Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster

We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.     

Number concepts for the concept empiricist

Dove (2009) and Machery (2007) both argue that recent findings about the nature of numerical representation present problems for Concept Empiricism (CE). I shall argue that, whilst this evidence does challenge certain versions of CE, such as Prinz (2002), it needn’t be seen as problematic to the general CE approach. Recent research can arguably be seen to support a CE account of number concepts. Neurological and behavioral evidence suggests that systems involved in the perception of numerical properties are also implicated in numerical cognition. Furthermore, the discovery of associations between spatial and numerical representations also lends independent support to a CE approach. Although these findings support CE in general, certain versions of the theory may need revising in order to accommodate them. In particular, it may be necessary to either jettison Prinz's (2002) Modal Specificity Hypothesis or to revise one’s method for individuating modal representational formats.     

Mathematical modeling of movement between residential placements: A systems analytic approach to understanding systems of care

Although the concept of a system of care for children and adolescents with a severe emotional disturbance has become core to treatment philosophy, very little research has focused on systems of care as systems. This article attempts to contribute to the development of a systems research paradigm in children's mental health as well as to add to the substantive knowledge of utilization of and movement between residential options in a statewide multiagency service delivery system. Information on residential placement gathered at six month intervals over a three year period is used to develop a mathematical model of the system of care. This model can help administrators to predict future needs for residential care, and to project probable outcomes of alternative strategies for meeting the needs of these children and adolescents.     

Time perception: Effects of sex and sound intensity on scales of subjective duration

Six women and six men reproduced ten time intervals varying in logarithmic steps between 1.3 and 20 s. The durations were indicated by white noise of 10, 25, 40 and 55 dB SL, different sound intensities in different sessions. It was found that (i) greater sound intensity entails shorter reproductions, and (ii) reproductions by male observers are shorter than those by female, although for both (i) and (ii) there is an interaction with the standard durations. The data were treated in accordance with the "parallel-clock model" (Eisler, 1975), whereby the parameters of the psychophysical power function are determined from duration reproduction data. As in previous experiments (Eisler, 1975), the data showed a break in the function entailing two segments. The effect of sound intensity could be attributed to the exponent, which was lower for stronger noise, and the effect of sex to the weight coefficient of the upper relative to the lower segment of the psychophysical function, the coefficient being lower for men.     

Differences in mathematical reasoning between typically achieving and gifted children

Mathematical giftedness refers to mastery in a specific mathematical domain at an earlier than expected age. The present study examined which cognitive processes accounted for differences in mathematical reasoning between gifted children (MRG) and their typically achieving peers (TA). Naming speed, phonological awareness, short-term memory, executive functioning, and working memory were examined in 51 children aged approximately 7 years. A series of stepwise regression models, using a contrast variable to capture differences in mathematical reasoning between MRG and TA children, were created to examine which cognitive domains accounted for differences in mathematical reasoning. Short-term memory (r²?=?.08) and visual-spatial working memory (r²?=?.39) emerged as the only cognitive predictors within a model that included gender, age, and fluid intelligence. This model captured all of the variance distinguishing mathematics reasoning between MRG and TA children, explaining an overall contribution of 70% of the variance in mathematical reasoning.     

Penrose's New Argument

It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive.     

Glivenko Type Theorems for Intuitionistic Modal Logics

In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that for intermediate predicate logics obtained by Umezawa [27] and Gabbay [15]. Another one is rather surprising.     

初中数学学习中教师归因与学生自我归因的比较研究

本文研究了初中数学学习中教师的信念与归因．学生自我的信念与归因以及师生归因的比较,得出如下几点结论：(1)在教师和学生的信念中男生在数学学习中更占优势。但在归因领域里却没有发现显著的性别差异。(2)对最好的学生,教师倾向于努力归因;对最差的学生,教师倾向于基础归囚。(3)最好的学生自我归因时倾向于基础和方法归因,最差的学生倾向于努力和方法归因。(4)师生归因维度上的一般趋势：造成数学学习成功的原因比较稳定、内源、可控;造成数学学习失败的原因也倾向于内源,但比较不稳定,不可控。(5)师生特定归因中的差异广泛存在,建议采取相应的教育对策。     

Animal cognition + optimal choice = behavior: A review of adaptive behavior and learning, 2nd Ed., by J. E. R. Staddon

Staddon discusses a vast array of topics in comparative psychology in this book. His view is that adaptive behavior in most cases is the result of optimal choice acting on an animal's knowledge about the world. Staddon refers to this as a functional teleonomic approach inasmuch as it attempts to understand an animal's behavior in terms of goals. He builds mathematical models based on this idea that are designed to reproduce specific sets of empirical observations, usually qualitatively. A natural consequence of Staddon's approach is that many models are developed, each of which applies to a specific set of observations. An alternative to functional teleonomy is a functional approach that builds on prior principles. In most cases, this approach favors a single‐theory account of behavior. Prior principles can be understood as functional stand‐ins for antecedent material causes, which means that these accounts are closer to mechanistic theories than are goal‐based teleonomic accounts. An ontological perspective, referred to as supervenient realism, is a means of understanding the relationship between functional theories and the material world. According to this perspective, the algorithmic operation of a successful functional theory may be understood to supervene on the material operation of the nervous system.     

音乐训练对认知能力的影响

在当今社会中, 越来越多的儿童接受音乐训练, 试图通过音乐训练提高认知能力。针对认知活动中的语言能力、空间能力以及数学能力, 探究音乐训练与认知能力的关系, 试图为音乐教育提供实证依据。研究结果表明, 尽管音乐训练与认知能力的关系较为复杂, 但是, 音乐训练与个体的语言知觉和产生能力以及空间视觉化能力都存在正相关, 且在一定程度上可以提高这些认知能力。