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Due to its relational form, its definite clause syntax and the possibility of writing metaprograms in the same language, it turns out that logic programming is a convenient programming language to represent, relax and solve constraint satisfaction problems (CSPs). Not only we can represent CSPs writing elegant logic programs in a declarative style, but we can also solve them in an efficient way by writing simple metaprograms adding new control strategies to the usual backtrack search strategy of logic programs. This paper defines the classes of CSPs we consider, shows the mapping between these CSPs and logic programs having the same semantics, and describes how to represent relaxation algorithms as logic metaprograms.