Supposition and representation in human reasoning

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.     

Sensorimotor representation and knowledge-based reasoning for spatial exploration and localisation

We investigate a hybrid system for autonomous exploration and navigation, and implement it in a virtual mobile agent, which operates in virtual spatial environments. The system is based on several distinguishing properties. The representation is not map-like, but based on sensorimotor features, i.e. on combinations of sensory features and motor actions. The system has a hybrid architecture, which integrates a bottom-up processing of sensorimotor features with a top-down, knowledge-based reasoning strategy. This strategy selects the optimal motor action in each step according to the principle of maximum information gain. Two sensorimotor levels with different behavioural granularity are implemented, a macro-level, which controls the movements of the agent in space, and a micro-level, which controls its eye movements. At each level, the same type of hybrid architecture and the same principle of information gain are used for sensorimotor control. The localisation performance of the system is tested with large sets of virtual rooms containing different mixtures of unique and non-unique objects. The results demonstrate that the system efficiently performs those exploratory motor actions that yield a maximum amount of information about the current environment. Localisation is typically achieved within a few steps. Furthermore, the computational complexity of the underlying computations is limited, and the system is robust with respect to minor variations in the spatial environments.     

Naming the parents of the THOG: Mental representation and reasoning

It was hypothesized that subjects misrepresent the THOG problem by confusing data and hypotheses. An abstract version of the problem in which the given exemplars and the hypothetical ones were designated by two different labels was used in three experiments. Experiment 1 showed that this version elicits a better performance than the standard version of the problem. Experiments 2 and 3 confirmed these results, by ruling out a possible alternative account of the facilitatory effect obtained in Experiment 1. The present results are discussed in relationship to the general issues of content effects and non-consequentialism in reasoning.     

Conditional reasoning, representation, and empirical evidence on a concrete task

This study examined interactions between empirical data, internal representations, and reasoning performance on a conditional reasoning task using a concrete apparatus. Subjects were asked an initial series of questions in order to determine the pattern of inferences they made after simple exposure to the apparatus. They were subsequently shown two different experimental manipulations designed to provide data about the internal structure of the apparatus without giving information about specific inferences. Some subjects did change their reasoning in response to the new data, although most remained stable throughout the experiment. These results are consistent with the idea that reasoning may require generation of an internal representation of a problem space. It was also concluded that the relation between reasoning and empirical evidence cannot be understood without supposing that evidence is often interpreted by subjects according to their reasoning patterns.     

Mental representation and hypothetico-deductive reasoning: The case of the THOG problem

Summary This article reports three experiments that deal with the source of the difficulty of Wason's (1977) THOG problem. The solution of this problem demands both the postulation of hypotheses and a combinatorial analysis of their consequences. Experiment 1 showed that the generation of the hypotheses is not in itself sufficient to solve the problem. Experiment 2 showed that a version presenting a plausible context for separating the level of data from that of hypotheses produced a better performance than both the original abstract version and a thematic version lacking the plausible context separating the levels. Experiment 3 gave evidence that this context can produce facilitation even with the geometric material of the classic version. This experiment also showed that a pictorial presentation of data and a verbal presentation of hypotheses affect performance negatively. The results demonstrate the role of problem representation in problem solving, and, in particular, the role of homogeneity in representing data and hypotheses in hypothetico-deductive reasoning.     

The mental representation and processes of spatial deductive reasoning with diagrams and sentences

This study has two main objectives. The first is to specify the nature of the mental representation and processes underlying spatial reasoning with diagrams and sentences. The second is to investigate whether mental representations reproduce geometrical relations relative to spatial reference frames. Forty participants solved 64 spatial reasoning problems that were displayed using diagrams or sentences. Problems varied with respect to their logical structure and geometrical content. We measured the premise's inspection times, the responses, and the response times. Problems were significantly (p < .01) easier to represent and solve when displayed as diagrams than as sentences, indicating that participants constructed mental models. Mental representations and spatial deductions also varied consistently with the geometrical content, suggesting that mental models reproduced this content relative to a viewer‐centred reference frame.     

The initial representation in reasoning towards an interpretation of conditional sentences

All accounts of human reasoning (whether presented at the symbolic or subsymbolic level) have to reckon with the temporal organization of the human processing systems and the ephemeral nature of the representations it uses. We present three new empirical tests for the hypothesis that people commence the interpretational process by constructing a minimal initial representation. In the case of if A then C the initial representation captures the occurrence of the consequent, C, within the context of the antecedent, A. Conditional inference problems are created by a categorical premise that affirms or denies A or C. The initial representation allows an inference when the explicitly represented information matches (e.g., the categorical premise A affirms the antecedent "A") but not when it mismatches (e.g., "not-A" denies A). Experiments 1 and 2 confirmed that people tend to accept the conclusion that "nothing follows" for the denial problems, as indeed they do not have a determinate initial-model conclusion. Experiment 3 demonstrated the other way round that the effect of problem type (affirmation versus denial) is reduced when we impede the possibility of inferring a determinate conclusion on the basis of the initial representation of both the affirmation and the denial problems.     

The initial representation in reasoning towards an interpretation of conditional sentences

All accounts of human reasoning (whether presented at the symbolic or subsymbolic level) have to reckon with the temporal organization of the human processing systems and the ephemeral nature of the representations it uses. We present three new empirical tests for the hypothesis that people commence the interpretational process by constructing a minimal initial representation. In the case of if A then C the initial representation captures the occurrence of the consequent, C, within the context of the antecedent, A. Conditional inference problems are created by a categorical premise that affirms or denies A or C. The initial representation allows an inference when the explicitly represented information matches (e.g., the categorical premise A affirms the antecedent “A”) but not when it mismatches (e.g., “not-A” denies A). Experiments 1 and 2 confirmed that people tend to accept the conclusion that “nothing follows” for the denial problems, as indeed they do not have a determinate initial-model conclusion. Experiment 3 demonstrated the other way round that the effect of problem type (affirmation versus denial) is reduced when we impede the possibility of inferring a determinate conclusion on the basis of the initial representation of both the affirmation and the denial problems.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Bayes nets and babies: infants' developing statistical reasoning abilities and their representation of causal knowledge

A fundamental assumption of the causal graphical model framework is the Markov assumption, which posits that learners can discriminate between two events that are dependent because of a direct causal relation between them and two events that are independent conditional on the value of another event(s). Sobel and Kirkham (2006) demonstrated that 8-month-old infants registered conditional independence information among a sequence of events; infants responded according to the Markov assumption in such a way that was inconsistent with models that rely on simple calculations of associative strength. The present experiment extends these findings to younger infants, and demonstrates that such responses potentially develop during the second half of the first year of life. These data are discussed in terms of a developmental trajectory between associative mechanisms and causal graphical models as representations of infants' causal and statistical learning.     

A computational account of children's analogical reasoning: balancing inhibitory control in working memory and relational representation

Theories accounting for the development of analogical reasoning tend to emphasize either the centrality of relational knowledge accretion or changes in information processing capability. Simulations in LISA (Hummel & Holyoak, 1997, 2003), a neurally inspired computer model of analogical reasoning, allow us to explore how these factors may collaboratively contribute to the development of analogy in young children. Simulations explain systematic variations in United States and Hong Kong children's performance on analogies between familiar scenes (Richland, Morrison & Holyoak, 2006; Richland, Chang, Morrison & Au, 2010). Specifically, changes in inhibition levels in the model's working-memory system explain the developmental progression in US children's ability to handle increases in relational complexity and distraction from object similarity during analogical reasoning. In contrast, changes in how relations are represented in the model best capture cross-cultural differences in performance between children of the same ages (3-4 years) in the United States and Hong Kong. We use these results and simulations to argue that the development of analogical reasoning in children may best be conceptualized as an equilibrium between knowledge accretion and the maturation of information processing capability.     

The power of representation and interpretation: Doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers

Abstract

Six highly familiar melodies were submitted to three transformations: reduction and two rhythmic group transformations. These three transformations offered the opportunity to compare the role of various means of melody recognition: melodic contour, harmonic structure, local surface cues. If melody recognition relies on melodic contour, an original melody would be easier to recognise after rhythmic group transformation than after reduction; the rhythmic group transformation, but not the reduction, preserves the melodic contour. If melody recognition depends on the harmonic structure, an original melody would be easier to recognise after reduction than after a rhythmic group transformation; the reduction, but not the rhythmic group transformation, respects the underlying harmonic structure. The results of two experiments, one with children and one with adults, showed that recognition was better for rhythmic group transformation but only when local surface cues were preserved, a result that could neither be predicted by the melodic contour hypothesis nor by the harmonic structure hypothesis. The results give support to the cue abstraction hypothesis, which suggests that melody recognition relies on the recognition of certain surface cues abstracted while hearing and which are then memorised. Recognition performances and speed of recognition served as dependent variables.     

Speed of reasoning and its relation to reasoning ability

The study investigates empirical properties of reasoning speed which is conceived as the fluency of solving reasoning problems. Responses and response times in reasoning tasks are modeled jointly to clarify the covariance structure of reasoning speed and reasoning ability. To determine underlying abilities, the predictive validities of two cognitive covariates, namely perceptual and executive attention, are investigated. A sample of N = 230 test takers completed a reasoning test, Advanced Progressive Matrices (APM), and attention tests indicating perceptual and executive attention. For modeling responses the two-parameter normal ogive model, and for modeling response times the two-parameter lognormal model was applied. Results suggest that reasoning speed is a unidimensional construct representing significant individual differences, and that reasoning speed and ability are negatively correlated but clearly distinguishable constructs. Perceptual and executive attention showed differential effects on reasoning speed and reasoning ability, i.e., reasoning speed is explained by executive attention only, while reasoning ability is explained by both covariates. Implications for the assessment of reasoning are discussed.     

Co-reference and reasoning

Memory &; Cognition - Co-reference occurs when two or more noun phrases refer to the same individual, as in the following inferential problem: Mark is kneeling by the fire or he is looking at...     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

The influence of complexity and reasoning direction on children's causal reasoning

Causal reasoning is the core and basis of cognition about the objective world. This experiment studied the development of causal reasoning in 86 3.5–4.5-year-olds using a ramp apparatus with two input holes and two output holes [Frye, D., Zelazo, P. D., & Palfai, T. (1995). Theory of mind and rule-based reasoning. Cognitive Development 10, 483–527]. Results revealed that: (1) children performed better on cause–effect inferences than on effect–cause inferences; (2) there was an effect of rule complexity such that uni-dimensional causal inferences were easier than bi-dimensional inferences which, in turn, were easier than tri-dimensional causal inferences; and (3) children's causal reasoning develops rapidly between the ages of age of 3.5 and 4 years.