Modal Algebra

In algebra and logic, a modal algebra is a structure such that

  • 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.

Stone's representation theorem can be generalized to the Jónsson–Tarski duality, which ensures that each modal algebra can be represented as the algebra of admissible sets in a modal general frame.

Read more about Modal AlgebraSee Also

Other articles related to "modal algebras, algebra, modal algebra":

General Frame - Jónsson–Tarski Duality
... General frames bear close connection to modal algebras ... it is a subalgebra of the power set Boolean algebra ... The combined structure is a modal algebra, which is called the dual algebra of F, and denoted by ...

Famous quotes containing the word algebra: