Semantic reasoning based on rough logic on n-dimensional approximate space

The universe is extended from subsets of U to subsets of Uⁿ in Pawlak rough logic theory. The subsequent discussions could be conducted on n-dimensional approximation space, which denote as M=(Uⁿ, R). The formal language in rough logic and the n-ary formulas have been put forward in this paper. According to discussing nary formulas in n-dimensional space based on the five rough logical values in Pawlak rough logic, some especial properties of n-ary formulas are gained. With the way of semantic reasoning, some forms of logical reasoning in classical logic have been studied. And we get some theorems which indicate that some forms of logical reasoning are also true in rough logic for five rough logical values.