Semantic reasoning study for rough logic about n-ary formulas

We begin this paper with a discussion of constructing a kind of formulas which are called n-ary formulas in an approximate space of rough set theory. These formulas are an expansion of the formulas in Pawlak rough logic, so that the domains of the n-ary formulas are extended from subsets of U to subsets of U n (=U×U×…×U) . In subsequent discussions we define five rough logical values based on Pawlak rough logic for the n-ary formulas in n-dimensional space, and study rough logical reasoning in semantics through these rough logical value operations. Of course, we get some theorems which indicate that some forms of logical reasoning in classical logic are also true in rough logic for some rough logical values, but because 5-value rough logic is different from classical 2-value logic, we naturally obtain some new properties.