This paper offers a critique of the framework of Constraint Satisfaction Problems. While this framework has been successful in studying search techniques, and has inspired some constraint programming languages, it has some weaknesses that leave it not directly applicable to the study of complex constraints (including so-called global constraints) in constraint programming languages. In particular, it deals poorly with semantic relations whose consistency can be determined algorithmically. In this paper the philosophy of the CLP Scheme is applied to extend the CSP framework to a form more suitable for addressing complex constraints, where both constraint satisfaction and constraint solving have a role. Some rough principles for local consistency conditions in the extended framework are developed, and appropriate notions of local consistency are formulated. These can be used as a coarse measure of the degree of constraint propagation achieved by implementations of complex constraints.
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