Modal K axiom

Not to be confused with the Axiom K of Martin-Löf type theory.

The K axiom of modal logic (named after Saul Kripke) is

  \Box (\phi \to \psi) \to \Box \phi \to \Box \psi

It is equivalent to any of the following statements.

• \Box (\phi \land \psi) \leftrightarrow \Box \phi \land \Box \psi
• \Box (\phi \to \psi) \land \Box \phi \to \Box \psi

References

• Any good book on modal logic.