 The question now arises whether the rules of BDMI and SDMI, applied to \(\alpha\), assign a value to \(\Pi^{\alpha}\) that is the same as the value assigned to \(\Pi^{\alpha} \otimes I^{\beta}\) when the rules are applied to the composite system \(\alpha \beta\) (a condition known as Property Composition), and vice versa (Property Decomposition). The answer to this question is negative: BDMI and SDMI violate Property Composition and Property Decomposition (for a proof, see Vermaas 1998).