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This idea [that modal operators perform quantification without making use of explicit variables and binding], when expressed mathematically, has turned out to be the most significant milestone in the history of modal logic.
Blackburn, van Benthem, Wolter, Handbook of modal logic, Elsevier, 2007
Carnielli, Pizzi, Modalities and Multimodalities, Springer, 2008
Yde Venema, website: algebraic- and coalgebraic aspects of modal logic. e.g §6 in the “handbook”.
Valentin Goranko and Martin Otto. “handbook” §5 Model theory of modal logic