摘要
引入命题逻辑公式的基于随机变量序列的随机真度概念,并说明其是已有文献中各种真度概念的共同一般化,证明全体公式的随机真度之集在[0,1]中没有孤立点.利用随机真度定义公式间的随机相似度,进而导出全体公式集上的一种伪距离——随机逻辑伪距离,证明在随机逻辑伪距离空间没有孤立点.指出随机真度是已有文献中各种命题逻辑真度的共同推广.利用概率论中的积分收敛定理,证明一个关于真度的极限定理,该定理沟通了已有各种真度之间的联系.证明随机逻辑伪距离空间中逻辑运算的连续性,并将概率逻辑学基本定理推广到多值命题逻辑.在随机逻辑伪距离空间中提出两种不同类型的近似推理模式.
In this paper, the concept of random truth degree of proposition formulas based on a random variable sequence is introduced, which is a common generalization of various concepts of truth degree existing in references, and the set of random truth degree of all logic formulas is proved to have no isolated point in [0,1 ]. The random similarity degree and random pseudo-metric space between two logic formulas are defined by means of random truth degrees, and the random logic pseudo-metric space is proved to have no isolated point. The random truth degree of proposition logic is a generation of various truth degree of proposition logic. Using convergence theorem of integration in probability, a limit theorem of truth degrees is given, which shows the connection of various truth degrees. Various logic operations are continuous in random logic pseudo-metric space, and the fundamental theorem of probab extended to the multi-valued proposition logic. Two diverse approximate reasoning ways are random logic pseudo-metric space. ility logic is proposed in
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2013年第3期231-241,共11页
Pattern Recognition and Artificial Intelligence
基金
湖南省重点建设学科项目
湖南省教育厅科学研究项目(No.11C1176)资助
关键词
命题逻辑
随机真度
随机相似度
随机逻辑伪距离空间
近似推理
Proposition Logic, Random Truth Degree, Random Similarity Degree, Random LogicPseudo-Metric Space, Approximate Reasoning
作者简介
刘晓玲，女，1977年生，硕士，讲师，主要研究方向为网络安全、多值逻辑．E-mail：lxlwork@126．com．
张家录（通讯作者），男，1964年生，硕士，教授，主要研究方向为非经典数理逻辑、近似推理．E-mail：410735@163．com
