Two experiments investigated the mental representation of spatial and nonspatial two-dimensional problems. The experiments were designed to contrast opposite predictions of the model theory of reasoning and the formal rules of inference theories. Half of the problems required more inferential steps but only one model, whereas the other half required fewer inferential steps but two models. According to the inference rules, theory problems that require more inferential steps should be harder, whereas the model-based theory predicts that problems that require two (...) models should be harder. In Experiments 1a and 1b we measured the problem solving time and the percentage of errors. In Experiments 2a and 2b the problems were presented segmented in two different displays. We measured the comprehension time for each display, the question answering times, and the percentage of errors. The results of all experiments supported the model theory predictions in both spatial and nonspatial domains. (shrink)

This article reports on a study of children's deductive reasoning in solving novel relational problems. Detailed protocols were obtained from 264 children (aged 9- 12 years) who verbalised their thinking as they solved the problems. The study included the development of a three-phase theory based on Johnson-Laird and Byrne's mental models perspective, but with some distinct modifications. These include a focus on the relational complexity entailed in model construction and in premise integration, and the advancement of four reasoning principles that (...) are applied throughout problem solution (in contrast to Johnson-Laird's falsification processes as the hallmark of deductive reasoning). The reported case studies and the results of statistical analyses supported predictions arising from the proposed theory, including the key role of the reasoning principles. The results also showed that problem difficulty is a function of relational complexity, not of the number of models to be constructed, as argued by Johnson-Laird and Byrne. (shrink)

This study investigated individual differences in the belief bias effect, which is the tendency to accept conclusions because they are believable rather than because they are logically valid. It was observed that the extent of an individual's belief bias effect was unrelated to a number of measures of reasoning competence. Instead, as predicted by mental models theory, it was related to a person's ability to generate alternative representations of premises: the more alternatives a person generated, the less likely they were (...) to show a belief bias effect. In contrast to belief effects, which were predicted by the number of alternatives generated, scores on logical reasoning tasks were predicted by an individual's understanding of the concept of logical necessity. These two mediating variables, ability to generate alternatives and understanding of logical necessity, were themselves predicted by similar variables, such as cognitive motivation and abstract reasoning ability. Our findings strongly support the mental models interpretation of the belief bias effect, and suggest that individual differences in this effect are associated with a specific ability to generate alternatives, rather than with a general logical competence. (shrink)

In certain contexts reasoners reject instances of the valid Modus Ponens and Modus Tollens inference form in conditional arguments. Byrne (1989) observed this suppression effect when a conditional premise is accompanied by a conditional containing an additional requirement. In an earlier study, Rumain, Connell, and Braine (1983) observed suppression of the invalid inferences "the denial of the antecedent" and "the affirmation of the consequent" when a conditional premise is accompanied by a conditional containing an alternative requirement. Here we present three (...) experiments showing that the results of Byrne (1989) and Rumain et al. (1983) are influenced by the answer procedure. When reasoners have to evaluate answer alternatives that only deal with the inferences that can be made with respect to the first conditional, then suppression is observed (Experiment 1). However, when reasoners are also given answer alternatives about the second conditional (Experiment 2) no suppression is observed. Moreover, contrary to the hypothesis of Byrne (1989), at least some of the reasoners do not combine the information of the two conditionals and do not give a conclusion based on the combined premise. Instead, we hypothesise that some of the reasoners have reasoned in two stages. In the first stage, they form a putative conclusion on the basis of the first conditional and the categorical premise, and in the second stage, they amend the putative conclusion in the light of the information in the second premise. This hypothesis was confirmed in Experiment 3. Finally, the results are discussed with respect to the mental model theory and reasoning research in general. (shrink)

An application of the Method of Analysis of Relational Complexity (MARC) to suppositional reasoning in the knight-knave task is outlined. The task requires testing suppositions derived from statements made by individuals who either always tell the truth or always lie. Relational complexity (RC) is defined as the number of unique entities that need to be processed in parallel to arrive at a solution. A selection of five ternary and five quaternary items were presented to 53 psychology students using a pencil (...) and paper format. A computer-administered version was presented to 50 students. As predicted, quaternary problems were associated with higher error rates and longer response times than ternary problems. The computer-administered form was more difficult than the pencil and paper version of the test. These differences are discussed in terms of RC theory and alternative processing accounts. Together, they indicate that the relational complexity metric is a useful and parsimonious way to quantify complexity of reasoning tasks. (shrink)

Johnson-Laird's mental models theory claims that reasoning is a semantic process of construction and manipulation of models in working memory of limited capacity. Accordingly, both a deduction and a given interpretation of a premise would be all the harder the higher the number of models they require. The purpose of the present experiment was twofold. First, it aimed to demonstrate that the interpretation of if...then conditional sentences in children (third, sixth, and ninth graders) evolves as a function of the number (...) of models the children can produce. We proposed a theory of conditional reasoning development that hypothesises a developmental trend of three successive levels of interpretations underlain by one, two, and then three models, i.e. conjunctive, biconditional, and conditional respectively. Second, we aimed to show that these different levels correlate with working memory capacities: the higher the working memory span, the higher the number of models underlying the conditional interpretation. These two hypotheses were verified, supporting the mental models theory. The results are compared with the rival theory of mental logic. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with determinate relations and not (...) with indeterminate ones. However, (a) there is no reason to presuppose that a rule-based procedure could not deal with indeterminate relations, and (b) applying a rule-based procedure to indeterminate relations should result in greater difficulty. Hence, none of the recent articles devoted to relational reasoning currently presents a conclusive case for discarding IRA by using the well-known determinate vs indeterminate problems comparison. (shrink)

The aim of the present research was to develop a difficulty model for logical reasoning problems involving complex ordered arrays used in the Graduate Record Examination. The approach used involved breaking down the problems into their basic cognitive elements such as the complexity of the rules used, the number of mental models required to represent the problem, and question type. Weightings for these different elements were derived from two experimental studies and from the reasoning literature. Based on these weights, difficulty (...) models were developed which were then tested against new data. The models had excellent predictive validity and showed the relative influence of rule based factors and factors relating to the number of underlying models. Different difficulty models were needed for different question types, suggesting that people used a variety of approaches and, at a wider level, that both mental models and mental rules may be used in reasoning. (shrink)