On the rough consistency measures of logic theories and approximate reasoning in rough logic

Abstract

This paper is mainly devoted to establishing a kind of graded reasoning method in the context of rough logic. To this end, a weak form of deduction theorem in rough logic is firstly obtained, then, based upon the weak deduction theorem and the notion of rough truth degree, a new kind of graded reasoning method in rough logic is presented. Moreover, to embody the idea of rough approximations, the notions of graded rough upper consequence and graded rough lower consequence are also proposed, which can be treated as the logical counterpart of rough upper and lower approximation, respectively. Compared with the existing graded reasoning method, the proposed method in the present paper does not employ the notion of rough similarity degree, and hence their fundamental starting points are different, however, they are also closely related, accordingly, a comparative study is performed between these two different graded reasoning methods. Lastly, based on the proposed graded reasoning method, the notions of rough (upper, lower) consistency degree are also proposed and their properties are investigated in detail.