modalities and multimodalities

This entry is about

8.2 Multimodal languages


The calculus of modal operators:

(1) ϕ 0\phi_0 a set of atomic modal parameters.

(1.1) 00 (zero) and idid are in ϕ 0\phi_0.

(2) ϕ\phi a class of modal parameters is defined from ϕ 0\phi_0 by closure under two formation operators \cup and \odot by the rules:

(2.1) aϕ 0a\in \phi_0 implies aϕa\in \phi.

(2.2) a,bϕa,b\in \phi implies abϕa\cup b\in \phi and abϕa\odot b\in \phi.

The class of modal operators indexed by modal parameters denoted by Θ\Theta is defined by:

(3) aϕa\in \phi implies [a]Θ[a]\in \Theta.

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