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.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Individual differences in logical intuitions on reasoning problems presented under two-response paradigm

ABSTRACT

Studies on individual differences in susceptibility to cognitive biases have identified several cognitive dispositions which were thought to predict reasoning by contributing to the efficiency of analytic thought. However, hybrid models suggest that differences between reasoners may arise already in the intuitive stages of the reasoning process. To address this possibility, we examined standard individual difference measures, mindware instantiation, and conflict detection efficiency as predictors of the accuracy on conflict problems presented under a two-response paradigm. We found that almost half of conflict reasoning problems were solved correctly already at the initial response stage and that the individual differences in initial reasoning performance were predicted by participants’ cognitive reflection, mindware instantiation, and detection efficiency. The findings advance the specification of hybrid dual-process models and provide corroborating evidence that a part of the link between bias susceptibility and cognitive dispositions is due to differences in intuitive processing.     

A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

Metacognitive experience and transfer of logical reasoning

The experiments examine the influence of metacognitive experience on the transfer of logical processes in a problem solving setting. Subjects were presented with two versions of Wason's (1966) selection task. Although they were able to perform successfully on the concrete tasks (following a minimal explanation of the correct solution on an initial trial), the majority were not able to transfer a successful method to the abstract tasks. Verbalization during, or following, the concrete tasks produced substantial transfer effects however. It is suggested that verbalization may lead to an increased awareness of past behaviour, particularly of those aspects necessary for successful solution.     

Conditional reasoning processes in a logical deduction game

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind. An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind. A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (AC) and Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning.     

Mental model construction in linear reasoning: Evidence for the construction of initial annotated models

According to the mental model theory, reasoners build an initial model representing the information given in the premises. In the context of relational reasoning, the question arises as to which kind of representation is used to cope with indeterminate or multimodel problems. The present article presents an array of possible answers arising from the initial construction of complete explicit models, partial explicit models, partial implicit models, a single isomeric model, or a single annotated model. Predictions generated from these views are tested in two experiments that vary the problem structure and the number of models consistent with the premises. Analyses of the premise processing times, answering times and accuracy show that the annotated model yields the best fit of the data. Implications of these findings for the mental model theory as developed for relational reasoning are discussed.     

Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

Evidence that logical reasoning depends on conscious processing

Humans, unlike other animals, are equipped with a powerful brain that permits conscious awareness and reflection. A growing trend in psychological science has questioned the benefits of consciousness, however. Testing a hypothesis advanced by [Lieberman, M. D., Gaunt, R., Gilbert, D. T., & Trope, Y. (2002). Reflection and reflexion: A social cognitive neuroscience approach to attributional inference. Advances in Experimental Social Psychology, 34, 199-249], four studies suggested that the conscious, reflective processing system is vital for logical reasoning. Substantial decrements in logical reasoning were found when a cognitive load manipulation preoccupied conscious processing, while hampering the nonconscious system with consciously suppressed thoughts failed to impair reasoning (Experiment 1). Nonconscious activation (priming) of the idea of logical reasoning increased the activation of logic-relevant concepts, but failed to improve logical reasoning performance (Experiments 2a-2c) unless the logical conclusions were largely intuitive and thus not reliant on logical reasoning (Experiment 3). Meanwhile, stimulating the conscious goal of reasoning well led to improvements in reasoning performance (Experiment 4). These findings offer evidence that logical reasoning is aided by the conscious, reflective processing system.     

On the short horizon of spontaneous iterative reasoning in logical puzzles and games

A reasoning strategy is iterative when the initial conclusion suggested by a set of premises is integrated into that set of premises in order to yield additional conclusions. Previous experimental studies on game theory-based strategic games (such as the beauty contest game) observed difficulty in reasoning iteratively, which has been partly attributed to bounded individual rationality. However, this difficulty has also been attributed to problems in adequately representing the beliefs, actions, and goals of other agents involved in the games. In four experiments, we observed similar difficulties in iterative reasoning in a variety of puzzles and games that did not involve social interactions with other agents, where they can only be caused by individual cognitive boundaries. Our findings are consistent with the hypothesis that an intrinsic difficulty in iterative reasoning originates from a tendency not to revise our initial mental representation of a problem in light of the initial conclusions that it implies.     

Negative emotions can attenuate the influence of beliefs on logical reasoning

Although the influence of beliefs on logical reasoning is well documented, how emotions modulate the effect of beliefs during reasoning remains unexamined. We instructed participants to reason about syllogisms involving neutral or emotionally charged content. We also manipulated the consistency of beliefs with logical validity. When content was neutral, participants exhibited the belief-bias effect observed in previous studies of reasoning. In contrast, when confronted with emotionally charged content participants were less likely to be influenced by their beliefs. Our results suggest that under certain conditions negative emotions can attenuate the influence of beliefs during logical reasoning. Drawing on the affect infusion model, we attribute this effect to a more vigilant, systematic scrutiny of beliefs in the presence of negative emotions.     

A new experimental method to identify the process of logical reasoning

Abstract: A new method to identify the process of logical reasoning is presented. In spite of its indispensability and importance, we have had few methods to identify a subject's reasoning process, except that of using verbal protocol data. In this paper, for the purpose of objective identification of the reasoning process, we propose a new method to obtain the subject's reasoning process, in terms of a resolution tree for a task of which the logical structure can be written by first-order predicate logic. The results of an experiment using this method are presented. They revealed some interesting features of human reasoning such as, large differences between subjects, remarkable parallel processes, and the existence of subgoals for each subject.     

Mental imagery,reasoning, and blindness

Although reasoning seems to be inextricably linked to seeing in the “mind's eye”, the evidence is equivocal. In three experiments, sighted, blindfolded sighted, and congenitally totally blind persons solved deductive inferences based on three sorts of relation: (a) visuo-spatial relations that are easy to envisage either visually or spatially, (b) visual relations that are easy to envisage visually but hard to envisage spatially, and (c) control relations that are hard to envisage both visually and spatially. In absolute terms, congenitally totally blind persons performed less accurately and more slowly than the sighted on all such tasks. In relative terms, however, the visual relations in comparison with control relations impeded the reasoning of sighted and blindfolded participants, whereas congenitally totally blind participants performed the same with the different sorts of relation. We conclude that mental images containing visual details that are irrelevant to an inference can even impede the process of reasoning. Persons who are blind from birth—and who thus do not tend to construct visual mental images—are immune to this visual-impedance effect.     

The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

Mental imagery, reasoning, and blindness

Although reasoning seems to be inextricably linked to seeing in the “mind's eye”, the evidence is equivocal. In three experiments, sighted, blindfolded sighted, and congenitally totally blind persons solved deductive inferences based on three sorts of relation: (a) visuo-spatial relations that are easy to envisage either visually or spatially, (b) visual relations that are easy to envisage visually but hard to envisage spatially, and (c) control relations that are hard to envisage both visually and spatially. In absolute terms, congenitally totally blind persons performed less accurately and more slowly than the sighted on all such tasks. In relative terms, however, the visual relations in comparison with control relations impeded the reasoning of sighted and blindfolded participants, whereas congenitally totally blind participants performed the same with the different sorts of relation. We conclude that mental images containing visual details that are irrelevant to an inference can even impede the process of reasoning. Persons who are blind from birth—and who thus do not tend to construct visual mental images—are immune to this visual-impedance effect.     

Syllogistic reasoning in varied narrative contexts: Aspects of logical and linguistic development

This experimental study examined the effects on syllogistic reasoning in grades 6 and 12 of certain contextual narrative variables. The experimental task consisted of 27 varied syllogistic problems based on information contained in three narrative texts—a fantasy passage, a realistic passage, and a contractual passage. Versions of these texts were constructed for each group reading level. Analysis of the data revealed several significant interactions between subject groups and treatment variables. In particular, younger subjects performed better than grade 12 subjects on problems following the fantasy narrative, while the older subjects did better with the other two passages. The results suggest that some orthodox views about concrete-versus formal-operational reasoning abilities and about the distinction between abstract and concrete materials need to be reassessed within a discourse-processing framework that is sensitive to the discourse worlds in which problems are embedded.The author wishes to acknowledge the support of an Isaak Walton Killam Doctoral Scholarship for this research.     

Cognitive and AI models of reasoning

Although relatively few in number, cognitive neuroscience studies of reasoning have two general implications for cognitive theories of deduction. First, an important distinction among these theories is whether they focus on the effect of personally relevant content on the processes and representations underlying deductive reasoning. Evidence is reviewed indicating that there is a neuroanatomical basis for both content-independent and content-dependent theories of deduction. Clinical and neuroimaging studies appear to show that content-independent reasoning is mediated by the left hemisphere, whereas content-dependent reasoning is mediated by regions in the right hemisphere and the bilateral ventromedial frontal cortex. In normal subjects, reasoning is likely to be based on contributions from both hemispheres. Second, clinical evidence indicates that the visuospatial processes used in deductive reasoning are mediated by the posterior areas of the left hemisphere, and that verbal and visuospatial reasoning representations overlap at the neuroanatomical level. This finding weighs against the claims of mental-model theory that deduction involves a significant nonverbal component. Further investigation, particularly with contemporary neuroimaging methods, is needed to test these preliminary conclusions.