CAJ | 학술논문

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.
인입명제라집공식적기우수궤변량서렬적수궤진도개념,병설명기시이유문헌중각충진도개념적공동일반화,증명전체공식적수궤진도지집재[0,1]중몰유고립점.이용수궤진도정의공식간적수궤상사도,진이도출전체공식집상적일충위거리———수궤라집위거리,증명재수궤라집위거리공간몰유고립점.지출수궤진도시이유문헌중각충명제라집진도적공동추엄.이용개솔론중적적분수렴정리,증명일개관우진도적겁한정리,해정리구통료이유각충진도지간적련계.증명수궤라집위거리공간중라집운산적련속성,병장개솔라집학기본정리추엄도다치명제라집.재수궤라집위거리공간중제출량충불동류형적근사추리모식.
@@@@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 probability logic is extended to the multi-valued proposition logic. Two diverse approximate reasoning ways are proposed in random logic pseudo-metric space.