (More)

This report presents a new proof method of partial correctness for logic programs with negation based on a proof modularity. We prove in a com-positional way that Fitting's or the well-founded semantics of the program is included in a speciication. We give conditions for an abstract semantics to be compositional and we base our proof method on this… (More)

The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical framework for domain reduction, explanations are proof trees explaining value removals. These proof trees are defined by… (More)