Logical knowledge and ordinary reasoning

This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.     

Confidence and accuracy in deductive reasoning

In two experiments, we investigated the relationship between confidence and accuracy in syllogistic reasoning. Participants judged the validity of conclusions and provided confidence ratings twice for each problem: once quickly and again after further deliberation. Correlations between confidence and accuracy were small or nonexistent. In addition, confidence and accuracy were mediated by different variables. Confidence judgments appeared to reflect external cues, so that confidence was greater when the participants were allowed additional time to think about the problem, as well as when the conclusion was either believable or unbelievable, rather than neutral. In contrast, accuracy changed little as a function of the amount of time available and did not differ for believable and neutral problems. These data support a model in which initial decisions are made quickly, on the basis of heuristic cues, and analytic processes are used to justify or rationalize the earlier decision.     

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.     

Individual differences in deductive reasoning

Three studies are reported, which examined individual differences in deductive reasoning as a function of intellectual ability and thinking style. Intellectual ability was a good predictor of logical performance on syllogisms, especially where there was a conflict between logic and believability. However, in the first two experiments there was no link between ability and performance on indicative selection tasks, in sharp contrast to previous research. This correlation did, however, return in the final study. Our data are consistent with the claim that the correlation with logical accuracy on abstract selection tasks is found primarily with participants of relatively high ability. At lower levels, pragmatically cued responses are given but those of slightly higher ability divorce the rule from the scenario and respond consistently (though incorrectly) across problems. Self-report questionnaires were generally poor predictors of performance, but a measure of the ability to generate alternative representations proved an excellent predictor. These results are consistent with a mental models approach to reasoning and also have implications for the debate about human rationality.     

Positive and negative cue redundancy in multiple cue probability learning

In two separate experiments, 80 introductory psychology students completed a two-cue probability learning task in which cue intercorrelation was positive or negative and cue validities were positive or negative. Results indicated that Ss did not learn the negative validity tasks. In addition, there were no significant differences between groups in achievement due to cue intercorrelation within any one experiment. However, the positive redundancy groups were significantly more consistent in the employment of their decision strategy than the negative redundancy groups when cue validities were positive. The negative redundancy groups were superior to positive redundancy groups in matching; again, when cue validities were positive.     

Logical reasoning,world knowledge,and mental imagery: Interconnections in cognitive processes

To better understand the role of problem content in verbal reasoning, the effect of two aspects of problem representation on conditional reasoning was examined. Specifically, this study focused on the effect of availability of knowledge schemata and mental imagery on recognition of indeterminacy. Four groups of 20 adults solved syllogisms that varied in imagery value and in tendency to access knowledge schemata (assessed by ratings of the relatedness of antecedent and consequent clauses of premises). When problems both were high in imagery value and had related clauses, performance was significantly better on indeterminate syllogisms. Access to schemata may permit elaborative processing and the generation of counterexamples to invalid inferences; imagery may support representation of problems and generation of elaborative information in memory.     

Logical reasoning in schizotypal personality

It was examined whether psychotic-like personality traits in a sample of 205 college students could predict logical reasoning deficits, akin to those seen in schizophrenia. The participants were tested on their ability to assess the logical validity of premises (Logical Reasoning Task), and completed a multi-dimensional schizotypy inventory (O-LIFE). Low accuracy was associated with increased levels of disorganized schizotypy (‘Cognitive Disorganization’), while elevated errors were associated with increased levels of positive (‘Unusual Experiences’), negative (‘Introvertive Anhedonia’) and impulsive (‘Impulsivity Non-conformity’) schizotypy. Nevertheless, multiple regression analyses revealed that negative schizotypy was retained as the only significant predictor after performance was corrected for random guessing, and the contribution of the average amount of time spent on each premise was controlled. The results suggest that, although most schizotypy dimensions have a detrimental effect on reasoning performance, possibly due to disadvantageous test-taking strategies, negative schizotypy is the most reliable predictor of logical reasoning deficits. It is proposed that social/interpersonal schizotypal traits, like negative symptoms of schizophrenia, are accompanied by deficient executive functions of working memory, which appear to undermine, inter alia, logical reasoning processing.     

Differential involvement of left prefrontal cortex in inductive and deductive reasoning

While inductive and deductive reasoning are considered distinct logical and psychological processes, little is known about their respective neural basis. To address this issue we scanned 16 subjects with fMRI, using an event-related design, while they engaged in inductive and deductive reasoning tasks. Both types of reasoning were characterized by activation of left lateral prefrontal and bilateral dorsal frontal, parietal, and occipital cortices. Neural responses unique to each type of reasoning determined from the Reasoning Type (deduction and induction) by Task (reasoning and baseline) interaction indicated greater involvement of left inferior frontal gyrus (BA 44) in deduction than induction, while left dorsolateral (BA 8/9) prefrontal gyrus showed greater activity during induction than deduction. This pattern suggests a dissociation within prefrontal cortex for deductive and inductive reasoning.     

Different developmental patterns of simple deductive and probabilistic inferential reasoning

In three studies, we examined simple counterexample-based and probabilistic reasoning in children 6, 7, and 9 years of age. In the first study, participants were asked to make conditional (if-then) inferences under both categorical (certain or uncertain) and probabilistic instructions. Results showed that 6-year-olds respond to both forms of inference in similar ways, but whereas probabilistic conditional inferences showed little development over this period, categorical inferences clearly improved between 6 and 7 years of age. An analysis of the children's justifications indicated that performance under categorical instructions was strongly related to counterexample generation at all ages, whereas this was true only for the younger children for inferences under probabilistic instructions. These findings were replicated in a second study, using problems that referred to concrete stimuli with varying probabilities of inference. A third study tested the hypothesis that children confused probability judgments with judgments of confidence and demonstrated a clear dissociation between these two constructs. Overall, these results show that children are capable of accurate conditional inferences under probabilistic instructions at a very early age and that the differentiation between categorical and probabilistic conditional reasoning is clear by at least 9 years ofage. These results are globally consistent with dual-process theories but suggest some difficulties for the way that the analytic-heuristic distinction underlying these theories has been conceptualized.     

Sources of difficulty in deductive reasoning: The THOG task

The THOG task presents four designs constructed from two shapes and two colours. Subjects are told that the experimenter has written down one of the shapes and one of the colours and are provided the rule that if, and only if, any design has either the shape or the colour, but not both, written down, then it is a THOG. Finally, they are given an exemplar and are asked to classify the remaining designs. Successful solution requires construction of hypotheses, reasoning under each hypothesis, and comparison of the results under each to reach a final conclusion. Few subjects are able to provide adequate responses on the standard version of the task. We present the results of four experiments, with 160 undergraduates each presented with one of eight versions of the task. Experiments 1 and 2 indicate that (1) some subjects think that the properties that are written down are identical to those of the exemplar, although these are not the same subjects who exhibit the modal error pattern, (2) many subjects correctly understand the disjunction of the rule but fail to consider the hypotheses, and (3) poor initial encoding of the problem is not easily corrected. Experiment 3 investigates the sufficiency of the claim of Griggs and Newstead (1982) that appropriate problem solution follows from explicit presentation of all problem information (including use of positive labels for properties that are not written down), and Experiment 4 investigates the necessity of the claim. The results of Experiments 3 and 4 show that presenting positive category labels does increase the frequency of correct solution; however, positive category labels are not necessary for such improvement. Separation of the labels of the THOG rule from those of the exemplar, or informing subjects that only one other design is a THOG, also increases the frequency of successful solution. The results suggest that many people have some fairly sophisticated reasoning skills. but application of these skills is easily discouraged when the features of the task lead to poor initial encoding.     

Thinking about THOG: Sources of error in a deductive reasoning problem

Summary Three experiments are reported which investigated performance on a number of variants of the THOG problem. Collectively, these experiments indicated that subjects are more accurate (a) when the problem is phrased in a way that clearly separates the properties of the positive instance provided from the properties about which hypotheses must be generated; and (b) when subjects are required to generate hypotheses about what might be the chosen properties. It is suggested that people have little difficulty in carrying out the various thought processes that are required to reach the correct solution to the standard THOG problem, but that it is beyond most people to carry out all of these processes simultaneously.     

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.     

Effects of directionality in deductive reasoning: II. Premise integration and conclusion evaluation

Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given-new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model.     

Shared and distinct cue utilization for metacognitive judgements during reasoning and memorisation

Metacognitive research is dominated by meta-memory studies; meta-reasoning research is nascent. Accessibility – the number of associations for a stimulus – is a reliable heuristic cue for Feeling of Knowing when answering knowledge questions. We used a similar cue, subjective accessibility, for exposing commonalities and differences between meta-reasoning and meta-memory. In Experiment 1, participants faced solvable Compound Remote Associate problems mixed with unsolvable random word triads. We collected initial Judgement of Solvability (iJOS), final JOS (fJOS) and confidence. Experiment 2 focused on confidence, controlling for potential interactions among judgements. In Experiment 3, the participants memorised the same triads and rated Ease of Learning and Judgement of Learning. sAccessibility was associated with all judgements. Notably, it reliably predicted memory judgements and confidence in the provided solutions. However, it was unreliable for judging solvability (iJOS and fJOS). The findings highlight the importance of studying meta-reasoning for exposing the biasing factors in reasoning processes and for getting a broad perspective on metacognitive processes.