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在论域上定义公式,并因其与粒相对应,使得粒空间得以形成.在粒空间中由粒之间的关系确定出粒语义推理,并对此进行讨论.通过粒计算,证得粒语义推理满足命题逻辑自然推理系统的每一推理规则,因此粒空间上的可靠性成立,这表明形式推理蕴涵粒语义推理.尽管粒空间上的完备性不成立,但结果表明粒语义推理是各经典推理模式的扩充,所以粒语义推理既拓宽推理研究的范围,又引进粒计算的研究方法,促成粒计算与逻辑推理的进一步融合.
The formula is defined on the universe of discourse, and because of its correspondence with the granule, the granule space is formed. Granular semantic reasoning is determined by the relation between the granule in the granule space, and the granule is discussed. Semantic reasoning fulfills every inference rule of natural reasoning system of propositional logic, so the reliability of granularity holds, which indicates that formal reasoning contains granular semantic reasoning.Although granular completeness does not hold, the results show that granular semantic inference Therefore, granular semantic reasoning not only broadens the scope of inference research, but also introduces the research methods of granular computing, which leads to the further integration of granular computing and logical reasoning.