粒空间中基于粒计算的粒语义推理  

Granularly Semantic Reasoning Based on Granular Computing in Granular Space

作　　者：闫林[1] 张学栋[1] 魏雁天[1] 何建仓[2] 

机构地区：[1]河南师范大学计算机与信息技术学院智能信息处理重点实验室,新乡453007 [2]河南师范大学计算机与信息技术学院能信息处理重点实验室,新乡453007

出　　处：《模式识别与人工智能》2008年第4期462-468,共7页Pattern Recognition and Artificial Intelligence

基　　金：河南省自然科学基金资助项目(No.0611055200)

摘　　要：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.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.

关 键 词：粒空间 粒语义推理 推理规则 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]