SAD as a mathematical assistant—how should we go from here to there?

The System for Automated Deduction (SAD) is developed in the framework of the Evidence Algorithm research project and is intended for automated processing of mathematical texts. The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground reasoning where a particular theorem proving problem is simplified and decomposed; (c) the level of background deduction where exhaustive combinatorial inference search in classical first-order logic is applied to prove end subgoals.

We present an overview of SAD describing the ideas behind the project, the system's design, and the process of problem formalization in the fashion of SAD. We show that the choice of classical first-order logic as the background logic of SAD is not too restrictive. For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory. We illustrate our approach with a series of examples, in particular, with the classical problem .     

Mathematical modal logic: A view of its evolution

This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.     

视频教学中教师的眼神注视能否促进学习?

教师的眼神注视是在视频学习中重要但易被忽视的元素。以往理论存在两种对立的观点：其中准社会交往理论和社会代理理论支持教师的眼神注视促进学习; 而基于多媒体学习认知理论与认知负荷理论认为教师的眼神注视会阻碍学习效果。通过汇总以往实证研究得出如下结论：首先, 教师的眼神注视对学习效果具有小的促进效应, 即教师的眼神注视能够促进学习者的保持成绩(d_保持 = 0.41)和迁移成绩(d_迁移 = 0.39); 其次, 在主观体验上, 教师的眼神注视对准社会交往也具有小的促进效应(d_{准社会交往} = 0.35), 而教师的眼神注视对认知负荷影响十分微弱(d_认知负荷 = -0.02); 最后, 在对学习材料的注意加工上, 教师的眼神注视总体上影响比较微弱(d_注视时间 = 0.06, d_{首次注视时间} = -0.15)。未来研究需要对不同注视类型、先前知识经验、学习材料性质以及认知神经方法进一步探究。     

高校教师教学水平评价概化理论预算限制下最佳样本量估计

使用“高校教师教学水平评价问卷”,要求566名学生对19名教师进行评价,对收集到的数据作不同的概化设计,包括t×i、（s：t）×i、（s：t）×（i：v）和（s：t）×（i：v）×o四种设计。基于概化理论,结合预算限制,统一LaGrange乘法公式,自行推导不同设计的最佳样本量公式,联合估计的方差分量,计算出不同设计的最佳样本量。结果表明：（1）LaGrange乘法统一公式表现出较强的通用性,能够适用于预算限制下各种概化设计;（2）评价场合是影响高校教师教学水平评价一个相当重要的因素;（3）（s：t）×（i：v）×o是高校教师教学水平评价概化理论预算限制下最优概化设计;（4）高校教师教学水平评价概化理论预算限制下,每位教师最佳评价学生人数为20人,每个维度最佳评价题目数为3题。     

Mind and Matter: A Physicist's View

Physics explores a universe of wonderful order, expressed in terms of beautiful mathematical equations. Mathematics itself is understood to be the exploration of a realm of noetic reality. Science describes matter in terms of concepts with mind-like qualities. The psychosomatic nature of human persons is best understood in terms of a dual-aspect monism, in which matter and mind are complementary aspects of a unitary being. The new science of complexity theory, with its dualities of parts/whole and energy/information, offers modest resources for the speculative exploration of this idea. The intrinsic unpredictabilities present in nature afford the metaphysical opportunity to consider dissipative systems as exhibiting top–down causality.     

Individual characteristics and career exploration in adolescence

The effects of gender, age and school grade on several career exploration dimensions measured by the Career Exploration Survey were investigated. Subjects were high school students facing an imminent career decision. Regression analyses indicated that sex and grade-level were the most significant and prevailing individual characteristics related to the adolescents' career exploration behaviours, reactions and beliefs. Implications for career exploration interventions are discussed.     

Periodicity of response in operant extinction

The distribution of responses during experimental extinction trials for a group of 11 rats, trained in the Skinner-box, was examined. Our analysis supports an earlier suggestion that the extinction trial may be separated into respondent and silent periods. Response rates during respondent periods show relatively little decline throughout the extinction period investigated, whereas silent periods increase with positive acceleration. The traditional exponential function used to describe response rates during experimental extinction trials should therefore be regarded as a very rough approximation to the mathematical characteristics of the animal's behaviour. Its use as a basis for quantifying critical intervening variables, such as habit strength or behaviour potentiality, is consequently seriously challenged.     

An axiomatization of family resemblance

We invoke concepts from the theory of hypergraphs to give a measure of the closeness of family resemblance, and to make precise the idea of a composite likeness. It is shown that for any positive integer m, for any general term possessing any extent of family resemblance strictly greater than m, there is a taxonomical representation of the term whereby each subordinate taxon has an extent of family resemblance strictly greater than m.     

整合智慧量表的编制及信效度检验

基于智慧的德才一体理论,编制包含良好品德和聪明才智二因子的整合智慧量表,以方便取样抽取中国大陆892名青年,检验其信效度。总量表的Cronbach's α和组合信度分别为0.89和0.94。四周后重测信度为0.85。验证性因素分析发现,量表的结构效度良好,CFI=0.91,IFI=0.91,TLI=0.90,RMSEA=0.07,SRMR=0.08,也具有良好的聚合效度和区分效度。与自我评估智慧量表、三维智慧量表、开放性和心理幸福感的相关分别为0.79、0.36、0.32和0.46,与生活满意度的相关不显著(p>0.05)。这说明整合智慧量表具有良好的信效度,是测量中国青年智慧的有效工具。     

Confirming Mathematical Theories: an Ontologically Agnostic Stance

The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying this move are qualitatively worse in mathematics than they are in science. This revised version was published online in June 2006 with corrections to the Cover Date.     

教师的存在能否促进视频学习?

随着网络教学和视频学习的普及, 近期大量研究关注视频学习过程中教师角色的作用。真人教师对学习的作用存在不同的理论解释：准社会交往理论、社会存在理论和社会代理理论支持真人教师能够促进学习; 而多媒体学习认知理论、认知负荷理论等则认为教师的存在会阻碍视频学习。汇总以往实证研究发现：第一, 教师对视频学习效果有比较弱的促进效应, 这主要体现在保持测验(d = 0.23)和迁移测验(d = 0.1)中; 第二, 教师对视频学习主观体验的影响主要体现在学习感知(d = 0.49), 学习兴趣(d = 0.5)和学习满意度(d = 2.21)上, 显示中等及大的效应; 第三, 教师的存在会降低学习者对视频学习材料的注视时间(d = -2.02)。未来研究仍需要从真人教师呈现方式、学习者特征、学习材料特征以及测量方式等方面加以探讨。     

Adult Attachment and Exploration: Linking Attachment Style to Motivation and Perceptions of Support in Adult Exploration

Taking an attachment theory perspective, the present studies investigated partner-related motives for exploration and perceptions of romantic partners as persons who might provide support for exploration. We argue, from an attachment theory perspective, that more avoidant persons may use exploration as a way to distance themselves from their partners, whereas more anxious persons may use exploration as a means of getting closer to or depending on their partners. Attachment theory also suggests that more insecure individuals will tend to see their partners as providing less support and less effective support for exploration. Our research found support for both of these hypotheses. In this article we also investigate potential mediating models for linking attachment style to motives for exploration and perceptions of partner support.     

多级计分测验中基于残差统计量的被试拟合研究

本文提出一种多级计分项目下的个人拟合统计量R, 考察它在检测6种常见的异常作答模式(作弊、猜测、随机、粗心、创新作答、混合异常)下的表现, 并与标准化对数似然统计量l_zp进行比较。结果表明：(1) 在异常作答覆盖率较低并且异常作答类型为作弊和猜测时, R的检测率显著高于l_zp; (2) 随着测验长度和被试异常程度的增加, 两种统计量的检测率都会上升; (3) 在一些条件下, R与l_zp检测效果接近。实证数据分析进一步展示了R统计量的使用方法和过程, 结果也表明R统计量具有较好的应用前景。     

Cognitive–motivational antecedents of career decision-making processes in Portuguese high school students: A longitudinal study

In this study we propose an integrated framework of the antecedents of identity development and well/ill-being for high school students (N = 462) in the transition to higher education/job market. One study was conducted to investigate the effects of basic psychological need-satisfaction/frustration (as proposed within self-determination theory) and career decision-making self-efficacy (posited by social cognitive career theory) on the identity dimensions and experienced well/ill-being. Three longitudinal nested models were tested: a need-satisfaction/self-efficacy main effects model, an identity main effects model and a reciprocal main-effects model. The reciprocal effects between the variables were favored by the data. Basic need-satisfaction and career decision making self-efficacy positively predicted proactive exploration and commitment-making, while basic need-frustration predicted both diminished well-being and ill-being. Reciprocally, proactive exploration investments positively predicted whereas ruminative exploration negatively predicted, need-satisfaction and career decision-making self-efficacy. Implications for the design of career interventions are discussed and suggestions for future research proposed.     

有“新”同享：共有消费促进对不熟悉产品的选择*

共有消费是多位消费者共同参与并承担开销的一种常见的消费活动。本研究基于风险转移理论, 探究了消费情境(单独消费vs.共有消费)对不熟悉产品偏好的作用机理及边界条件。通过5个实验, 结果发现：相比于单独消费情境下的消费者, 在共有消费情境下的消费者更愿意尝试不熟悉的产品。原因在于共有消费情境会转移消费风险, 使得消费者对不熟悉产品的感知风险降低。但是该效应仅发生于产品风险较低的产品。同时, 当共有消费群体的关系较为疏远时, 该效应会消失甚至逆转。     

正念训练对冲动性不同要素的影响：基于双加工理论

正念是指对当下身心体验不带有评判地觉察。基于双加工理论,以正念为核心的训练对个体冲动性不同要素均具有明显干预效果。一方面,有助于降低因情感系统引发的冲动驱力：通过调整个体的奖赏评估与预期,缓和诱发冲动的压力与负性情绪反应,减弱自动化反应的联结和强度;另一方面,提升个体由认知控制系统调节的冲动控制力：增强个体的认知控制和行为抑制能力。由于冲动性驱动因素和控制因素二者加工时序的先后差异和作用方向对抗性特点,正念训练促进两类要素的积极交互影响,缩小冲动性“驱动”与“控制”力量之间的不平衡,为个体更好地回应自身反应与外界刺激提供了有利缓冲,是降低个体冲动性的有效干预手段。     

内群体偏爱与儿童基于贡献的分配公平性:心理理论的调节作用

本研究考察了贡献和内群体偏爱两种分配动机对儿童分配公平性的影响,并探讨了心理理论在其中的作用。通过比较63名6~8岁儿童在不同群体条件下对贡献不同的接受者的分配结果和分配策略的差异,结果发现：（1）在所有群体条件下,儿童都会分配给贡献多的接受者更多的资源,但当外群体成员贡献多且内群体成员贡献少时,儿童也会分配给贡献多的接受者相比于其他群体条件更少的资源,并更多的采用群体关系策略对这一行为作出解释;（2）心理理论能力越高的儿童分配给贡献多的接受者的资源数量受群体关系的影响越小,且使用贡献策略的频率越高,使用群体关系策略的频率越低。这些结果表明6~8岁儿童在资源分配过程中会优先考虑公平动机,且心理理论能力强的儿童更少表现出内群体偏爱。     

Abductive inference in defeasible reasoning: a model for research programmes

Abduction is regarded as the inference process that goes from observations to explanations within a more general context or theoretical framework. There are good characterizations of abduction of surprising observations in monotonic theories. Also, in normal logic programs there are a tight relation among SLDNF and the abduction of negative literals. However, a problem that faces abduction is the explanation of anomalous observations, i.e., observations that are contradictory with respect to the current theory. For this reason, in this work we will consider the problem of embedding abduction of surprising and anomalous observations in defeasible (nonmonotonic) theories. We discuss some issues arising the pragmatic acceptance of abductive inferences in defeasible theories, and how to accommodate anomalous observations and characterize all the possible outcomes that a defeasible theory may face when confronted with new evidence. We explore the use of partial structures approach as a semantic foundation for our system. Finally, we discuss an application of our system as a formal device for representing the methodology of scientific research programmes. In this representation, a programme is regarded as a defeasible theory that draws predictions. When confronted with surprising or anomalous observations, the programme protects itself by means of heuristic procedures, which are represented in our system as abductive inference procedures.     

How to be a structuralist all the way down

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down.