 A note on notation and the level of technicality To discuss aspects of multi-modal logic, this entry assumes basic knowledge of  modal logic,  specifically about its language and its relational  ‘possible worlds’  semantics (though other semantic models will be mentioned too). In particular, a relational model is understood as a tuple containing a set of possible worlds, one or more (typically binary) relations between them, and a valuation indicating what each possible world actually represents. Such structures can be described by different modal languages. We will use \(\cL\) to denote the standard propositional language, and \(\cL_{\left\{ O_1, \ldots, O_n \right\}}\) to denote its extension with modalities \(O_1\), …, \(O_n\). Given a relational model M and a formula \(\varphi\), we will use \(\llbracket \varphi \rrbracket^{M}\) to denote the set of worlds in M where \(\varphi\) holds. Readers can find more details about the basics of modal logic not only in the referred SEP entries, but also in the initial chapters of Blackburn, Rijke, &amp; Venema (2001) and van Benthem (2010), and also in Blackburn &amp; van Benthem (2006).