At the “functional level”, Semantic Web Services (SWS) are described akin to planning operators, with preconditions and effects relative to an ontology; the ontology provides the formal vocabulary and an axiomatisation of the underlying domain. Composing such SWS is similar to planning. A key obstacle in doing so effectively is handling the ontology axioms, which act as state constraints. Computing the outcome of an action involves the frame and ramification problems, and corresponds to belief update. The complexity of such updates motivates the search for tractable classes. Herein we investigate a class that is of practical relevance because it deals with many commonly used ontology axioms, in particular with attribute cardinality upper bounds which are not handled by other known tractable classes. We present an update computation that is exponential only in a comparatively uncritical parameter; we present an approximate update which is polynomial in that parameter as well.