  The relational and holistic interpretations of properties mark a radical shift from the standard interpretation of properties in orthodox quantum mechanics. Other advocates of the modal interpretation have chosen not to follow this interpretation, and opted for a modal interpretation that does not violate property composition. While the property assignment above does not assume any preferred partition of the universe (the partition of the universe into a particle pair and the rest of the universe is as good as the partition of the universe into the L-particle and the rest of the universe), proponents of property composition postulated that there is a preferred partition of the universe into ‘atomic’ systems and accordingly a preferred factorization of the Hilbert space of the universe. This preferred factorization is supposed to be the basis for the ‘core’ property assignment: Properties are prescribed to atomic systems according to a property assignment that is a generalization of the bi-orthogonal decomposition property  assignment.[28]  And the properties of complex systems are postulated to be compositions of the properties of their atomic systems (see the entry on modal interpretations of quantum theory, section 2, and Bacciagaluppi and Dickson 1999). The challenge for this atomic modal interpretation is to justify the assumption that there is a preferred partition of the universe, and to provide some idea about how such factorization should look like.