A model of transitive choice

We report a formal model of transitive inference based on protocols from experiments on squirrel monkeys solving the 5-term series problem (McGonigle & Chalmers, 1977, 1992). These studies generate databases featuring transitive choice, task transfer (where at first a significant decrement is observed, and later substantial improvement without explicit training), and, finally, a Symbolic Distance Effect (SDE) based on decision-time data. Using a rule-based (production) system, we first established rule stacks at the group, then at the individual level, on the basis of triadic transfer performance first recorded in the McGonigle and Chalmers (1977) study. The models for each subject then accommodated data from the more intensive, later study with the same subjects (McGonigle & Chalmers, 1992). We found the initial model capable of dealing with all choice and reaction-time phenomena reported thus far, with only small changes in a rule search procedure. In common with an independent assay by McGonigle and Chalmers (1992), our model-based reassessment of decision times indicates that a major source of reaction time variation is item prominence in the rule stack rather than interitem (ordinal) distance per se.     

Primate errors in transitive ‘inference’: a two-tier learning model

Transitive performance (TP) is a learning-based behaviour exhibited by a wide range of species, where if a subject has been taught to prefer A when presented with the pair AB but to prefer B when presented with the pair BC, then the subject will also prefer A when presented with the novel pair AC. Most explanations of TP assume that subjects recognize and learn an underlying sequence from observing the training pairs. However, data from squirrel monkeys (Saimiri sciureus) and young children contradict this, showing that when three different items (a triad) are drawn from the sequence, subjects' performance degrades systematically (McGonigle and Chalmers, Nature 267:694-696, 1977; Chalmers and McGonigle, Journal of Experimental Child Psychology 37:355-377, 1984; Harris and McGonigle, The Quarterly Journal of Experimental Psychology 47B:319-348, 1994). We present here the two-tier model, the first learning model of TP which accounts for this systematic performance degradation. Our model assumes primate TP is based on a general-purpose task learning system rather than a special-purpose sequence-learning system. It supports the hypothesis of Heckers et al. (Hippocampus 14:153-162, 2004) that TP is an expression of two separate general learning elements: one for associating actions and contexts, another for prioritising associations when more than one context is present. The two-tier model also provides explanations for why phased training is important for helping subjects learn the initial training pairs and why some subjects fail to do so. It also supports the Harris and McGonigle (The Quarterly Journal of Experimental Psychology 47B:319-348, 1994) explanation of why, once the training pairs have been acquired, subjects perform transitive choice automatically on two-item diads, but not when exposed to triads from the same sequence.     

Transitive choices by a simple, fully connected, backpropagation neural network: implications for the comparative study of transitive inference.

In search of the minimal requirements for transitive reasoning, a simple neural network was trained and tested on the non-verbal version of the conventional "five-term-series task" – a paradigm used with human adults, children and a variety of non-human species. The transitive performance of the network was analogous in several aspects to that reported for children and animals. The three effects usually associated with transitive choices i.e. "symbolic distance", "lexical marking" and "end-anchor", were also clearly shown by the neural network. In a second experiment, where the training conditions were manipulated, the network failed to match the behavioural pattern reported for human adults in the test following an ordered presentation of the premises. However, it mimicked young children's performance when tested with a novel comparison term. Although we do not intend to suggest a new model of transitive inference, we conclude, in line with other authors, that a simple error-correcting rule can generate transitive behaviour similar to the choice pattern of children and animals in the binary form of the five-term-series task without requiring high-order logical or paralogical abilities. The analysis of the training history and of the final internal structure of the network reveals the associative strategy employed. However, our results indicate that the scope of the associative strategy used by the network might be limited. The extent to which the conventional five-term-series task, in absence of appropriate manipulations of training and testing conditions, is suitable to detect cognitive differences across species is also discussed on the basis of our results. Accepted after revision: 29 May 2001 Electronic Publication     

Are children any more logical than monkeys on the five-term series problem?

Six-year-old children were tested on several versions of the five-term transitivity problem as used by B. O. McGonigle and M. Chalmers (1977, Nature (London), 267, 694–696) with squirrel monkeys as subjects. Both binary and triadic versions of the tests were administered in both verbal and nonverbal modes to help determine whether or not any major procedural differences between the monkey version and that used conventionally in research with children might account for the monkey's apparently nonlogical solution of the problem. The main result is that children showed very similar response profiles to that of monkeys in all the conditions used. In addition, “labeling”, direct seriation, and “association” post-tests suggest that nonlogical strategies can underwrite ostensibly impeccable transitive “reasoning” in child as well as monkey.     

Measuring the ability of transitive reasoning,using product and strategy information

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.     

Does the autistic child have a metarepresentational deficit?

This study examines the claim that autistic children lack a “theory of mind” because of an inability to metarepresent. We argue that if autistic children have a “metarepresentational” deficit in Leslie's (1987, 1988) sense of the term, then they should have difficulty not only with mental representations such as false beliefs, but also with external representations such as photographs. Autistic children's understanding of photographic representations was tested using Zaitchik's (1990) task. This task is modelled on the false belief task (Baron-Cohen, Leslie, & Frith, 1985: Wimmer & Perner, 1983) but involves “false” photographs where a photographic representation does not conform with the current state of the real world. Like Zaitchik (1990) we found that normal 3 and 4-year-olds found this task as difficult as the false belief task. In sharp contrast, however, the autistic children in our study passed the photograph task but failed the false belief task. As both tasks require the ability to decouple, this evidence challenges the view that autistic children lack “metarepresentational” ability in Leslie's sense. However, the results leave open the question of whether autistic children have a metarepresentational ability in the different sense of the term intended by Pylyshyn (1978), that is, representing the relationship between a representation and what it represents.     

In search of counter-examples: Deductive rationality in human reasoning

Dual-process theories come in many forms. They draw on the distinction between associative, heuristic, tacit, intuitive, or implicit processes (System 1) and rule-based, analytic, explicit processes (System 2). We present the results of contextual manipulations that have a bearing on the supposed primacy of System 1 (Stanovich & West, 2000). Experiment 1 showed that people who evaluated logically valid or invalid conditional inferences under a timing constraint (N=56), showed a smaller effect of logical validity than did people who were not placed under a timing constraint (N= 44). Experiment 2 similarly showed that stressing the logical constraint that only inferences that follow necessarily are to be endorsed (N = 36) increased the size of the validity effect, as compared to that of participants (N=33) given the standard instruction to make "logical" inferences. These findings concur with the thesis in dual-processing frameworks that "Rationality-2 processes" (Evans & Over, 1996), "test procedures" (Chater & Oaksford, 1999), or "conclusion validation processes" (Johnson-Laird & Byrne, 1991; Schroyens, Schaeken, & d'Ydewalle, 2001) serve to override the results of System 1 processes.     

Factors and processes in children's transitive deductions

Transitive tasks are important for understanding how children develop socio-cognitively. However, developmental research has been restricted largely to questions surrounding maturation. We asked 6-, 7- and 8-year-olds (N?=?117) to solve a composite of five different transitive tasks. Tasks included conditions asking about item-C (associated with the marked relation) in addition to the usual case of asking only about item-A (associated with the unmarked relation). Here, children found resolving item-C much easier than resolving item-A, a finding running counter to long-standing assumptions about transitive reasoning. Considering gender perhaps for the first time, boys exhibited higher transitive scores than girls overall. Finally, analysing in the context of one recent and well-specified theory of spatial transitive reasoning, we generated the prediction that reporting the full series should be easier than deducing any one item from that series. This prediction was not upheld. We discuss amendments necessary to accommodate all our earlier findings.     

Young children's comprehension of English SVO word order revisited: Testing the same children in act-out and intermodal preferential looking tasks

Act-out and intermodal preferential looking (IPL) tasks were administered to 67 English children aged 2–0, 2–9 and 3–5 to assess their comprehension of canonical SVO transitive word order with both familiar and novel verbs. Children at 3–5 and at 2–9 showed evidence of comprehending word order in both verb conditions and both tasks, although children at 2–9 performed better with familiar than with novel verbs in the act-out task. Children at 2–0 showed no evidence of comprehending word order in either task with novel verbs; with familiar verbs they showed competence in the IPL task but not in the act-out task. The difference in performance for familiar and novel verbs from the same children at 2–0, on the IPL task, and at 2–9, on the act-out task, is consistent with the hypothesis that early linguistic/cognitive representations are graded in strength, with early representations still weak and very task dependent. However, these representations also become more abstract with development, as indicated by the familiarity effect even in the more sensitive IPL task.     

3～5岁幼儿在视野阻隔任务中的长度传递性推理

设计视野阻隔任务,控制了短时记忆和直接比较的两难问题,考察3～5岁幼儿长度传递性推理能力的发展趋势和传递性推理这一认知过程的发展序列。以2(间隔长度)×2(摆放方式)×4(年龄)的三因素混合设计,研究了240名幼儿,结果表明:(1)3～4岁是长度传递性推理能力的快速发展期,4岁以后的幼儿大部分具备了这一能力,发展速度趋于平缓;(2)任务类型影响推理成绩;(3)基于传递关系的推理依据与推理总成绩显著正相关。研究认为:年仅4岁幼儿具备传递性推理能力蕴含教育价值;传递性推理的认知过程经历了四个可辨别的发展序列,依次主要发生在36～42个月、43～48个月、49～54个月和55～60个月的幼儿当中。     

5~6岁儿童传递推理能力的发展特点

通过有效的实验设计,在控制儿童记忆容量影响的前提下,考察了5~6岁儿童在长度传递推理和重量传递推理能力上的发展水平。结果表明:(1)5~6岁是儿童传递推理能力迅速发展的时期。在大概6岁左右,大多数儿童已经能够进行真正意义上的传递推理。(2)此年龄儿童在长度传递推理和重量传递推理能力上不具有显著差异。(3)条件排列的一致与不一致对于被试的推理成绩并不具有显著影响。     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Metalinguistic awareness and theory of mind: Just two words for the same thing?

Three- to 5-year-old children were tested on a traditional False Belief task, in which children have to predict where a protagonist will look for an unexpectedly moved object, and a new metalinguistic task. In this task children named an item (e.g., “rabbit”) and they had to monitor that another person used a synonym for naming the same item (e.g., “bunny”). Both tasks were mastered about the age of 4 years with a strong correlation between the two tasks that remained above .70 even after partialling out control measures and verbal intelligence. Moreover, younger children's difficulties with the metalinguistic task did not extend to a control task of equivalent logical structure and complexity. A simplified version of the task in which children had to produce synonyms themselves yielded very similar results. The findings confirm that metalinguistic awareness can be demonstrated around 4 years and they support the theory that the ability to understand belief relates to the development of understanding representations.     

On the emergence of the discriminative mode for transitive-inference

Transitive-inference tasks play increasing roles in many areas of cognitive science. However, discrepancies between the two competing paradigms (classical-Piagetian and IP-paradigm) imply that one paradigm fails to index its target (deductive) competence. Here, potential flaws of one were addressed using considerations from the other. Children of 5–7 years (N=216) solved 3-term transitive problems, some implying a single largest item, and some not. Findings indicate a discriminative competence (a Transitive-Switch) at least 2 years before competence in actually deducing correct solutions. Interestingly, although the transitive-switch was constant across age with both memory and inference increasing with age, it was nevertheless a much stronger predictor of transitive performance than either memory or age. A predictive relationship between memory and inference held for the 5- and 6-year-olds but not the 7-year-olds; suggesting as it approaches maturity, transitive-inference becomes independent of memory. Coincidental with this latter finding, only the 7-year-olds’ transitive performance approximated a deductive competence. As the initial validation of the IP-paradigm rested on acceptance of its age estimate of 4 years, its claim to index deduction must now be revisited.     

Transitive inference in rats (Rattus norvegicus).

Although Piagetian theory proposes that the ability to make transitive inferences is confined to humans above age 7, recent evidence has suggested that this logical ability may be more broad based. In nonverbal tests, transitive inference has been demonstrated in preschool children and 2 species of nonhuman primates. In these experiments, I demonstrate evidence of transitive inference in rats (Rattus norvegicus). I used an ordered series of 5 olfactory stimuli (A < B < C < D < E) from which correct inferences were made about the novel B versus D pair. Control procedures indicated that performance did not depend on the recency with which the correct answer was rewarded during training and may be disrupted by the addition of logically inconsistent premises (F > E and A > F). The possibility that logical transitivity may reflect a form of spatial paralogic rather than formal deductions from a syllogistic-verbal system is discussed.     

Distinguishing logic from association in the solution of an invisible displacement task by children (Homo sapiens) and dogs (Canis familiaris): using negation of disjunction

Prior research on the ability to solve the Piagetian invisible displacement task has focused on prerequisite representational capacity. This study examines the additional prerequisite of deduction. As in other tasks (e.g., conservation and transitivity), it is difficult to distinguish between behavior that reflects logical inference from behavior that reflects associative generalization. Using the role of negation in logic whereby negative feedback about one belief increases the certainty of another (e.g., a disjunctive syllogism), task-naive dogs (Canis familiaris; n=19) and 4- to 6-year-old children (Homo sapiens; n=24) were given a task wherein a desirable object was shown to have disappeared from a container after it had passed behind 3 separate screens. As predicted, children (as per logic of negated disjunction) tended to increase their speed of checking the 3rd screen after failing to find the object behind the first 2 screens, whereas dogs (as per associative extinction) tended to significantly decrease their speed of checking the 3rd screen after failing to find the object behind the first 2 screens.     

Developmental differences in memory for cross‐modal associations

Associative learning is critical to normal cognitive development in children. However, young adults typically outperform children on paired‐associate tasks involving visual, verbal and spatial location stimuli. The present experiment investigated cross‐modal odour–place associative memory in children (7–10 years) and young adults (18–24 years). During the study phase, six odours were individually presented and paired with one of 12 spatial locations on a board. During the test phase, participants were presented with the six stimuli individually and were asked to place each stimulus on the correct spatial location. Children committed significantly more errors on the odour–place task than did young adults. However, item recognition memory for the odours or spatial locations involved in the odour–place associative memory task was similar between children and young adults. Therefore, poor odour–place associative memory in children did not result from impaired memory for the individual odours or spatial locations involved in the associations. The results suggest that cross‐modal associative memory is not fully developed in children.     

3—7岁儿童不同类型的传递性推理的发展研究

本研究从发展的角度研究了3-7岁儿童在解决三类传递性推理问题时能力发展和策略发展状况,真传递性推理指推理的传递性是确定的,个体根据前提关系可以做出确定的传递性推理结论,不确定性传递性推理指该类推理的传递性是不确定的,关系是否传递需要根据实际的情况和社会经验来确定,否定性传递性推理指根据前提关系得出不能进行传递性的必然结论。结果表明：（1）三类传递性推理的解题能力随年龄的增长而不断增强,在7岁左右初步形成。（2）三类传递性推理,能力发展有不同的起始点、快速发展期以及初步形成期。真传递性推理发展最早最快,不确定传递性推理最晚最慢。（3）3-7岁儿童解决三类传递性推理问题时使用了猜测、视觉判断、定向反应、经验推测和逻辑推理等策略,然而随着年龄的增大,主导策略由准策略向真策略转换。     

Enhanced discrimination in autism

Children with autism are superior to typically developing children at visual search tasks (O'Riordan, Plaisted, Driver, & Baron-Cohen, in press; Plaisted, O'Riordan, & Baron-Cohen, l998b). This study investigates the reasons for this phenomenon. The performance of children with autism and of typically developing children was compared on a series of visual search tasks to investigate two related problems. The first issue was whether the critical determinant of search rate in children is the discriminability of the display items, as it is in normal adults. The second question investigated was whether the superior performance of individuals with autism on visual search tasks is due to an enhanced ability to discriminate between display items. The results demonstrated that discriminability is the rate-determining factor for children with and without autism, replicating earlier findings with normal adults, and that children with autism have an enhanced ability to discriminate between display items. Thus, it seems that an enhanced ability to discriminate between display items underlies superior visual search in autism.     

4—6岁幼儿空间方位传递性推理能力的发展

该研究旨在探查4、5、6岁幼儿空间上下和前后方位传递性推理能力的发展水平及不同实验条件(一致、模糊、冲突)下儿童的传递性推理能力。为了尽量降低记忆对推理的影响,要求幼儿在前提呈现的条件下按前提方位关系进行传递性推理操作。被试为幼儿园4、5、6岁组儿童各24人,其中男女各半。主要结果表明：4岁幼儿开始萌发空间前后和上下方位的传递性推理能力;从4岁到6岁,“上下”方位传递性推理能力的发展优于“前后”方位;4—6岁幼儿还不能完全摆脱知觉干扰因素的影响,形成稳定的传递性推理能力。