  In the examples we have given so far (as well as in those considered by Gillon), non-collective construals always correspond to partitions of the denotation of the mass noun phrase. However, some interpretations correspond to a more general notion, that of a “covering”: a set X is a covering of a set Y just in case the sum of the elements of X is identical with the sum of the elements of  Y.[18] Thus, with This livestock carried that furniture, it may be that some pieces of furniture were repeatedly part of the furniture carried by some of the livestock. The relation of carrying thus applies between elements of a covering of [this livestock] and elements of a covering of [that furniture]. So it seems that the semantics of mass nouns should leave room, not only for partitions, but also for all kinds of  coverings.[19]