Multiple explanations for multiply quantified sentences: are multiple models necessary?

Johnson-Laird, Byrne, and Tabossi (1989) presented a theory of deductive reasoning for inference problems using multiply quantified premises (e.g., "All of the squares are connected to some of the circles"). Their theory classifies such problems into those that require subjects to construct only 1 mental model and those that require multiple models. They presented data that corroborate the theory. This article shows that Johnson-Laird et al.'s major results can be explained without invoking mental models or, in fact, deductive reasoning at all. Furthermore, it is demonstrated that, contrary to the assumption of these authors, reversing the order of the quantifiers in a multiply quantified sentence may produce a sentence that is both more difficult to comprehend and more ambiguous. Finally, some implications for theories of how people understand multiply quantified sentences are noted.     

The influence of relational complexity and strategy selection on children's reasoning in the Latin Square Task

The present study focused on children's deductive reasoning when performing the Latin Square Task, an experimental task designed to explore the influence of relational complexity. Building on Birney, Halford, and Andrew's (2006) research, we created a version of the task that minimized nonrelational factors and introduced new categories of items. The results of two experiments conducted with school-aged children yielded an apparent dilution of complexity effects and suggest that specific inferential strategies can reduce the relational complexity that children need to process. A theoretical account is proposed emphasizing the influence of adaptive selection of strategies that mediate processing capacity constraints in reasoning development.     

Paralogical reasoning: Evans, Johnson-Laird, and Byrne on liar and truth-teller puzzles

People's performance on knight/knave problems is deliberate. They make assumptions, draw deductive inferences from them, and evaluate the consequences of these inferences. In an initial paper on this topic (Rips, 1989), I proposed a model for a subset of such problems that depend on sentential reasoning. The main component of the model is a set of natural-deduction rules, drawn from prior work on propositional inference. This natural-deduction framework seems well suited to explain the reasoning that subjects display on these problems, since it incorporates a mechanism for making assumptions and following them up. Moreover, the number of assumptions and rule applications needed to solve a problem yields an intuitively appealing measure of how difficult the problem should be. In accord with this prediction, the experiments found increases in error rates and reaction times as a function of the assumptions-plus-inferences measure. In their note, Johnson-Laird and Byrne sketch a possible alternative. Their account posits five processing strategies tailored to this problem domain and a mechanism for evaluating sentential arguments based on mental models. The mental-model component is a variation on the usual truth-table method, where individual models correspond to truth-table rows. The main prediction of this component is that the more models subjects must consider, the harder the problem. However, the experiment reported here found no evidence for this prediction. Problems with larger numbers of models do not yield higher error rates than those with few. What does cause difficulties for subjects is scope relations among connectives, a fact that inference-rule theories can easily explain. Given these findings, it's not surprising that the predictive burden for knight/knave problems must be carried by Johnson-Laird and Byrne's strategies, rather than by mental models. These strategies control the order in which subjects consider parts of the problem, and they provide possible stopping points. There are, however, several difficulties with these strategies. Of their four new strategies, Johnson-Laird and Byrne offer no evidence at all for two of them. Of the remaining two, only one accounts for a significant proportion of the variance when allowance is made for confounding variables. Moreover, all four strategies are ad hoc, rather than being derived from some more general theory. Certainly, much remains to be done in filling out the picture of how such problems are handled, as both Evans and Johnson-Laird and Byrne point out.(ABSTRACT TRUNCATED AT 400 WORDS)     

Relational integration in older adults

Reasoning requires making inferences based on information gleaned from a set of relations. The relational complexity of a problem increases with the number of relations that must be considered simultaneously to make a correct inference. Previous work (Viskontas, Morrison, Holyoak, Hummel, & Knowlton, ) has shown that older adults have difficulty integrating multiple relations during analogical reasoning, especially when required to inhibit irrelevant information. We report two experiments that examined the ability to integrate multiple relations in younger, middle-aged, and older adults performing two other reasoning tasks. These tasks systematically varied relational complexity, and required either inductive reasoning (a version of the Raven's Matrices Task) or transitive inference. Our results show that as people age they have increasing difficulty in solving problems that require them to integrate multiple relations. This difficulty may stem from a decrease in working memory capacity.     

Cue redundancy and extra logical inferences in a deductive reasoning task

This study investigated the influence of extraexperimental knowledge on deductive reasoning. Two groups of subjects solved modified abstract or concrete versions of Wason’s (1966) four-card selection problem in which the “if-then” implication rule provided the sole cue to underlying logical structure. Six other groups solved abstract or concrete comparison problems in which additional information was supplied by varying the relationship between antecedents and consequents in a manner consistent with logical structure. Selection responses and subjects’ explanations were analyzed using log-linear models of data arrayed in multiway contingency tables. Results showed improved performance for concrete over abstract problems and for both abstract and concrete problems that included relational information. Subjects capitalized upon the redundancy between the implication rule and the relational cues to reason effectively with either abstract or concrete stimuli.     

The Effect of an Irrelevant Premise on Temporal and Spatial Reasoning

The mental model theory of reasoning postulates that individuals reason by constructing models of the situation described by premises. The more models reasoners have to build, the harder a problem will be. Byrne and Johnson-Laird (1989) confirmed this prediction with spatial problems and Schaeken et al. (1996 a, b) with temporal ones. There is, however, a problem with these studies. All the multiple-model problems and some of the one-model problems contained an irrelevant premise. As Rips (1994) argues, it is possible that an irrelevant premise would complicate the search for a derivation. The present paper reports an experiment which explicitly manipulated the presence of such an irrelevant premise in both one-model and multiple-model problems. The results corroborate the predictions of the mental model theory.     

The role of relational reasoning in children's addition concepts

The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.     

Model theory of deduction: a unified computational approach

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.
Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal foundation. We validate the theory through a computational model (UNICORE) which allows fine-grained predictions of subjects' performance in different reasoning domains.
The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.
Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure.     

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”.     

Beyond belief bias: Reasoning from conceptual structures by mental models manipulation

Mental models constitute an alternative to the rule-based systems in the explanation of human reasoning (Johnson-Laird, 1983). In this paper, we claim that the concept of believability generally used to categorize content and context effects is of little use within a semantic theory. Thus, we propose the use of categories that are directly extracted from subjective relations among concepts within the reasoning problem. We demonstrate that manipulations based on this kind of categorization produce predictable patterns of responses in reasoning problems. We present two experiments to test our predictions, using conditional and syllogistic reasoning problems, and in both cases, we demonstrate the influence of conceptual knowledge not only in natural contexts, but also in experimentally created artificial contexts.     

Evidence for Mental-model-based Reasoning: A Comparison of Reasoning with Time and Space Concepts

Johnson-Laird (1983) has argued that spatial reasoning is based on the construction and manipulation of mental models in memory. The present article addresses the question of whether reasoning about time relations is constrained by the same factors as reasoning about spatial relations. An experiment is reported that explored the similarities and the differences in the performance of subjects in comparable spatial and temporal reasoning tasks. The results indicated that, in both the temporal and the spatial content domains, the data were in agreement with the view that subjects solved problems by constructing models in memory rather than with a logical rule conceptualisation of reasoning. An analysis of the premise-reading times on the basis of premise-linking order provided support for an on-line process of mental models construction, and offered an explanation for the finding that spatial problems that did require an inference of transitivity were easier than problems that did not. No essential differences in processing and performance were observed across the two content domains, although in the time domain the correctness data were in agreement with both the mental models theory and the logical rules view. The results are discussed with respect to the mental models theory and the structural characteristics of the problems.     

The effects of formal order and spatial content on reasoning in three dimensions

This study investigates the effects of formal order and spatial content on reasoning in three dimensions in view of the Formal Rules theory and the Mental Models theory of spatial reasoning. Twenty‐six subjects solved 144 spatial deductive problems that varied by the formal order of the entities (referential order, referential continuity) and the spatial content (dimension, orientation, and direction). There were two dependant variables: the correct responses and their response times. The number of mental models and the formal derivations underlying the deductions allowed comparison of opposite predictions made by the Formal Rules theory and the Mental Models theory of spatial reasoning. The results overwhelmingly supported the Mental Models theory's predictions. The effects of referential order showed that problems yielding two possible mental models were significantly more difficult than problems based on one mental model, although the former problems involved a shorter formal derivation than the latter. The effects of referential continuity also generalized the Mental Models theory's prediction to reasoning in all three dimensions. The effects of referential continuity showed that problems that required independent layouts in memory were reliably more difficult than problems that allowed the continuous integration of the entities in a mental model. We obtained these results despite the fact that the former condition required a shorter formal derivation than the latter. The effects of spatial content were also reliable despite the fact that the formal derivations were the same across spatial content. Thus, spatial deductions were significantly easier to make in 1D than in 2D and in 2D than 3D. Deductions were also significantly easier to make from left to right along the horizontal axis of a mental model, and from top to bottom along the vertical axis rather than from the respective opposite directions. The effects of spatial content suggest that mental models reproduce spatial relations relative to reference frames.     

Dual systems Competence ←-→ Procedural processing: A relational developmental systems approach to reasoning

Many current psychological models of reasoning minimize the role of deductive processes in human thought. In the present paper, we argue that deduction is an important part of ordinary cognition and we propose that a dual systems Competence ←-→ Procedural processing model conceptualized within relational developmental systems theory offers the most coherent and productive framework for integrating and explaining the sometimes conflicting findings on the development of deductive reasoning across the lifespan. This model invokes a distinction that is quite similar to, though not identical with, the system 2–system 1 dichotomy employed in other dual systems models. In addition, the Competence ←-→ Procedural processing model maintains the more specific distinction between algorithmic and reflective subsystems of system 2. In this account, the algorithmic system is represented as a kind of mental logic while the reflective system is the seat of practical and epistemic self-regulation, including emergent epistemic and metalogical norms. While the proposed systems of mind often appear as split-off component features in other dual systems models, relational developmental systems theory conceives of them as the highly complex and relationally integrated outcome of a self-organizing and self-regulating adaptive developmental process.     

Testing the Mental Model Theory of Propositional Reasoning

Johnson-Laird, Byrne, and Schaeken (1992) present a theory of propositional reasoning by mental models. The present study provides a comprehensive test of the predictions of that theory for the difficulty of simple disjunctive and conditional inferences. The results are largely consistent with the complex pattern of predictions. They are discussed in the light of recently proposed modifications of the original theory.     

Cultural Difference in Stereotype Perceptions and Performances in Nonverbal Deductive Reasoning and Creativity

A total of 182 undergraduate students from China and the United States participated in a study examining the presence of stereotypical perceptions regarding creativity and deductive reasoning abilities, as well as the influence of stereotype on participants' performance on deductive reasoning and creativity in nonverbal form. The results showed that participants from both China and the United States believed that Americans have better creativity abilities than Chinese and that Chinese have better deductive reasoning skills than Americans. Significant cultural difference in the performances on the measures of creativity was found. The cultural difference in deductive reasoning was found between Chinese participants in China and the Caucasian (not the Asian) participants in the United States, which were somewhat congruent to the stereotypical perceptions. However, the study did not find that stereotypic perceptions directly influenced participants' performance on deductive reasoning and creativity.     

Children's development of analogical reasoning: insights from scene analogy problems

We explored how relational complexity and featural distraction, as varied in scene analogy problems, affect children's analogical reasoning performance. Results with 3- and 4-year-olds, 6- and 7-year-olds, 9- to 11-year-olds, and 13- and 14-year-olds indicate that when children can identify the critical structural relations in a scene analogy problem, development of their ability to reason analogically interacts with both relational complexity and featural distraction. Error patterns suggest that children are more likely to select a distracting object than to make a relational error for problems that present both possibilities. This tendency decreases with age, and older children make fewer errors overall. The results suggest that changes in analogical reasoning with age depend on the interplay among increases in relational knowledge, the capacity to integrate multiple relations, and inhibitory control over featural distraction.     

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。     

Complexity of categorical syllogisms: An integration of two metrics

The complexity of categorical syllogisms was assessed using the relational complexity metric, which is based on the number of entities that are related in a single cognitive representation. This was compared with number of mental models in an experiment in which adult participants solved all 64 syllogisms. Both metrics accounted for similarly large proportions of the variance, showing that complexity depends on the number of categories that are related in a representation of the combined premises, whether represented in multiple mental models, or by a single model. This obviates the difficulty with mental models theory due to equivocal evidence for construction of more than one mental model. The “no valid conclusion” response was used for complex syllogisms that had valid conclusions. The results are interpreted as showing that the relational complexity metric can be applied to syllogistic reasoning, and can be integrated with mental models theory, which together account for a wide range of cognitive performances.     

How do investors make predictions? Insights from analogical reasoning research

Previous work on investor decision making has focused almost exclusively on information specific to the company being judged. Consequently, every decision is viewed as a novel event, disconnected from the investor's existing knowledge. In this study, the analogical reasoning literature provides the theoretical support for arguing that investors frequently utilize existing knowledge as a basis for generating predictions about a company's future. The specific proposal is that investors transfer their existing knowledge via two different forms of analogical reasoning. The first, relational reasoning, is based primarily on structural correspondence between a novel company and an existing schema. The second, literal similarity reasoning, is based primarily on surface correspondence of a novel company and a previously encountered company. Our theoretical framework is tested in a study in which experienced investors predict the outcome of a novel company's strategy after reading about the experiences of other companies who implemented a similar strategy. The results are consistent with the occurrence of both relational and literal similarity reasoning, with relational reasoning emerging as the dominant approach to generating investors' predictions. Copyright © 2000 John Wiley & Sons, Ltd.     

Reinstatement, floating conclusions, and the credulity of Mental Model reasoning

Johnson-Laird and coworkers’ Mental Model theory of propositional reasoning is shown to be somewhere in between what logicians have defined as “credulous” and “skeptical” with respect to the conclusions it draws on default reasoning problems. It is then argued that in situations where skeptical reasoning has been shown to lead to problematic conclusions due to not being skeptical enough, the bolder Mental Model theory will likewise make counterintuitive predictions. This claim is supported by the consideration of two of those situations, namely problems involving reinstatement and floating conclusions. It is discussed how the recent “principle of pragmatic modulation” could be a first step in order to overcome the mild credulity of Mental Model reasoning.