An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen     

印尼留学生汉语主动句被动句命题表征项目顺序

采用句子-图形验证任务初步探讨了不同汉语水平的印尼留学生理解汉语主动句、被动句所形成的命题表征中的项目顺序特点。结果表明,初级汉语水平印尼留学生理解汉语主动句、被动句后所建构的命题表征中项目顺序均为“受事→施事”;中级汉语水平印尼留学生理解汉语主动句所形成的命题表征项目顺序为“施事→受事”,而其理解汉语被动句所形成的命题表征项目顺序为“受事→施事”。母语主动句、被动句的理解特点影响印尼留学生汉语主动句、被动句命题表征项目顺序;这种影响作用与其汉语水平有一定的关系。     

Is ZF a hack?: Comparing the complexity of some (formalist interpretations of) foundational systems for mathematics

This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.

The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.

The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.

(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.)     

Effects of object complexity and type on the gaze behavior of children with pervasive developmental disorder

The looking behavior of children with pervasive developmental disorder (PDD) and age- and IQ-matched normal control children was studied using infrared oculography. Stimuli varying in complexity and topic were presented to test whether children with PDD have specific abnormalities in looking behavior to complex stimuli and/or to faces. All children showed more and longer fixations on the complex objects than on the simple objects, especially the complex nonsense figure, but group differences were not found. The results show no evidence for specific abnormalities in looking behavior to either faces or to complex stimuli in high functioning children with PDD.     

DO INFANTS SHOW GENERALIZED IMITATION OF GESTURES?

Two experiments were conducted to investigate generalized imitation of manual gestures in 1- to 2-year-old infants. In Experiment 1, 6 infants were first trained four baseline matching relations (e.g., when instructed "Do this", to raise their arms after they saw the experimenter do so). Next, four novel gestures that the infants did not match in probe trials were selected as target behaviors during generalized imitation Test 1; models of these gestures were presented on unreinforced matching trials interspersed with intermittently reinforced baseline matching trials. None of the infants matched the target behaviors. To ensure that these behaviors were in the infants' motor skills repertoires, the infants were next trained to produce them, at least once, under stimulus control that did not include an antecedent model of the target behavior. In repeat generalized imitation trials (Test 2), the infants again failed to match the target behaviors. Five infants (3 from Experiment 1) participated in Experiment 2, which was identical to Experiment 1 except that, following generalized imitation Test 1, the motor-skills training was implemented to a higher criterion (21 responses per target behavior), and in a multiple-baseline, across-target-behaviors procedure. In the final generalized imitation test, 1 infant matched one, and another infant matched two target behaviors; the remaining 17 target behaviors still were not matched. The results did not provide convincing evidence of generalized imitation, even though baseline matching was well maintained and the target behaviors were in the infants' motor skills repertoires, raising the question of what are the conditions that reliably give rise to generalized imitation.     

On ethical order

The existent ethical relationships are the result of the historical amalgamation of objective and subjective conditions. Ethical relationships are essential relationships in the real and rational order, which are maintained by a system of regulations on morals, laws and customs, and infused with a spirit of subjectivity. Rationality and legitimacy are the primary concerns of those relationships. A distinction between morals and ethos needs to be made when studying ethical order. Sound ethical order lies in effective regulation of morals and effective control of law. In the process of social reform, ethical order promotes social development through the dialectical movement of freedom and necessity. A harmonious society is a society which is based on legitimate and just ethical order. Translated by Cui Hui from Lunlixue yanjiu 伦理学研究 (Studies in Ethics), 2007, (5): 1–8     

Impaired discriminative fear-conditioning resulting from elevated fear responding to learned safety cues among individuals with panic disorder

Classical fear-conditioning is central to many etiologic accounts of panic disorder (PD), but few lab-based conditioning studies in PD have been conducted. One conditioning perspective proposes associative-learning deficits characterized by deficient safety learning among PD patients. The current study of PD assesses acquisition and retention of discriminative aversive conditioning using a fear-potentiated startle paradigm. This paradigm was chosen for its specific capacity to independently assess safety- and danger learning in the service of characterizing putative anomalies in each type of learning among those with PD. Though no group difference in fear-potentiated startle was found at retention, acquisition results demonstrate impaired discriminative learning among PD patients as indexed by measures of conditioned startle-potentiation to learned safety and danger cues. Importantly, this discrimination deficit was driven by enhanced startle-potentiation to the learned safety cue rather than aberrant reactivity to the danger cue. Consistent with this finding, PD patients relative to healthy individuals reported higher expectancies of dangerous outcomes in the presence of the safety cue, but equal danger expectancies during exposure to the danger cue. Such results link PD to impaired discrimination learning, reflecting elevated fear responding to learned safety cues.     

Single and double alternation learning in rats: The role of set size and correction

In many experiments, rats have evidenced extreme difficulty mastering alternation patterns. In three experiments, we explored rats’ ability to learn double alternation patterns and possible reasons behind their past difficulties with such patterns. In Experiment 1, rats learned single and double alternation patterns. In the second and third experiment, we explored the role of correction and interference from stimulus set size on rats’ learning of double alternation patterns. Our results showed that rats easily learned both single and double alternation patterns and that stimulus set size had no noticeable effect on learning double alternation patterns. Findings additionally evidenced that correction played an important role in rats’ learning double alternation patterns.     

Impact of auditory selective attention on verbal short-term memory and vocabulary development

This study investigated the role of auditory selective attention capacities as a possible mediator of the well-established association between verbal short-term memory (STM) and vocabulary development. A total of 47 6- and 7-year-olds were administered verbal immediate serial recall and auditory attention tasks. Both task types probed processing of item and serial order information because recent studies have shown this distinction to be critical when exploring relations between STM and lexical development. Multiple regression and variance partitioning analyses highlighted two variables as determinants of vocabulary development: (a) a serial order processing variable shared by STM order recall and a selective attention task for sequence information and (b) an attentional variable shared by selective attention measures targeting item or sequence information. The current study highlights the need for integrative STM models, accounting for conjoined influences of attentional capacities and serial order processing capacities on STM performance and the establishment of the lexical language network.     

The role of the right posterior parietal cortex in temporal order judgment

Perceived order of two consecutive stimuli may not correspond to the order of their physical onsets. Such a disagreement presumably results from a difference in the speed of stimulus processing toward central decision mechanisms. Since previous evidence suggests that the right posterior parietal cortex (PPC) plays a role in modulating the processing speed of a visual target, we applied single-pulse TMS over the region in 14 normal subjects, while they judged the temporal order of two consecutive visual stimuli. Stimulus-onset-asynchrony (SOA) randomly varied between -100 and 100 ms in 20-ms steps (with a positive SOA when a target appeared on the right hemi-field before the other on the left), and a point of subjective simultaneity was measured for individual subjects. TMS stimulation was time-locked at 50, 100, 150, and 200 ms after the onset of the first stimulus, and results in trials with TMS on right PPC were compared with those in trials without TMS. TMS over the right PPC delayed the detection of a visual target in the contralateral, i.e., left hemi-field by 24 (+/-7 SE) ms and 16 (+/-4 SE) ms, when the stimulation was given at 50 and 100 ms after the first target onset. In contrast, TMS on the left PPC was not effective. These results show that the right PPC is important in a timely detection of a target appearing on the left visual field, especially in competition with another target simultaneously appearing in the opposite field.