 Kim initially maintained that the modal operator versions are equivalent to the above possible world definitions of weak and strong supervenience respectively (see esp. 1987, 79–82). But they are not; they are stronger. On certain assumptions (e.g. that modal operators are to be understood as quantifiers over worlds), the modal operator versions of strong and weak supervenience respectively entail the possible world versions; but not vice versa (McLaughlin 1995).