A lattice-valued modal propositional logic system LMP(X)

In this paper, two operators N and P are introduced into LP(X), then a new lattice-valued modal propositional logic system LMP(X) is given. With possible world semantics, N and P are described. Furthermore, some properties on semantics and syntax are discussed, and some important conclusions are obtained, including the soundness theorem, deduction theorem and consistence theorem.