Abstract Based on a universal set, formulas are introduced and each formula corresponds to a granule. This gives rise to the definition of the granular space in which the granularly semantic reasoning is discussed. The reasoning is determined by the relationships among granules. By means of granular computing, it is proved that the granularly semantic reasoning satisfies each deductive rule in naturally deductive system of propositional logic. Thus, the soundness on the granular space is obtained, which means the formal reasoning can imply the granularly semantic reasoning. Although the completeness on the granular space is untenable, the results indicate that the granularly semantic reasoning is an expansion of the schemes of reasoning in propositional logic. Hence, the granularly semantic reasoning enlarges the scope of researches on reasoning as well as introduces a new method for the study of granular computing. Moreover, it promotes the integration of granular computing and logical reasoning.
2008, Vol. 21 
