(n+2)-角的平移

以三角范畴的八面体公理为基础,研究了三角范畴的(n+2)-角的平移性质。当三角范畴T存在一个(n+2)-角时,利用数学归纳法证明了T的(n+2)-角平移后还是(n+2)-角。     

Suzumura模糊条件满足程度的研究

在Georgescu定义的模糊选择函数下，将Suzumura提出的显示偏好第一公理FARP，显示偏好第二公理SEARP和基本三元非循环BTA，以及Sugden提出的最小一致性条件MC推广到模糊选择函数中，给出它们的程度描述，并讨论它们之间的关系及它们与弱显示偏好公理程度WAFRP（C），弱一致性公理程度WFCA（C），Fα2（C）及Fβ2^＋（C）之间的关系．     

Unitarity as Preservation of Entropy and Entanglement in Quantum Systems

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite quantum systems. ⁶ We would also like to dedicate this work to the memory of Asher Peres, whose contributions and sharp comments guided the first steps of the present article.     

How to make sense of the common prior assumption under incomplete information

Recent contributions have questioned the meaningfulness of the Common Prior Assumption (CPA) in situations of incomplete information. We characterize the CPA in terms of the primitives (individuals' belief hierarchies) without reference to an ex ante stage. The key is to rule out “agreeing to disagree” about any aspect of beliefs. Our results also yield a generalization of single-person Bayesian updating to situations without perfect recall. The entire analysis is carried out locally at the “true state”, using beliefs only, rather than beliefs-plus-knowledge. We discuss the role of truth assumptions on beliefs for a satisfactory notion of the CPA, and point out an important conceptual discontinuity between the case of two and many individuals.     

The axiom of choice and the law of excluded middle in weak set theories

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于主动数据库属性依赖及公理系统的研究

在主动数据库的理论与应用研究中，更新传播算法的应用，保证了系统在属性依赖方面的相容性。本文基于不变式方式和PATH路径公理系统，给出了一种更新传播算法，对该算法的正确性、可终止性进行了论证，并进行了时间复杂度分析。     

Lifting elementary embeddings <Emphasis Type="Italic">j</Emphasis>: <Emphasis Type="Italic">V</Emphasis><Subscript>λ</Subscript> → <Emphasis Type="Italic">V</Emphasis><Subscript>λ</Subscript>

We describe a fairly general procedure for preserving I₃ embeddings j: V _λ → V _λ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I₃ embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency was established assuming an I₁ embedding.      

ZY3代数的一个公理系统

本文指出ZY3代数的原公理系统是不独立的,并给出ZY3代数的一个新的公理系统。     

关于BCK／BCI－代数的几个等价公理系

分别给出ＢＣＫ－代数，蕴涵ＢＣＫ－代数，ＢＣＩ－代数及蕴涵ＢＣＩ－代数的一个等价公理系，说明了蕴涵ＢＣＩ－代数是蕴涵ＢＣＫ－代数的自然推广，亦说明了蕴涵性是“双Ｂ”代数的“固有属性”．     

关于拓扑空间中的累次极限

在G肖盖著的《拓扑学》一书中有如下一个命题: 令(a_(m,n))是一个由N×N到T_2空间的映射,如果,则。在本文中,举出一个反例说明上述命题不能成立,并得到一些修正的结论:令(a_(m,n))是由N×N到拓扑空间X的映射,且ⅰ)若X是T_3空间,则; ⅱ)若X是T_2空间,则当且仅当是X的紧子集。