 The core idea of supervenience is captured by the slogan, “there cannot be an A-difference without a B-difference.” It is important to notice the word ‘cannot’. Supervenience claims do not merely say that it just so happens that there is no A-difference without a B-difference; they say that there cannot be one. A-properties supervene on B-properties if and only if a difference in A-properties requires a difference in B-properties—or, equivalently, if and only if exact similarity with respect to B-properties guarantees exact similarity with respect to A-properties. Supervenience claims thus have modal force. The kind of modal force can vary; different supervenience claims might attribute different kinds of necessity to the connection between B-properties and A-properties (see  Section 3.1.)  Even when the modality is fixed, however, there are a number of distinct claims that might be expressed by the slogan. A good deal of philosophical work has gone into distinguishing these forms of supervenience, and into examining their pairwise logical relations.