A Comparison between Lattice-Valued Propositional Logic LP(X) and Gradational Lattice-Valued Propositional Logic Lvpl

In order to provide a logical foundation for uncertain information processing theory, especially for the fuzziness, the incomparability uncertain information in the reasoning, Xu presented the lattice implication algebra by combining lattice and implication algebra in 1993 [1]. After then, he and his research group have established the lattice-valued propositional logic LP(X) and gradational lattice-valued propositional logic Lvpl, lattice-valued first-order logic and gradational latticevalued first-order logic and applied them to automated and approximated reasoning [2]-[12]. As we know, during the uncertainty reasoning process based on Lvpl the chosen of the value set T and the implication operator is very important. Chen researched uncertainty reasoning based on lattice-valued firstorder logic L →