模态逻辑的集合论语义与互模拟不变性

含有命题变元的非良基集合能够被看作解释模态语言的模型。任给非良基集合a,一个命题变元p在a上真当且仅当p属于a。命题联结词的解释与古典命题逻辑相同。一个公式3A在a上真当且仅当存在集合b属于a,使得A在b上是真的。在一个集合中,属于关系被看作可及关系。在这种思想下,我们可以定义从模态语言到一阶集合论语言的标准翻译。对任意模态公式A和集合变元x,可以递归定义一阶集合论语言的公式ST(A,x)。在关系语义学下,van Benthem刻画定理是说,在带有唯一的二元关系符号R的一阶语言中,任何一阶公式等价于某个模态公式的标准翻译当且仅当这个一阶公式在互模拟下保持不变。因此,模态语言是该一阶关系语言的互模拟不变片段。同样,我们可以在集合上定义互模拟关系,证明van Benthem刻画定理对于集合论语义和集合上的互模拟不变片段成立,即模态语言是一阶集合论语言的集合互模拟不变片段。     

图的典范装饰与方程组的典范解

在集合论ZFC-＋AFA中,每个图有唯一装饰,每个方程组有唯一解。但是,在集合论ZFC-4-SAFA和ZFC-4-FAFA中,每个图并非只有一个装饰,每个方程组并非只有一个解。笔者通过定义互模拟坍塌概念,在可达点图的典范装饰概念的基础上导出方程组的典范解,提出并证明：在上述三种具体的非良基集合论中,每个可达点图都有唯一的典范装饰,每个方程组有唯一的典范解。     

论模态逻辑的集合论语义

引入非良基集合可以为模态逻辑提供一种新的语义学。这种语义是在集合上解释模态语言,使用集合中作为元素的集合之间的属于关系解释模态词,并在集合中采用命题变元作为本元,从而解释原子命题的真假。在这种新的语义下,从模型构造的角度看可以引入几种非标准的集合运算：不交并、生成子集合、p-态射、树展开等等,证明模态公式在这些运算下的保持或不变结果。利用这些结果还可以证明一些集合类不是模态可定义的。     

论基础公理与反基础公理

"循环并不可恶"。本文在此基础上讨论基础公理和反基础公理。首先指出基础公理原本就是一条有争议的公理;第二,说明基础公理的局限性;第三,详细论述反基础公理家族中的三个成员,并给出它们两两不相容的一个证明;第四,分析反基础公理导致集合论域在V=WF上不断扩张的方法,并指出这种扩张的方法与数系扩张的方法相同;最后结论:良基集合理论(ZFC)与非良基集合理论(ZFC~-+AFA(或者ZFC和ZFC~-+FAFA或者ZFC和ZFC~-+SAFA))之间的关系类似于欧几里得几何学与非欧几何学之间的关系。     

幼儿在集合比较中运用数数的实验研究

本研究中运用了两个实验探讨数数干预和测查条件对儿童在集合比较中运用数数的影响。干预对3岁儿童(M=3：9)没有影响。在平均年龄为4岁4个月时．干预组儿童比控制组儿童更倾向于用数数比较集合．自然组儿童也比传统组更倾向于用数数。许多4岁儿童在无干预时不用数数可能是因为,1)不知数数比视觉性比较更有效,或2)他们在集合比较中的数数极易受测查情景因素的影响。儿童在集合比较中的数数运用与他们的数数水平密切关联。     

非良基集合的外延公理

近年来,由于非良基集合在人工智能、认知科学及哲学等领域都有很重要的应用,它的研究越来越受到人们的关注。判断两个对象的同一性是集合论中最基本的问题,然而,与良基集合不同的是,非良基集合难以找到其最基本的组成成分,这样通常的外延公理就无法判断两个非良基集合（例如x={x}和y={y}）相等。为了找到判断两个非良基集合相等的标准,我们必须强化通常的外延公理。利用Aczel四种非良基公理（AFA,SAFA,FAFA和BAFA）,我们推出了四种判断两个非良基集合相等的标准,并且举例说明对于给定的两个非良基集合,如何判断它们相等,从而解决“循环集合”相等的问题。此外,笔者进一步论证判断这四种非良基集合相等的标准是通常外延公理的扩张,而不是替代。为此,本文首先给出了集合和图的一些基本定义和结果;其次讨论了由四种非良基公理AFA,SAFA,FAFA和BAFA分别确定的四种集合全域A,S,F和B;最后,讨论了外延公理的扩张。     

3~5岁幼儿一位数大小比较的信息加工模式

主要探讨我国幼儿对数量大小比较的信息加工模式。实验1探讨幼儿对一位数大小比较的发展状况及其心理表征特点,被试为3岁、4岁与5岁幼儿各20人,要求被试对1-9两两进行大小比较,然后对不同年龄幼儿对比成绩进行比较与聚类分析。实验2进一步探讨幼儿对数字的语义编码情况及其与数的大小比较的关系,被试与实验1相同,要求被试对1-9每个数字作出大、中或小的编码,然后分析数字的语义编码成绩与大小比较成绩的关系。实验3采用因果设计,探讨幼儿关于数字的语义编码对他们关于数的大小判断的影响,被试为30名4岁幼儿,随机分成训练组与控制组,对训练组被试进行数字语义编码训练,然后比较两组被试大小比较的成绩。结果表明：(1)幼儿一位数大小比较直接受其对数的语义表征的影响;(2)随着年龄的增长,幼儿对数的表征逐步表现出离散聚类模式,相应地,对一位数大小比较的信息加工过程就表现为由无序的、随机的过程逐步发展成为层次编码比较的过程。     

方差分析的统计检验力和效果大小的常用方法比较

本文对用方差分析统计检验力和效果大小进行估计的几种不同方法作了简要的介绍和比较。     

分歧中的互补:皮亚杰和维果茨基发展心理学理论的比较研究

目前对皮亚杰和维果茨基发展心理学理论的比较研究多采用比较差异性和寻找相似点的方法,而该文试图在皮亚杰和维果茨基的心理学理论的分歧点中探寻两者的互补性：从儿童自我中心言语的理论分歧中看人类发展方向的互补性;从对发展过程本质的不同理解看互补性;从理解成人和同伴对儿童发展的影响中看互补性;从理解发展阶段普遍性的分歧看互补性：从心理调节观的分歧看互补性。     

《维果茨基全集》中文本解读

《维果茨基全集》中文本于2016年11月在我国出版面世,这是继20世纪80年代苏联《维果茨基文集》俄文版之后世界上最全的版本,它的出版是中国心理学界,乃至整个学术界、理论界值得庆贺的一件大事。本文拟从出版缘起、主要内容和学术价值三方面对《维果茨基全集》中文本进行解读,希望有助于国内学者和公众能比较全面和准确地了解维果茨基的学术思想,把握维果茨基理论和方法的精要,激发学界同仁对维果茨基思想的研究热情。     

The Graph Conception of Set

The non-well-founded set theories described by Aczel (1988) have received attention from category theorists and computer scientists, but have been largely ignored by philosophers. At the root of this neglect might lie the impression that these theories do not embody a conception of set, but are rather of mere technical interest. This paper attempts to dispel this impression. I present a conception of set which may be taken as lying behind a non-well-founded set theory. I argue that the axiom AFA is justified on the conception, which provides, contra Rieger (Mind 109:241–253, 2000), a rationale for restricting attention to the system based on this axiom. By making use of formal and informal considerations, I then make a case that most of the other axioms of this system are also justified on the conception. I conclude by commenting on the significance of the conception for the debate about the justification of the Axiom of Foundation.     

Weakly higher order cylindric algebras and finite axiomatization of the representables

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras. Supported by the Hungarian National Foundation for Scientific Research grant T73601.     

The Divine Fractal: 1st Order Extensional Theology

Philosophia - In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions....     

The Structure of Causal Sets

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets.     

Program Constructions that are Safe for Bisimulation

It has been known since the seventies that the formulas of modal logic are invariant for bisimulations between possible worlds models — while conversely, all bisimulation-invariant first-order formulas are modally definable. In this paper, we extend this semantic style of analysis from modal formulas to dynamic program operations. We show that the usual regular operations are safe for bisimulation, in the sense that the transition relations of their values respect any given bisimulation for their arguments. Our main result is a complete syntactic characterization of all first-order definable program operations that are safe for bisimulation. This is a semantic functional completeness result for programming, which may be contrasted with the more usual analysis in terms of computational power. The 'Safety Theorem' can be modulated in several ways. We conclude with a list of variants, extensions, and further developments.     

Mathematical foundations of consciousness

We employ the Zermelo–Fränkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo–Fränkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so-called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question.