部分二值逻辑中Sheffer函数的构造与判定算法

在深入研究部分二值逻辑中Sheffer函数的基础上,根据部分二值逻辑中准完备集的最小覆盖,提出了一种高效地构造部分二值逻辑中Sheffer函数的算法,此算法能够构造出部分二值逻辑中的全部Sheffer函数,在构造算法的基础上,进一步提出了一种部分二值逻辑中Sheffer函数的判定算法,此算法和传统判定算法相比,避免了繁琐的计算,可以说是一种较简单的判定算法。     

Three-valued completion for abductive logic programs

In this paper, we propose a three-valued completion semantics for abductive logic programs, which solves some problems associated with the Console et al. two-valued completion semantics. The semantics is a generalization of Kunen's completion semantics for general logic programs, which is known to correspond very well to a class of effective proof procedures for general logic programs. Secondly, we propose a proof procedure for abductive logic programs, which is a generalization of a proof procedure for general logic programs based on constructive negation. This proof procedure is sound and complete with respect to the proposed semantics. By generalizing a number of results on general logic programs to the class of abductive logic programs, we present further evidence for the idea that limited forms of abduction can be added quite naturally to general logic programs.     

二值命题逻辑中基于信息限制的随机真度

以随机真度为基础,提出了二值命题逻辑中公式的在有限信息Γ限制下的随机真度概念。以此为基础定义了公式的Γ-限制随机相似度和Γ-限制随机伪距离,得到了在有限信息Γ限制下公式到理论结论集的Γ-限制随机伪距离的Γ-限制随机真度表示式,为二值命题逻辑中基于有限信息限制的近似推理的随机化研究提供数值化工具。     

A multiple valued logic: a tutorial and appreciation

This tutorial places the developments and potential of multiple-valued signals and logic in the relevant context of binary and two-valued signals. It covers: the role of multivalued logic (MVL) in the binary world; multivalued representation; binary-related radices; multivalued functions; storage techniques in MVL; and implementation issues. An overview of applications is included     

Borel型概率计量逻辑

视全体赋值之集为通常乘积拓扑空间,利用该空间上的Borel概率测度在二值命题逻辑中引入了公式的概率真度概念.该方法既克服了计量逻辑学要求赋值集上的概率测度必须为均匀概率测度的无穷可数乘积的局限,又弥补了概率逻辑学只讲局部而缺乏整体性的不足;证明了计量逻辑学中公式的真度、随机真度以及概率逻辑学中公式的概率等概念都可作为本文提出的概率真度的特例而纳入到统一的框架中,从而实现了计量逻辑学与概率逻辑学的融合与统一;证明了逻辑闭理论与赋值空间中的拓扑闭集是一一对应的以及概率真度函数与赋值空间上的Borel概率测度是一样多的等若干结论;本文的第4节给出了公式的概率真度的公理化定义,证明了公式集上满足Kolmogorov公理的任一[0,1]值函数均可由赋值空间上的某Borel概率测度按本文的方法所表出,从而建立了二值命题逻辑框架下的概率计量逻辑的理论体系.     

Borel probabilistic and quantitative logic

The present paper introduces the notion of the probabilistic truth degree of a formula by means of Borel probability measures on the set of all valuations,endowed with the usual product topology,in classical two-valued propositional logic.This approach not only overcomes the limitations of quantitative logic,which require the probability measures on the set of all valuations to be the countably infinite product of uniform probability measures,but also remedies the drawback that probability logic behaves onl...     

二值命题逻辑中基于条件真度的近似推理

以公式真度为基础,给出了二值命题逻辑中基于条件真度的逻辑度量的真度表示式,提出了两类在信息Г下的误差不大于ε结论模式,证明了两类结论模式的等价性,并讨论了基于条件真度和真度的近似推理及其关系问题。     

Theory of truth degrees of formulas in (L)ukasiewicz n-valued propositional logic and a limit theorem

The concept of truth degrees of formulas in (L)ukasiewicz n-valued proposi tional logic Ln is proposed. A limit theorem is obtained, which says that the truth function (T)n induced by truth degrees converges to the integrated truth function (T) when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued (L)ukasiewicz logic and the continuous valued (L)ukasiewicz logic. Moreover, the results obrained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.     

Theory of （n） truth degrees of formulas in modal logic and a consistency theorem

The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic. Supported by the National Natural Science Foundation of China (Grant Nos. 10331010 and 10771129), and the Foundation of 211 Construction of Shaanxi Normal University     

二值命题逻辑理论的结论类型和分类

以公式真度为基础,研究了二值命题逻辑系统中有限理论逻辑推出的结论类型和分别基于公式真度以及逻辑等价的分类问题,给出了分类定理以及同一理论结论的相似度的一个下界。     

二值命题逻辑系统的T-真度理论（I）

在二值命题逻辑系统中引入了公式的T-真度概念,并讨论其逻辑运算性质。以此为基础定义了公式的T-相似度和T-伪距离,得到了公式到有限理论结论集的T-伪距离的T-真度表示式,为研究二值命题逻辑系统基于T-真度的近似推理问题提供数值化工具。     

On the power of fuzzy logic

In this article we address the issues brought up by Elkan in his article, “The paradoxical success of fuzzy logic,” [IEEE Expert, 3–8 (1994)]. Elkan's work has caused concern since it purportedly reveals a Fuzzy Logic weakness regarding its theoretical foundations. A further investigation of Elkan's theorem (“Theorem 1”) revealed that its conclusion is not correct. After indicating the points where we disagree with Elkan, we reformulate Theorem 1, calling this new version “Theorem 2.” Theorems 1 and 2 have the same hypotheses but different conclusions. According to Theorem 2 there is a region of points that do hold the equivalence in the hypotheses of Theorem 1. In other words, one does not need to change the definition of logical equivalence in Theorem 1 in order to prove that Fuzzy Logic does not collapse to a two-valued logic. In a further analysis of Theorem 2 we show that Elkan's work does not affect the power of Fuzzy Logic to model vagueness. © 1996 John Wiley & Sons, Inc.     

Built-in test for folded programmable logic arrays

Implementing a function using a programmable logic array (PLA) can often be very expensive in terms of area. Folding rows and/or columns of a PLA usually leads to a reduction in area. In this paper the problem of fault detection in folded PLAs is considered. A new fault, the ‘cutpoint’ fault, is described and universal test sets for the detection of this fault are presented. Modifications to existing built-in universally testable design techniques for nonfolded PLAs are presented; the new designs are now applicable to folded PLAs.     

系统L中τ(A→X)≥α型逻辑不等式的解问题

二值命题逻辑L中τ(A→X)≥α型基于真度的逻辑不等式在二值命题逻辑系统L的近似推理研究中有着重要应用。通过F(Sn)中公式是逻辑不等式τ(A→X)≥α解的几个充要条件,给出了该逻辑不等式的解集表示及其按真度相等关系和逻辑等价关系的分类定理,得到了等价类的结构表示和等价类个数结论,为基于真度的逻辑不等式问题的进一步研究和应用提供结构性方法。     

Methods of Continuous Logic in Control

Continuous logic, its problems, and methods were outlined, and its basic operations were defined. The algebra of continuous logic was described, and its main functions of one, two, and three variables were listed. The laws of this logic were presented and contrasted with the laws of the discrete two-valued logic. Described were the problems of listing all continuous-logic functions of a given number of variables and representing them in a standard form. The difference between these forms and their counterparts in the two-valued logic was shown. Minimization procedures for the continuous-logic functions and their decomposition into functions of a smaller number of variables were described. The distinctions of these procedures from their counterparts in the two-valued logic were noted. The problems of analysis and synthesis of the continuous-logic functions were formulated, and methods for their solution were presented. The problem of synthesis was shown not to be necessarily solvable. The fundamentals of the continuous-logic differential and integral calculuses were presented. Any continuous-logic function was shown to have no-derivative points. The problem of completeness was described for the continuous logic together with the existing results and their distinctions from the discrete case. Numerous applications of the continuous logic to mathematics, engineering, economics, social sciences, and so on were described, and its perspectives were estimated.     

Compatibility relation algorithm for the folding of programmable logic arrays

The basic principles of an algorithm for the folding of programmable logic arrays (PLAs) are presented in this paper. The algorithm is valid for both column and row folding, although it has been described considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), is then derived from the compatibility matrix. The algorithm presented in this paper is based on the FCM concept and the folding theorem, which states that the existence of an n x m FCM is both necessary and sufficient to fold 2m columns of an M-column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the reordering of the rows are readily determined. It has been conjectured that the algorithm produces the maximum folding of the PLA in all cases.     

Countering the loss of extended vigilance in supervisory control using a fuzzy logic model

When an operator first detects unusual and/or infrequent or irregular signals in a system, the operator does not need to take any action, but must increase his/her level of attention and be alert for any more serious signals that may confirm a problem with the system. This is referred to as extended vigilance. The purpose of this study was to construct a fuzzy vigilance-measuring model for countering the loss of extended vigilance. The model extends two-valued logic (“Yes” or “No”) to multi-valued logic through fuzzy sets. Then a fuzzy logic alarm was developed by the model for combating the extended vigilance decrement. The first experiment compared the effect of the fuzzy measuring model with signal detection theory (SDT) and discussed the relationship between preliminary and extended vigilance for a simulated feed-water monitoring system. The results indicated that the sensitivity of the fuzzy vigilance-measuring model is better than index d′ and β, and that the preliminary vigilance significantly influences the extended vigilance. The second experiment verified the effect of the fuzzy logic alarm. The results indicated that the effect of the fuzzy logic alarm for combating the extended vigilance decrement is significant. When the preliminary vigilance is poor, an appropriate alarm will improve the extended vigilance. However, if the preliminary vigilance is very poor, the improvement of the extended vigilance will be limited.Relevance to industry: The extended vigilance is a new and important issue in human performance problems in industry, particularly in such areas as air-traffic control, industrial inspection and power plant monitor. The measuring model of vigilance could be applied to develop an alarm for promoting supervisory performance of human and human–machine detectors.     

二值命题逻辑中Γ限制蕴涵度量与近似推理

基于某信息限制下若A则B的推理思想,以真度为基础,在二值命题逻辑系统中引入有限信息限制下的公式蕴涵度概念,由此定义了信息限制蕴涵度量,并通过信息限制蕴涵度量的真度表示式,给出一系列与有限理论结论集相关的限制蕴涵度量不等式,对二值命题逻辑中基于信息限制蕴涵度量的近似推理问题进行讨论。     

扩展Toffoli门及其在多输出电路设计中的应用

用量子计算电路实现布尔逻辑运算是发展量子计算的一个重要目标。提出了量子扩展Toffoli门,及其在实现多输出逻辑电路中的转换算法。该算法将传统PLA文件的SOP积项转换到实现等价逻辑功能的量子Toffoli积项,能够用量子扩展Toffoli门实现。通过MCNC基准电路的测试结果表明,与经典PLA描述相比,用扩展Toffoli门能够更有效地描述多输出逻辑函数。     

Logical-Probabilistic Calculus: A Tool for Studying the Reliability and Safety of Structurally Complex Systems

The concept of the probabilistic logic is briefly described as an extension of inductive logic. A clear distinction is made between the probabilistic logic and logical-probabilistic calculus—the branch of mathematics that defines the rules of computation and operation with two-valued (true and false) statements. The logical-probabilistic calculus is based on the algebra of logic and rules of substitution of logical arguments in functions of the algebra of logic by their truth probabilities, and logical operations by arithmetical operations.