The modal operators governing 'strong' and 'weak' global supervenience quantify over different ranges of possible worlds, making transitivity through intermediate forms non-trivial.

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global supervenience(Modal supervenience relations in philosophy of mind and metaphysics): A globally supervenes on B if and only if no two possible worlds share the same global pattern of distribution of B-properties while differing in their global pattern of distribution of A-properties.
modal operators: unary connectives
possible worlds(Leibniz's modal semantics, anticipating contemporary possible-worlds semantics): Worlds that have existence in a tenuous sense; fictional worlds used to characterize the nature of possibles that are never actualized
strong supervenience(Conceded by Kim to not be entailed by global supervenience): A supervenience relation where, across all possible worlds, any individual that shares B-properties with another individual also shares A-properties with that individual
transitivity

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