Reasoning with Complements

This paper develops a method to determine consistenly the integration of spatial integrity specifications, particularly for the case when two constraints, c1 and c2, are applied between three classes A, B, C (i.e., A c1 B and B c2 C), as such scenarios give rise to an implied consistency constraint c3 that holds between A and C. To determine c3, the mere composition reasoning with c1 and c2 is often insufficient, as it lacks consideration of the interferes that come through c1’s and c2’s complements. Two augmentation methods are introduced, one with a constraint’s complement to yield the specified constraint between all pairs of members of A and C, the other as the least upper bound of c1 and c2 with the constraints’ poset of possible transitions between constraints.