一阶模糊谓词逻辑公式的解释模型真度理论及其应用

基于一阶模糊谓词逻辑公式的有限和可数解释真度的理论,引入了一阶模糊谓词逻辑公式的解释模型及解释模型真度的概念,并讨论了它们的一系列性质及其在近似推理中的应用.     

一种将数学神秘化的倾向--评《无穷小量的命运及对数学发展动力的思考》一文

陈学云在文献[1]中给出一个结论:我们必须丢掉用数学真理性来解释数学适用性的幻想.我们认为这实际上是在宣扬一种数学神秘主义的观点;而数学主体内容的发展摧毁的是旧形而上学的先验"真理"观;具体数学理论在人类实践活动中显示出来的适用性,依赖于其具体的"真理"性.     

Lukasiewicz 命题逻辑系统一种新的理论的相容度

根据演绎定理和完备性定理,应用公式真度理论在Lukasiewicz命题模糊逻辑系统中讨论理论Γ的相容性,根据矛盾式■是Γ-结论的真度的大小,提出了一种新的极指标和相容度的概念.给出了理论Γ相容、不相容及其它相关结论的充分必要条件,并且获得了相容度与发散度之间联系的重要关系式.     

测量的误差和不确定度

本给出了测量的误差和不确定度的概念，并阐述了它们之间的联系和区别。     

The case for an interval-based representation of linguistic truth

This paper develops an interval-based approach to the concept of linguistic truth. A special-purpose interval logic is defined, and it is argued that, for many applications, this logic provides a potentially useful alternative to the conventional fuzzy logic.The key idea is to interpret the numerical truth value v(p) of a proposition p as a degree of belief in the logical certainty of p, in which case p is regarded as true, for example, if v(p) falls within a certain range, say, the interval [0.7, 1]. This leads to a logic which, although being only a special case of fuzzy logic, appears to be no less linguistically correct and at the same time offers definite advantages in terms of mathematical simplicity and computational speed.It is also shown that this same interval logic can be generalized to a lattice-based logic having the capacity to accommodate propositions p which employ fuzzy predicates of type 2.     

Opinion evolution based on cellular automata rules in small world networks

In this paper,we apply cellular automata rules,which can be given by a truth table,to human memory.We design each memory as a tracking survey mode that keeps the most recent three opinions.Each cellular automata rule,as a personal mechanism,gives the final ruling in one time period based on the data stored in one’s memory.The key focus of the paper is to research the evolution of people’s attitudes to the same question.Based on a great deal of empirical observations from computer simulations,all the rules can be classified into 20 groups.We highlight the fact that the phenomenon shown by some rules belonging to the same group will be altered within several steps by other rules in different groups.It is truly amazing that,compared with the last hundreds of presidential voting in America,the eras of important events in America’s history coincide with the simulation results obtained by our model.     

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

Abstract We prove that there are non-recursive r.e. sets A and C with A < _T C such that for every set . Both authors are supported by “863” and the National Science Foundation of China     

关于一些概率统计理论的一点认识

近来,林群从哲学的角度用公式相对真理/绝对真理=0.9阐述了微积分的内涵,并探究了计算数学、概率统计等学科领域乃至日常生活现象也同样蕴藏着该哲学公式.基于林群等在《概率论初步设想》中对大数定律和中心极限定理等概率统计学理论的哲学内涵分析,用一些数值算例展示概率统计学中这些常用理论所蕴含的这一哲学公式.     

关于特征值问题有限元方法研究的一个说法

受林群的微积分哲学公式((相对真理)/(绝对真理)=0.9)的启示,总结了近些年来关于特征值问题有限元方法的研究,并发现其背后同样隐藏着该哲学公式,换句话说,所追求的是特征值问题的有限元数值解和真解的零距离,其实就是追求真解的过程,要经多道(即0.9,0.99,0.999,…),再将比例,即(数值解)/(真解),提到1.     

Weighted logics for artificial intelligence – an introductory discussion

Before presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas.