On Implication Algebras Based on Lattices and Their Dual Algebras

Abstract:

      This paper gives out that the relationship among lattice implication algebras, MV algebras, R₀ algebras and other implication algebras based on lattices, and their dual algebras are established. Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.