L*n系统中理论的相对发散度和相对相容度

利用公式的Σr-真度(文中称为相对真度)理论,在模糊命题逻辑系统(L*n)中提出了任意理论Γ相对于特定理论Γ0的相对发散度和ηΓ0-相容度概念.对于有限理论,给出了其相对于特定理论Γ0的δΓ0-相容度概念,并对两种相容度的性质作了初步探究,揭示了二者之间的内在联系.同时给出任意理论Γ相对于特定理论Γ0的相容、不相容及完全相容的定义及其等价刻画.     

系统Ln中公式相对于有限理论的Γ-绝对真度理论

将多值逻辑中的∑-α重言式理论与计量逻辑学中的真度理论相结合,在n值Lukasiewicz命题逻辑系统中引入了公式相对于有限理论Γ的Γ-绝对真度概念,讨论了它的若干性质.利用Γ-绝对真度定义了公式间的Γ-绝对相似度与伪距离,为进一步建立n值Lulcasiewicz命题逻辑系统相对于有限理论Γ的近似推理奠定了基础.     

系统L_n中公式相对于有限理论的Г-绝对真度理论

将多值逻辑中的∑-α重言式理论与计量逻辑学中的真度理论相结合,在n值Lukasiewicz命题逻辑系统中引入了公式相对于有限理论Γ的Γ-绝对真度概念,讨论了它的若干性质.利用Γ-绝对真度定义了公式间的Γ-绝对相似度与伪距离,为进一步建立n值Lukasiewicz命题逻辑系统相对于有限理论Γ的近似推理奠定了基础.     

逻辑系统中理论的下真度与相容度(Ⅰ)

引入模糊逻辑系统中理论的下真度与不相容度的新概念,简化理论相容度的定义,给出理论的下真度、发散度、不相容度与相容度之间的关系。     

二值命题逻辑中的三种Γ近似推理模式及其等价性

在二值命题逻辑中引入了公式的Γ蕴涵真度,证明了全体有限理论的蕴涵真度值在[0,1]中稠密.在Γ蕴涵真度的基础上,定义了公式间的Γ蕴涵相似度及伪距离.最后讨论了基于Γ蕴涵真度的三种近似推理模式,得出了这三种近似推理模式之间是等价的结论.     

有限Boole语义中基于前提信息的随机真度

本文研究了有限Boole语义中基于前提信息的随机化问题.利用赋值集的随机化方法,提出了公式的基于前提信息Γ的Γ-随机真度,得到了Γ-随机真度的MP规则,HS规则和交推理规则.通过引入公式间的Γ-随机相似度和Γ-伪距离,建立了Γ-随机逻辑度量空间,在有限Boole语义上推广了基于前提信息的近似推理理论.     

命题模糊逻辑系统Π和G(o)d中理论的相容度与下真度的计算公式(II)

讨论命题模糊逻辑系统Π和G(o)d中理论相容度与下真度的计算问题.引入逻辑公式的核、零核及理论的核的新概念,得到命题模糊逻辑系统Π和G(o)d中理论相容度与下真度的计算公式,给出理论不相容的新的充要条件.     

命题模糊逻辑系统П和God中理论的相容度与下真度的计算公式（Ⅱ）

讨论命题模糊逻辑系统П和God中理论相容度与下真度的计算问题。引入逻辑公式的核、零核及理论的核的新概念，得到命题模糊逻辑系统Ⅱ和God中理论相容度与下真度的计算公式，给出理论不相容的新的充要条件。     

经典命题逻辑中公式的Γ-随机真度与近似推理

利用概率空间的无穷乘积,在经典二值命题逻辑中引入了公式的Γ-随机真度概念以及公式间的Γ-相似度概念.进而导出了全体公式集上的一种伪距离,建立了逻辑度量空间.最后提出了基于Γ-随机真度的三种不同的近似推理模式,并且证明了这三种近似推理模式之间是相互等价的.     

系统(￡)*n的逻辑性质及其应用

证明了系统(￡)*n中的可满足性定理,紧致性定理和可判定性定理,完善了系统(￡)*n的理论体系,并将这些性质应用到计量逻辑学中,给出了∑Γ-真度和条件真度存在的充要条件.     

Banach空间中的广义Schauder基和广义A-proper映射的广义拓扑度

本文给出Banach空间中广义Schauder基的新概念及其几个性质定理,举出了具有广义Schauder基的不可分Banach空间实例。作为广义Schauder基的应用,还推广了A-proper映射的广义拓扑度和一些著名的不动点定理。     

Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations

We prove Girsanov-type theorems for Hilbert space-valued stochastic differential equations and apply them to a parameter estimation problem for linear infinite dimensional stochastic differential equations. In particular we construct the asymptotic statistical theory of the estimator, proving strong consistency and asymptotic normality.     

New fixed point theorems for <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript>-compact mappings in Banach spaces

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.     

Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布

利用势为3的均匀概率空间的无穷乘积在G■del三值命题逻辑中引入了公式的真度概念,给出了真度推理规则,证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑的近似推理理论奠定了基础．     

Periodic solutions for functional-differential equations of mixed type

In this paper we study the existence of ω-periodic solutions for some functional-differential equations of mixed type. Among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities. We use here the coincidence degree theory of Mawhin.     

Existence of non-trivial solution for superlinear system of integral equations and its applications

1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio...     

SOLUTIONS FOR SUPERLINEAR(n-1,1)CONJUGATE BOUNDARY VALUE PROBLEMS

1 IntroductionIn this paPer) we are concerned with positive and nontrivial solutions for superlinear (n -1, 1) conjugate boundary value problem:where f: [0, 1] x R1 - R1 is continuous.In case n = 2, (1) describes various phenomena, such as nonlinear diffusion generated -by nonlinear $ourcesl thermal ignition of gases, and concentration in chendcal or biologicalproblems, see, for examPle [1-5]. Also, [6] used the second order case in modeling the one-dimensional Dirichlet problem;In case f(x,…     

Topological model theory with an interior operator: Consistency properties and back — and forth arguments

The logicL(I) is introduced. Compactness and Löwenheim-Skolem theorems for topological models are proved. Several axiomatizations are given and proved to be complete. Interpolation- and preservation theorems are proved using consistency properties. A Back and Forth criterion for elementary equivalence is proved. Most of the results are extended (appropriately) to infinitary logic.     

Theory of truth degrees of propositions in two-valued logic

By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.