Spahn modalities and multimodalities (changes)

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• 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 $[a]\in \Theta$.