MP logical algebra

In this paper, we define a logical algebra named MP-algebra and discuss its algebraic properties. We find that MP algebra not only takes Boole algebra, MV-algebra and R₀ algebra as its special examples but also holds the subdirect representation theorem same as that of on Boole algebra, MV algebra and R₀ algebra. We also explore the basic properties of implication operation of MP-algebra. We prove that an MP-algebra is also a residuated lattice with many good properties. The conclusions we got show that MP-algebra is a well-structure logic algebra when it is taken as the logic truth degree set.