关于Erdos-Moser定理的研究

本文主要研究Erdos-Moser定理。在简单介绍了反推数学的一些基础知识后,首先研究了Erdos-Moser定理的证明论强度：存在一个可计算的二元二染色函数使得任何无穷∑20集合都不是该函数的传递集,同时存在一个可计算的二元二染色函数使得每一个该函数的无穷传递集都是超免疫的。其次,我们进一步考虑了稳定性Erdos—Moser定理,证明了在二阶算术子系统RCA0下稳定性Erdos-Moser定理是不可证的并且对每一个可计算的稳定性二色二阶函数,我们构造了一个Ф’可计算的无穷传递集。     

量词模态逻辑的代数语义学(Ⅳ,上)──关于含BARCAN公式的非正规模态系统情形

预备性引言。依照SaulA．Kripke内在[1]中的说法,一命题模态系统叫做正规的,如果它包含Feys的系统T（即VonWright的系统M,参看[2],[3]并在分离规则MP（modusponens）及N-规则下封闭。但是一般都把系统的正规性理解为包含系统K（即【4］中的T（C》并在MP及N一规则下封闭即可。我们知道K的唯一二条模态公理模式为（。）D（AHB）rp（DArpDB）如果没有这条公理模式,则KriPke语义无从谈起,亦即系统便没有BF．Chellas卜］中的所谓“标准模型”了。同样,如果不在规则MP下封闭则谈不上思维规律。这样,非正规模态系统便只能是N…     

过火的家规逼出了“花心女郎”

惠梅是父母近40岁才得到的独生女儿。其父母年轻时有过许多梦想,后来过得并不如意。父母便把希望寄托在女儿身上。为强迫刚读小学的女儿学这学那,他们给惠梅定下一条又一条的家规,不准这样,应该那样。惠梅倒也被逼着学了不少东西,功课也不错,她父母便眼巴巴地盼着女儿能到大都市去过上体面的生活。     

项目反应理论的分数分布的预测作用

1引言在心理和教育测量的实践过程中,测试者常常会从已实施过的测验项目里根据需要挑选一组项目重新组成新的测验。如果测试者事先能够通过一定的方法预测到关于这组测验分数的大致信息,这对编制不同要求的测验、检查教学效果以及评价学生能力有很大的帮助。在项目反应理论（IRT）中,预测分数的一般做法是通过测验特性函数来计算的（HambletomandSwaminathan,1985）。但是这样计算的结果只能知道在能力参数θ的某个水平上的分数．从本质上来说这是属于条件概率的点估计。为了了解在能力θ的整个范围里的测验分数的变化趋向,本文利用…     

"中国哲学","道术",还是可道术化的广义哲学?

将中国古代学术中的某一部分叫做"哲学",并按照冯友兰先生的主张,认为"科学的方法,即是哲学的方法"[1],然后循名责实地建构出一个"逻辑的、科学的"中国哲学,这条道路已将中国古学研究和使古学当代化的努力引入了困境.最近受到关注的"中国哲学的合法性危机"的讨论只是它的一种表现.这困境可比拟于用现代西医的方法来使中医"科学化"的情况.强迫实施"中西医结合"所导致的是中医思想源头的枯萎,被"废医存药"(其实"药"也在被现成化和胶囊化,或者被危险地"有效成分"化).于是,中医的本来面貌和它的当代活力就离我们越来越远了.     

回头是土

早年读鲁迅关于写作技巧的传授,有一条叫做——一直写下去,不要回头。那时年轻,有些不解。为什么不能回头呢?看看自己的脚印,歪斜了就校正,如果笔直,便一直走下去,有什么不好呢?存疑。很多年。有一天,忽然就懂了。原来,鲁迅在传授和不自信作斗争的经验。面向前方,坚定地走下去,任它成功或是失败,     

市场预测与类比推理

类比推理又叫做类推法,在市场预测中,类推法在以下几个方面得到广泛的应用.1、由一种商品类推另一种商品.如果已知A、B两种商品有许多相似之处,则可由A商品的市场销售规律     

每一个非零的可计算可枚举强有界图灵度都具有反成杯性质

可计算Lipschitz图灵归约（c1-归约）是指用函数被x→x＋c约束的图灵归约,其中c是常数;而ibT归约则通过限制用函数为恒等函数得到。我们通称c1-,ibT-归约为强有界图灵归约。我们证明：对于r=cl,ibT,在可计算可枚举r-度构成的偏序结构（Rr,≤）中,每一个非零的a都具有反成杯性质。为此,我们证明一个新结论：对于每一个不可计算的可计算可枚举集合A,都存在一个不可计算的可计算可枚举B,使得对所有满足A≤wtt C的可计算可枚举集合C都有B≤ibT C。结合关于可计算偏移的已知性质,我们便可得到上述主要定理。     

纵向汉明距离判别法：对潜在属性的发展追踪

研究通过在纵向诊断数据分析中引入计算简单、耗时少的汉明距离判别法(HDD),提出了纵向HDD (Long-HDD)。与HDD相比,Long-HDD额外使用汉明距离刻画个体在相邻时间点上对属性掌握的相依性,以利用前一时间点信息提高当前时间点的分类准确性。三个模拟研究的结果主要表明：在分析纵向诊断数据时,与参数化模型相比,Long-HDD的分类准确性几乎不受样本量影响,在样本量较小时表现更优;且其计算耗时更少,更有利于提供及时性诊断反馈。实证研究结果表明Long-HDD可用于分析实践测评数据,且其追踪诊断结果与参数化模型的存在一致性。     

强迫症的临床表现

强迫症的基本症状是强迫观念和强迫动作,患者可仅有强迫观念或强迫动作,或既有强迫观念又有强迫动作。强迫观念包括强迫想法、想象和冲动等;强迫行为指重复出现的仪式动作,主要包括强迫洗涤、强迫检查、强迫计数等。一、强迫观念表现为反复而持久的观念、思想、印象和冲动念头。力图摆脫,但为摆脱不了而紧张烦恼、心烦意乱、焦虑不安。强迫观念可有下面几种表现形式。 1.强迫思想:强迫性怀疑,患者对已完成的事情总是放心不下,要反复多次检查确实无误后才能放下心     

Spatial navigation: Cognitive variables involved in route retracing among an elderly population

The cognitive processes involved in route retracing are not well known. This study aims to highlight them in an elderly population in which contradictory results have been obtained, certain studies showing specific difficulties for route retracing, others not. Thirty-nine elderly subjects performed a route-learning task (forward-backward) in a garden, then completed spatial knowledge tasks and standardised cognitive tests. Results show four factors that were predictive of route retracing performance: route repetition, the pointing task, and two standardised cognitive tests, one assessing spatial working memory, and another global cognitive efficiency. According to these results, route retracing involves route and survey knowledge (i.e., egocentric and allocentric strategy), and the integration of forward-backward perspectives is underpinned by the spatial working memory. Moreover, the subjects did not make more errors in route retracing than in the route repetition task, suggesting that a real environment could compensate for a failing allocentric strategy.     

The three-class ideal observer for univariate normal data: Decision variable and ROC surface properties

Although a fully general extension of ROC analysis to classification tasks with more than two classes has yet to be developed, the potential benefits to be gained from a practical performance evaluation methodology for classification tasks with three classes have motivated a number of research groups to propose methods based on constrained or simplified observer or data models. Here we consider an ideal observer in a task with underlying data drawn from three univariate normal distributions. We investigate the behavior of the resulting ideal observer’s decision variables and ROC surface. In particular, we show that the pair of ideal observer decision variables is constrained to a parametric curve in two-dimensional likelihood ratio space, and that the decision boundary line segments used by the ideal observer can intersect this curve in at most six places. From this, we further show that the resulting ROC surface has at most four degrees of freedom at any point, and not the five that would be required, in general, for a surface in a six-dimensional space to be non-degenerate. In light of the difficulties we have previously pointed out in generalizing the well-known area under the ROC curve performance metric to tasks with three or more classes, the problem of developing a suitable and fully general performance metric for classification tasks with three or more classes remains unsolved.     

Are There Enough Injective Sets?

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed some light on the problem whether there are (enough) injective sets in CZF. We show that no two element set is injective unless the law of excluded middle is admitted for negated formulas, and that the axiom of power set is required for proving that “there are strongly enough injective sets”. The latter notion is abstracted from the singleton embedding into the power set, which ensures enough injectives both in every topos and in IZF. We further show that it is consistent with CZF to assume that the only injective sets are the singletons. In particular, assuming the consistency of CZF one cannot prove in CZF that there are enough injective sets. As a complement we revisit the duality between injective and projective sets from the point of view of intuitionistic type theory.     

Predicting the shape of distance functions in curve tracing: Evidence for a zoom lens operator

Jolicoeur, Ullman, and MacKay (1986) showed that the time to confirm that two dots are on the same curve increases monotonically, but nonlinearly, as the curve distance between the two dots increases. These displays contained two curves and two dots. On same trials, the two dots were on the same curve (target curve), while the other curve served as a foil (distractor curve). The monotonically increasing effects of curve distance on response times for same trials suggested that the intervening curve segment was traced. In the present investigation of the source of the nonlinearity in these distance functions, it was hypothesized that differences in the distractor curves may have allowed a curve tracing operator with zoom lens properties to widen its receptive field while tracing parts of certain target curves. The wider receptive field may have allowed faster tracing over certain segments, owing to a reduced number of shifts required by the operator to scan the curve. The consequence of training certain segments of the curve more quickly than other segments of the curve would be a nonlinear effect of distance. A new set of stimuli was created for testing this hypothesis directly. Fairly linear distance effects were found for stimuli that contained a distractor curve that constrained the breadth of the postulated curve tracing operator, whereas stimuli that contained a distractor curve that could allow for a larger receptive field yielded nonlinear distance functions. The results are compared with the predictions of three quantitative models: pixel-by-pixel tracing; Jolicoeur, Ullman, and MacKay's (1991) bipartite operator; and a new zoom lens model, analogous to the zoom lens model of visual attention. The results were fit best by the latter model, in which tracing is accomplished by tracking the curve with a variably sized local operator.     

Evaluating Creativity Through the Degrees of Solidity of Its Assessment: A Relational Approach

In this paper, we introduce a new approach to creativity assessment. Arguably, one of the main obstacles to creativity assessment is that creativity criteria are likely to change depending on what is assessed and who is making the assessment. We argue that we might be able to solve this problem by adopting a relational ontology, i.e., an ontology according to which beings of the world acquire their properties by relating to other beings. First, we present the main consequences of this ontological approach for creativity assessment: (a) Accounting for the creativity of a given object involves retracing the beings (including criteria) that relate it to its alleged creativity; (b) One can assess the creativity of this object by looking at the number of beings that substantiate this relation, i.e., by looking at what we call the “degree of solidity” of the relation; (c) One can thus account for the specificity of various forms of creativity and, at the same time, compare them in terms of solidity. Building on these ontological assumptions, we then present a new assessment technique, the Objection Counting Technique, before putting it to the test using an excerpt taken from a naturally occurring brainstorming session.     

Likelihood-Based Clustering of Meta-Analytic SROC Curves

Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and sensitivities arising from different studies might vary just because the underlying cut-off value had been different. To cope with the cut-off value problem interest is usually directed towards the receiver operating characteristic (ROC) curve which consists of pairs of sensitivities and false-positive rates (1-specificity). In the context of meta-analysis one pair represents one study and the associated diagram is called an SROC curve where the S stands for “summary”. In meta-analysis of diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC curve. Here, we focus instead on finding sub-groups or components in the data representing different diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which is characterised by one parameter only. Each single study can be represented by a specific value of that parameter. Hence we focus on the distribution of these parameter estimates and suggest modelling a potential heterogeneous or cluster structure by a mixture of specifically parameterised normal densities. We point out that this mixture is completely nonparametric and the associated mixture likelihood is well-defined and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies to be analysed. Several meta-analytic applications on diagnostic studies, including AUDIT and AUDIT-C for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders, as well as diagnostic accuracy inspection data on metal fatigue of aircraft spare parts, are discussed to illustrate the methodology.     

FUTURE TIME PERSPECTIVE AND HUMAN COGNITION: AN EVOLUTIONAL VIEW

The creation of future time perspective is one of the culminating accomplishments of the human cognitive system. For the purpose of uncovering the implications of this achievement, a hypothetical retracing of the evolutional development of biological information processing systems is attempted. The retracing goes through four stages concerning the software architecture of such a system; fixed-I/O (reflex), flexible-I/O (adaptive learning), motivational subprogram (typically emotions), and cognitive information processing. Through the retracing it is shown that most of the information processing modes of biological systems already emerge as early as the flexible-I/O stage, which are subsequently developed and refined till reaching the stage of creating future time perspective as a context-free cognitive background upon which survival-oriented behaviors can be planned ahead of time.     

The “pure-study” learning curve: The learning curve without cumulative testing

The customary assumption in the study of human learning using alternating study and test trials is that learning occurs during study trials and that test trials are useful only to measure learning. In fact, tests seem to play little role in the development of learning, because the learning curve is similar even when the number of test trials varies widely (Tulving, Journal of Verbal Learning and Verbal Behavior 6:175-184, 1967). However, this outcome seems odd, because other research has shown that testing fosters greater long-term learning than does studying. We report three experiments addressing whether tests affect the shape of the learning curve. In two of the experiments, we examined this issue by varying the number of spaced study trials in a sequence and examining performance on only a single test trial at the end of the series (a "pure-study" learning curve). We compared these pure-study learning curves to standard learning curves and found that the standard curves increase more rapidly and reach a higher level in both free recall (Exp. 1) and paired-associate learning (Exp. 2). In Experiment 3, we provided additional study trials in the "pure-study" condition to determine whether the standard (study-test) condition would prove superior to a study-study condition. The standard condition still produced better retention on both immediate and delayed tests. Our experiments show that test trials play an important role in the development of learning using both free-recall (Exps. 1 and 3) and paired-associate (Exp. 2) procedures. Theories of learning have emphasized processes that occur during study, but our results show that processes engaged during tests are also critical.     

The continuous end-state comfort effect: weighted integration of multiple biases

The grasp orientation when grasping an object is frequently aligned in anticipation of the intended rotation of the object (end-state comfort effect). We analyzed grasp orientation selection in a continuous task to determine the mechanisms underlying the end-state comfort effect. Participants had to grasp a box by a circular handle—which allowed for arbitrary grasp orientations—and then had to rotate the box by various angles. Experiments 1 and 2 revealed both that the rotation’s direction considerably determined grasp orientations and that end-postures varied considerably. Experiments 3 and 4 further showed that visual stimuli and initial arm postures biased grasp orientations if the intended rotation could be easily achieved. The data show that end-state comfort but also other factors determine grasp orientation selection. A simple mechanism that integrates multiple weighted biases can account for the data.     

On a hitherto unexploited extension of the finitary standpoint

P. Bernays has pointed out that, in order to prove the consistency of classical number theory, it is necessary to extend Hilbert's finitary standpoint by admitting certain abstract concepts in addition to the combinatorial concepts referring to symbols. The abstract concepts that so far have been used for this purpose are those of the constructive theory of ordinals and those of intuitionistic logic. It is shown that the concept of a computable function of finite simple type over the integers can be used instead, where no other procedures of constructing such functions are necessary except simple recursion by an integral variable and substitution of functions in each other (starting with trivial functions).