Rongh逻辑公式的语义分析及基于语义分析推理的研究  

Semantic Analyses for Formulas in Rough Logic and Reasoning Study Based on the Semantic Analysis

作　　者：闫林[1] 王全蕊[1] 刘延[1] 

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

出　　处：《模式识别与人工智能》2006年第4期433-438,共6页Pattern Recognition and Artificial Intelligence

基　　金：河南省自然科学基金(No.0611055200)

摘　　要：在粗糙集理论的近似空间M=(U,R)中展开讨论,其目的是要把Pawlak粗糙逻辑中的公式进行推广,将其所涉及的论域从与U有关扩展到n个U的笛卡尔积U^n之上,并对这些推广的n元公式进行研究,讨论以Paw-lak粗糙逻辑中的5种逻辑值为基础,并在n元公式上对此进行推广定义,针对这些关于n元公式的粗糙逻辑值,从语义出发,研究n元公式之间的逻辑推理关系,其结果是经典逻辑中的一些逻辑推理的结论对于某些粗糙逻辑值仍然成立,但自然也增添新的性质。In the first place, a discussion is made to construct a kind of formulas called n -ary tormulas in an ap Pawlak proximate space of rough set theory. These formulas are an expansion of the formulas in rough logic, so that the domains of the n -ary formulas are extended from subsets of U to subsets of U^n （ = U × U × … × U ） . Then based on Pawlak rough logic , five logical values are defined for the n -ary formulas, and through these logical value operations the study about rough logical reasoning in semantics is discussed. Some properties indicate that some forms of logical reasoning in classical logic are also true in rough logic for some rough logical values. However, because 5-value rough logic is different from classical 2-value logic, some new properties are naturally obtained.

关 键 词：近似空间 粗糙真 粗糙假 等价关系 划分 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]