A framework for learning constraints: Preliminary report

Constraints represent a powerful way of specifying knowledge in any problem solving domain. Typically the appropriate constraints for a given problem need to be fully specified. In general it is difficult to describe the appropriate constraints in every problem setting. Hence automatic constraint acquisition is an important problem. In this paper we develop a model for automatic constraint acquisition. We show that a universal scheme for generalizing constraints specified on variables across any domain, whether continuous or discrete, is not feasible. Here we provide a generalization model for constraints specified in the form of relations with explicit enumeration of allowed tuples. We provide a scheme to generalize the constraints expressed in this form in our model. We discuss the properties of the generalized constraint obtained from input constraints. We also show that this scheme provides a uniform method of generalization for any type of constraint on variables with finite and discrete domain. In the end we elaborate upon the different applications of our scheme. We show how learning in our scheme can help improve the search efficiency in a CSP,