Abstracting Numerical Values in CLP(H, N)

ing Numerical Values in CLP(H,N) Gerda Janssens1, Maurice Bruynooghe1, Vincent Englebert2 1 Department of Computer Science, K.U. Leuven Celestijnenlaan 200A, B-3001 Heverlee, Belgium 2 Institut d'Informatique, Facult es Universitaires Notre Dame de la Paix rue GrandGagnage 21, B-5000 Namur, Belgium Abstract. The paper de nes approximations for the numerical leaves of variables in CLP(H,N) constraint systems. The abstractions are based on intervals which are computed by narrowing rules. The novelty of this approach lays in the fact that intervals are used as abstraction and that narrowing rules do not only correspond to numerical constraints but also to uni cation constraints. In the rst abstraction the impact of the narrowing rules is limited. A prototype implementation has been developed and the obtained results are su ciently precise to recognise (future) redundant constraints. The abstraction can be extended (1) by incorporating the narrowing rules more globally (uni cation constraints are abstracted by a Prop-like abstraction, numeric constraints are kept in concrete form) and (2) by deriving ordinal relationships between variables.