# Explanation-based generalization and constraint propagation with interval labels

## Abstract

Two ways of applying EBG to constraint propagation with interval labels are presented. The first method, CP-EBG-1, is described by a straightforward use of a Prolog EBG implementation. The second, CP-EBG-2, performs two phases: First, constraint propagation is done and, using EBG, a generalized final labelling is derived but no extra conditions are learned. Second, constraint propagation is again performed using the final labellings of phase 1 as the initial labelling. This time, conditions are learned which form the desired concept description.

It is shown that CP-EBG-2 learns more general concept descriptions than CP-EBG-1. A proof is outlined that CP-EBG-2 produces correct concept descriptions for the class of constraints using linear equations and interval arithmetic. Central to this proof- and to possible proofs for other constraint classes - is the notion of a *moderate* generalization. It guarantees that a generalization which was learned from one instance and which is now used in a new situation, does not lead to the exclusion of any solution for this new situation.

## Keywords

Explanation-based generalization constraint propagation interval labels moderate generalization## Preview

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