粒及粒计算在逻辑推理中的应用

讨论了信息粒的结构及其实例。基于Rough集方法定义了决策规则粒,构造了决策规则粒库,它被用作逻辑推理。定义了粒语言,描述了这种语言的语法、语义、粒语句的运算法则和粒之相关的几个性质。定义了粒之间的相互包含(inclusion)和相似(closeness)。基于这些概念,构造了一种逻辑推理的新模型。这种推理模式的特点在于它既是逻辑的又是集合论的。所谓逻辑的就是说推理是遵循一种逻辑运算;所谓集合论的是指这种推理可利用对应于这种逻辑公式的意义集的运算进行推理,还用实例说明了这种推理模式是可行和有效的。

Granules and Applications of Granular Computing in Logical Reasoning

The structure and real examples of information granules are discussed in this paper The granules of decision rules are defined based on a rough set approach Granular language is defined Syntax and semantics are also described Operation rules of the granular statements are given Some properties of the language are also discussed Inclusion and closeness between granules are established Granulation base corresponding to decision rules is also constructed A reasoning model based on the concepts is proposed, and may be used in logical reasoning The characteristic of the reasoning model is both logic and set theory By "logic" it is meant that the reasoning obeys the logical derivability; By "set theory" it is meant that the operations corresponding to the meaning sets of logical formulas obey the methods in set theory Finally, the validity and feasibility of the reasoning are illustrated with real examples