- is a Boolean algebra,
- is a unary operation on A satisfying and for all x, y in A.
Modal algebras provide models of propositional modal logics in the same way as Boolean algebras are models of classical logic. In particular, the variety of all modal algebras is the equivalent algebraic semantics of the modal logic K in the sense of abstract algebraic logic, and the lattice of its subvarieties is dually isomorphic to the lattice of normal modal logics.
A. Chagrov and M. Zakharyaschev, Modal Logic, Oxford Logic Guides vol. 35, Oxford University Press, 1997. ISBN 0-19-853779-4