A semantically complete extension sequence of the system (?)

In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the prepositional calculus formal system (?)*. The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions {(?)_n~*} of the system ? is proposed, and the completeness of (?)_n~* is proved.     

BL*系统的一种扩张及相关性质

对BR₀代数,Boole 代数以及BL*系统,命题演算形式系统L进行了研究。首先讨论了BR₀代数与Boole 代数间的相互关系,随后在BL*系统中分别添加公理模式(A →B) →¬A ∨ B或(A →(B → C)) →(A ∧ B → C)得到BL*系统的两种扩张,并证明了BL*系统的这两种扩张与命题演算形式系统L之间是等价的。     

A semantically complete extension sequence of the system $$\mathcal{L}^* $$

In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the propositional calculus formal system . The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions { } of the system is proposed, and the completeness of is proved.     

The completeness and applications of the formal system L

Since the formal deductive system L\{\}*was built up in 1997, it has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system L\{\}* is still an open problem. In this paper, the properties and structure of R0 algebras are further studied, and it is shown that every tautology on the R0 interval [0,1] is also a tautology on any R0 algebra. Furthermore, based on the particular structure of L\{\}*_Lindenbaum algebra, the completeness and strong completeness of the system L\{\}* are proved. Some applications of the system L\{\}* in fuzzy reasoning are also discussed, and the obtained results and examples show that the system L\{\}* is suprior to some other important fuzzy logic systems.     

A fuzzy logic system based on Schweizer-Sklar t-norm

In recent years, the basic research of fuzzy logic and fuzzy reasoning is growing ac- tively day by day, such as the basic logic system BL proposed by Hajek[1]; fuzzy logic system MTL proposed by Esteva and Godo[2]; fuzzy reasoning, implication operators …     

F-SHIQ公理体系及其OWL扩展

随着计算机和Internet的快速发展,语义网和描述逻辑在人工智能等领域扮演着越来越重要的角色。但在日常生活中,越来越多不确定的、不完整的知识需要解决,而现存的OWL只能表述确定的完整的概念和关系。为了能够表示和推理模糊知识,给出了一个基于描述逻辑SHIQ的全新的模糊描述逻辑公理体系——F-SHIQ公理体系,并以此公理体系为基础,扩展了OWL本体语言,能够描述和推理模糊知识。该文首先给出了系统详细的定义、公理、定理以及定理的证明;然后详述了如何用FSRL,即基于F-SHIQ的OWL扩展,来表示和推理模糊信息;最后通过一个例子来检验扩展语言的应用效果。     

Gdel区间值逻辑系统的广义拟重言式

吴洪博博士将王国俊教授在R0逻辑系统中的广义重言式理论推广到Gdel逻辑系统中,通过定义两个同构映射,得到其逻辑系统F(S)的一个分划。将这一理论推广到区间值模糊命题逻辑系统中,定义了两个新的区间同构映射,最终得到区间值逻辑系统F(S)的一个分划。     

可拓信息-知识-智能形式化体系研究

利用可拓论和可拓方法，把信息、知识和智能统一在一个形式化体系中，用可拓推理和可拓变换，去建立生成策略的推理规则，把可拓集合和关联函数作为策略生成和策略评价的定量化工具，探讨建立“可拓信息-知识-智能形式化体系”．给出了建立该体系的框架和主要功能模块．这一研究为利用计算机辅助解决矛盾问题提供可行的工具，为提高计算机的智能化水平创造基础条件．     

逻辑系统L*和BL*的广义演绎定理的逆定理

利用形式推演方法，给出逻辑系统L*和BL*的广义演绎定理逆定理的证明，并利用系统BL*的完备性定理及广义演绎定理证明系统BL*的强可靠性定理。     

The completeness and applications of the formal system B

Since the formal deductive system (?) was built up in 1997, it has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system (?) is still an open problem. In this paper, the properties and structure of R0 algebras are further studied, and it is shown that every tautology on the R0 interval [0,1] is also a tautology on any R0 algebra. Furthermore, based on the particular structure of (?) -Lindenbaum algebra, the completeness and strong completeness of the system (?) are proved. Some applications of the system (?) in fuzzy reasoning are also discussed, and the obtained results and examples show that the system (?) is suprior to some other important fuzzy logic systems.     

命题模糊逻辑系统中有限理论的弱相容度

推广了命题模糊逻辑系统中有限理论相容性的概念。以理论Г是否同时推出命题A和命题┐A为基准点引进了有限理论弱相容度的新概念,讨论了其性质,并给出了判定它大小的一系列准则。     

命题演算形式系统在Isabelle／HOL中的形式化

本文针对命题演算形式系统,在机器辅助定理证明系统Isabelle／HOL中为其建立逻辑模型,并分别形式化验证了PC和ND的主要性质,以及完备性定理的证明。通过对PC和ND的分析和验证表明,采用机器辅助定理证明系统,对以数理逻辑为平台的各种形式系统进行严格的分析和证明是可行的。     

四值非链格值命题逻辑系统L4P(X)的语义归结方法*

为了提高归结方法处理带有不可比较性信息的能力,给出了四值格值命题逻辑系统上的语义归结原理,并证明了其可靠性和完备性,其上归结原理的研究为归结算法的实现提供了理论基础,从而为处理含有不可比真值的格值逻辑系统在智能推理系统中的实际应用提供了有力的支持。     

A three-dimensional probabilistic fuzzy control system for network queue management

A novel probabilistic fuzzy control system is proposed to treat the congestion avoidance problem in transmission control protocol （TCP） networks. Studies on traffic measurement of TCP networks have shown that the packet traffic exhibits long range dependent properties called self-similarity, which degrades the network performance greatly. The probabilistic fuzzy control （PFC） system is used to handle the complex stochastic features of self-similar traffic and the modeling uncertainties in the network system. A three-dimensional （3-D） membership function （MF） is embedded in the PFC to express and describe the stochastic feature of network traffic. The 3-D MF has extended the traditional fuzzy planar mapping and further provides a spatial mapping among ＂fuzziness-randomness-state＂. The additional stochastic expression of 3-D MF provides the PFC an additional freedom to handle the stochastic features of self-similar traffic. Simulation experiments show that the proposed control method achieves superior performance compared to traditional control schemes in a stochastic environment.     

A ‘Natural Logic’ inference system using the Lambek calculus

This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem (1997), Sánchez (1991) and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek-based system we propose extends the system by Fyodorov et~al. (2003), which is based on the Ajdukiewicz/Bar-Hillel (AB) calculus Bar Hillel, (1964). This enables the system to deal with new kinds of inferences, involving relative clauses, non-constituent coordination, and meaning postulates that involve complex expressions. Basing the system on the Lambek calculus leads to problems with non-normalized proof terms, which are treated by using normalization axioms.     

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.     

A dynamic safety system based on sensor fusion

Machines in industry, including industrial robots, have in many cases dramatically reduced the man-made work and improved the work environment. New machines introduce, however, new risk factors. Traditionally machines are safeguarded by means that more or less rigidly separates the machines from the personnel. This works well in many traditional areas, i.e., where industrial robots are involved. There is however a risk that the safety system limits the valuable flexibility of the robot, which can be considered as a quality that tends to become even more valuable in the progress of programming possibilities and sensor technology. This article shows an example how a safety system can be designed to achieve increased flexibility in co-operation between human and production safety strategy. The proposed safety system is totally based on sensor information that monitors the working area, calculate the safety level and improve the system dynamically, e.g., reduce the robot capability in conjunction to the system safety level. The safety system gain information from the sensors and calculates a risk level which controls the robot speed, i.e., the speed is reduced to achieve a sufficiently low risk level. The sensor data is combined with fuzzy-based sensor fusion and fuzzy rules. The safety system is based on sensor information, hence it automatically adjusts to changes in the guarded area as long as the functionality of the sensors is maintained. Finally, we present a system implementation in an industrial robot application.     

Completeness of the Accumulation Calculus

The accumulation calculs(AC for short)is an interval based temporal logic to specify and reason about hybrid real-time systems.This paper presents a formal proof system for AC,and proves that the system is complete relative to that of Interval Temporal Logic(ITL for short)on real domain.     

A neuro-fuzzy-sliding mode controller using nonlinear sliding surface applied to the coupled tanks system

The aim of this paper is to develop a neuro-fuzzy-sliding mode controller （NFSMC） with a nonlinear sliding surface for a coupled tank system. The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation. A first-order nonlinear sliding surface is presented, on which the developed sliding mode controller （SMC） is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in SMC, a fixed boundary layer around the switch surface is used. Within the boundary layer, where the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to drive the system states into the boundary layer. Moreover, to compute the equivalent controller, a feed-forward neural network （NN） is used. The weights of the net are updated such that the corrective control term of the NFSMC goes to zero. Then, this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain. Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.