Closure properties of classes of spatio-temporal objects under Boolean set operations

We study a model for spatio-temporal objects, introduced by Chomicki and Revesz (1999), in which spatio-temporal data is specified by a spatial reference object together with a geometric transformation that determines the movement of the reference object in time. We give complete results concerning closure under Boolean set operators for the different classes of spatio-temporal objects introduced by these authors (in particular, we also answer a conjecture by Chomicki and Revesz negatively). Since only a few classes are closed under all set operators, we suggest that their model should be extended in order to increase its practical applicability.