 The resulting logic is axiomatised by the fusion of \(S_5\) modal logics for the universal modality \(U\) and each one of the \(\Box_{\mathbf{x}}\) modalities, plus the addition of axioms of the form \(U \phi \rightarrow \Box_{\mathbf{x}}\phi\), and \(\Box_{\mathbf{x}}\phi \rightarrow \Box_{\mathbf{y}}\phi\) whenever \(\sim_{\mathbf{y}} \subseteq \sim_{\mathbf{x}}\). 