 By contrast, according to the other version the properties ascribed to the system do not have a relational character. This proposal therefore faces consistency questions about the assignments of definite values to observables according to different ways of splitting up the total system into components. Consider, for example, the three-component composite system \(\alpha \beta \chi\). We could apply the biorthogonal decomposition theorem to the two-component system (i) \(\alpha(\beta \chi)\), or (ii) \(\beta(\chi \alpha)\) or (iii) \(\chi(\alpha \beta)\). Suppose that, as a result of this, in case (i) the system \(\alpha\) has the definite-valued property \(P\), in case (ii) the system \(\beta\) has the definite-valued property \(Q\), and in case (iii) the system \(\alpha \beta\) has the definite-valued property \(R\). How do the definite-valued properties of \(\alpha\) and \(\beta\) relate to those of \(\alpha \beta\)? Are the definite-values properties of system \(\alpha \beta\) \(P \amp Q\), or \(R\), or both?