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Belief Constraint Satisfaction Problems

Every problem that can be described by a set of variables and a set of constraints among those variables can easily be cast as a Constraint Satisfaction Problem (CSP). In spite of its simplicity, the standard CSP has proven unsuited for modeling ill-defined decision problems, especially, under uncertain circumstances. In such situation, uncertainty evokes the need for softness. Moreover, when the relevance of some constraints depends on other factors, we should prioritize those constraints. Eventually, the modeled uncertainty, as well as the expressed soft and prioritized constraints induce preferences over the solutions set. Previous work employing mathematical uncertainty theories are either uncertainty-based frameworks or preference-based ones. In this paper, we propose a unifying CSP extension, based on the Dempster-Shafer theory, which deals jointly with all these four concepts, i.e., uncertainty, soft and prioritized constraints and preferences over the solutions.