Finding satisfying assignments for the variables involved in a set of constraints can be cast as a (bounded) model generation problem: search for (bounded) models of a theory in some logic. The state-of-the-art approach for bounded model generation for rich knowledge representation languages like Answer Set Programming (ASP) and FO(.) and a CSP modeling language such as Zinc, is ground-and-solve: reduce the theory to a ground or propositional one and apply a search algorithm to the resulting theory.
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