This entry is about * Carnielli, Pizzi, [[modalities and multimodalities]], Springer, 2008 ## 8.2 Multimodal languages (p.206) The calculus of modal operators: (1) $\phi_0$ a set of *atomic modal parameters*. (1.1) $0$ (zero) and $id$ are in $\phi_0$. (2) $\phi$ a class of modal parameters is defined from $\phi_0$ by closure under two formation operators $\cup$ and $\odot$ by the rules: (2.1) $a\in \phi_0$ implies $a\in \phi$. (2.2) $a,b\in \phi$ implies $a\cup b\in \phi$ and $a\odot b\in \phi$. The *class of modal operators indexed by modal parameters* denoted by $\Theta$ is defined by: (3) $a\in \phi$ implies $[a]\in \Theta$.