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Compactness theorems of fuzzy semantics

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Chinese Science Bulletin 2000年第2期45卷 120-125页

作者： WANG Guojun Institute of Mathematics, shaanxi normal university, xi’an/710062. {2. Institute of Mathematics Shaanxi Nornial University Xi’an China

The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.

关键词： fuzzy semantics compactness loglc compactness inductive set point compactness Lukasiewicz semantics.

The connectedness of H(λ) unit interval and H(λ) real line

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Chinese Science Bulletin 1997年第23期42卷 2016-2017页

作者： LI ShenggangDepartment of Mathematics, shaanxi normal university, xi’an 710062. china Department of Mathematics Shaanxi Normal University Xi’an China

JUST like in classical mathematics, fuzzy unit interval I(L) and fuzzy real line R(L), thebasic and important research objects of fuzzy mathematics, also interest a good few *** 1992. Wang and Xu, by refining the topology of I(L), defined a new fuzzy unit in-terval——H(λ) unit interval I(L), and established the Stone-Cech compactification theoryfor weakly induced L-fuzzy topological spaces. In 1993, Zhang and Liu introduced the con-cept of weak inducification of L-fuzzy topological space, and in this way, I(L) is exactly

关键词： real line The connectedness of H unit interval and H line

Quasi-formal deductive system for fuzzy propositional calculus

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Chinese Science Bulletin 1997年第14期42卷 1154-1157页

作者： WANG GuojunInstitute of Mathematics, shaanxi normal university, xi’an 710062. china Institute of Mathematics Shaanxi Normal University Xi’ an China

ELKAN’s report 'The paradoxical success of fuzzy logic' at the 11th IA Annual Conferenceof America in July, 1993 caused quite a great stir in the research field of IA as well as fuzzysystems, fifteen scholars published papers thereupon to refute it and finally Elkan answeredthem with his paper 'The paradoxical controversy over fuzzy logic'. An exclusive analysiscan be found in Prof. Wu Wangming’s paper. It seems from this event that fuzzy proposi-

关键词： ΣR-tautology α-mod us ponens α-hypothetical syllogism quasi-formal deductive system.

Finite automata based on quantum logic and monadic second-order quantum logic

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Science china(Information Sciences) 2010年第1期53卷 101-114页

作者： LI YongMing College of Computer Science, shaanxi normal university, xi’an 710062. china 1. College of Computer Science Shaanxi Normal University Xi’an 710062 China

We introduce monadic second-order quantum logic and prove that the behaviors of finite automata based on quantum logic are precisely the quantum languages definable with sentences of our monadic secondorder quantum logic. This generalizes Büchi’s and Elgot’s fundamental theorems to quantum logic setting. We also consider first-order quantum logic and show that star-free quantum languages and aperiodic quantum languages introduced here coincide with the first-order quantum definable ones. This generalizes Schützenberger’s fundamental theorems to quantum logic setting. The determinazation of finite automata based on quantum logic is studied by introducing the generalized subset construction method. Then the Kleene theorem in the frame of quantum logic is presented here.

关键词： quantum logic finite automaton monadic second quantum logic quantum language quantum computation Kleene theorem

Implicational lattices and generalization of Stone's representation theorem

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Chinese Science Bulletin 1998年第12期43卷 997-1000页

作者： WANG Guojun Institute of Mathematics, shaanxi normal university, xi’an 710062. china Institute of Mathematics Shaanxi Normal University Xi’an China

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone’s representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.

关键词： Stone’s representation theorem R 0_semantic Lindenbaum algebra implicational lattice fuzzy implicational space representation theorem of regular implicational lattices.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. Department of Mathematics, Sichuan university, Chengdu 610064, china 2. Department of Mathematics,{2., xi’an 710062. china Department of Mathematics Sichuan University Chengdu China Department of Mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

Maximal contractions in Boolean algebras

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Science china(Information Sciences) 2012年第9期55卷 2044-2055页

作者： SHI Huixian & WANG GuoJun Institute of Mathematics,shaanxi normal {2.,xi’an 710062.china 1. Institute of Mathematics Shaanxi Normal University Xi’an 710062 China

In the present paper,the concepts of deductive element and maximal contraction are introduced in Boolean algebras,and corresponding theories of consistency and maximal contractions are *** algorithm principle is proposed to compute all maximal contractions for a consistent set with respect to its refutation in Boolean *** is pointed out that the quotient algebra of the first-order language with respect to its provable equivalence relation constitutes a Boolean algebra,and hence the computation of R-contractions for closed formulas in first-order languages can be converted into the one in Boolean algebras proposed in this ***,the concept of basic element is introduced in Boolean algebras,which contributes to the definitions of clause and Horn clause transplanted from logic to a special type of Boolean algebras generated by basic *** is also pointed out that the computation of R-contractions for clauses in the classical propositional logic can be converted into the one in Boolean algebras generated by basic elements proposed in this paper.

关键词： deductive element consistency maximal contraction minimal subtraction basic element clause

Antichains and their application for enumerating ternary logic functions

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Chinese Science Bulletin 1997年第1期42卷 83-84页

作者： WANG GuojunDepartment of Mathematics, shaanxi normal university, xi’an 710062. china Department of Mathematics Shaanxi Normal University Xi’an China

MUKAIDONO proposed and systematically investigated the theory of regular ternary logic functions that meets the need of uncertain inferences. The enumeration of ternary logic functions is very complicated and several results have been obtained only in the case where the number of variables is less than 7. In this letter we offer a new possible way to solve the prob-

关键词： Antichains and their application for enumerating ternary logic functions

The nonlinear standing wave inside the space of liquid

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Science china(Physics,Mechanics & Astronomy) 2010年第3期53卷 496-503页

作者： WANG ChengHui & LIN ShuYu Institute of Applied Acoustics, shaanxi normal university, xi’an 710062. china 1. Institute of Applied Acoustics Shaanxi Normal University Xi’an 710062 China

Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.

关键词： nonlinear acoustic wave equation nonlinear standing wave perturbation method fundamental wave second harmonic