6. Soft CLP

Abstract

The framework presented in the previous chapters shows how the soft constraint idea can give us an easy way to model non-crisp problems. To program applications we need, nevertheless, a language where we can use soft constraints. This is why we extend the Constraint Logic Programming (CLP) formalism in order to handle semiring-based constraints.

This allows us to perform in the same language both constraint solving and optimization. In fact, constraints based on semirings are able to model both classical constraint solving and more sophisticated features like uncertainty, probability, fuzziness, and optimization. We then provide this class of languages with three equivalent semantics: model-theoretic, fix-point, and proof-theoretic, in the style of classical CLP programs.