Researches on Rough Truth of Rough Axioms Based on Granular Computing

The concept, rough truth, is first presented in rough logic. It is a logical value, and lies between truth and falsity. By combining rough logic with modal logic, rough validity of the rough axioms is studied in this paper, which has close links with the logical value: rough truth. Because an axiom of modal logic corresponds to a rough axiom, the study of this paper actually focuses on the analysis of rough truth of the axioms in modal logic, which is based on a structure constructed in this paper. The structure is linked with a series of special states. The research on rough truth connects the special states with the rough axioms. At the same time, granular computing is introduced to the research process. As an approach to data processing, granular computing plays an important role in determining whether a rough axiom is roughly true or not. Thus, the study also demonstrates a way of research on granular computing. The conclusions show that each rough axiom is roughly true at every state of the structure, which means that each rough axiom is roughly valid. This is the desired result.