 The modal property attributions as reviewed above raise consistency questions when a system can be split up into components in different ways. 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? This problem was addressed by different authors during the 1990s (see Vermaas 1999, Bacciagaluppi 1996).