  Modal interpretations vary in their property assignment. For simplicity, we shall focus on modal interpretations in which the property assignment is based on the so-called Schmidt biorthogonal-decomposition theorem (see Kochen 1985, Dieks 1989, and Healey 1989). Let S1 and S2 be systems associated with the Hilbert spaces HS1 and HS2, respectively. There exist bases {|αi&gt;} and {|βi&gt;} for HS1 and HS2 respectively such that the state of S1+S2 can be expressed as a linear combination of the following form of vectors from these bases: