Abstract:

The concept of MR₀ algebra was introduced, and some major properties were discussed. Then the isomorphism theorems of MR₀ algebra were given. Additionally, the modal logic system K₁ was formed, which can be proved to be a complete system under MR₀ semantics. Finally, the modal logic system K₂ that proved to be soundness was formed through fuzzifying of the evaluation V in the Kripke model， and the modal logic system K₃ was formed and proved to be complete through the fuzzifying of the binary relationship R in the Kripke model.

Key words: modal logic; MR0 algebra; M filter; fuzzfication; completion