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.     

Conditional reasoning by mental models: chronometric and developmental evidence

The aim of this article is to verify two predictions resulting from the mental models theory of conditional reasoning. First, the denial of antecedent (DA) and modus tollens (MT) inferences should take longer to verify than modus ponens (MP) and affirmation of consequent (AC) because the former require subjects to flesh out the initial model whereas the latter do not. This prediction was confirmed in two reaction time experiments in adults. In line with Evans' proposal (Evans, J. St. B. T. (1993). The mental model theory of conditional reasoning: critical appraisal and revision. Cognition, 48, 1-20), there was a strong directionality effect: inferences from antecedent to consequent (MP and DA) took less time to verify than the inferences in the opposite direction (AC and MT). Second, the development of conditional reasoning should result from the increasing capacity to construct and coordinate more and more models. As a consequence, the pattern of conditional inference production should evolve with age from a one-model conjunctive pattern (production of MP and AC more frequent than DA and MT) to a three-model conditional production pattern (higher production rate for MP and MT than for DA and AC). This prediction was confirmed using an inference production task in children, adolescents, and adults.     

Asymmetries in predictive and diagnostic reasoning

In this article, we address the apparent discrepancy between causal Bayes net theories of cognition, which posit that judgments of uncertainty are generated from causal beliefs in a way that respects the norms of probability, and evidence that probability judgments based on causal beliefs are systematically in error. One purported source of bias is the ease of reasoning forward from cause to effect (predictive reasoning) versus backward from effect to cause (diagnostic reasoning). Using causal Bayes nets, we developed a normative formulation of how predictive and diagnostic probability judgments should vary with the strength of alternative causes, causal power, and prior probability. This model was tested through two experiments that elicited predictive and diagnostic judgments as well as judgments of the causal parameters for a variety of scenarios that were designed to differ in strength of alternatives. Model predictions fit the diagnostic judgments closely, but predictive judgments displayed systematic neglect of alternative causes, yielding a relatively poor fit. Three additional experiments provided more evidence of the neglect of alternative causes in predictive reasoning and ruled out pragmatic explanations. We conclude that people use causal structure to generate probability judgments in a sophisticated but not entirely veridical way.     

Updating situation models

The authors examined how situation models are updated during text comprehension. If comprehenders keep track of the evolving situation, they should update their models such that the most current information, the here and now, is more available than outdated information. Contrary to this updating hypothesis, E. J. O'Brien, M. L. Rizzella, J. E. Albrecht, and J. G. Halleran (1998) obtained results suggesting that outdated or incorrect information may still influence the comprehension process. The authors of the current study demonstrate that the nature of E. J. O'Brien et al.'s materials were the likely cause of this pattern of results. Hence, the current authors constructed materials that circumvent identified confounds and in a reading-time experiment obtained evidence supporting the here-and-now hypothesis.     

Falsifying mental models: Testing the predictions of theories of syllogistic reasoning

Four experiments are reported that tested the claim, drawn from mental models theory, that reasoners attempt to construct alternative representations of problems that might falsify preliminary conclusions they have drawn. In Experiment 1, participants were asked to indicate which alternative conclusion(s) they had considered in a syllogistic reasoning task. In Experiments 2-4, participants were asked to draw diagrams consistent with the premises, on the assumption that these diagrams would provide insights into the mental representation being used. In none of the experiments was there any evidence that people constructed more models for multiple-model than for single-model syllogisms, nor was there any correlation between number of models constructed and overall accuracy. The results are interpreted as showing that falsification of the kind proposed by mental models theory may not routinely occur in reasoning.     

Phonological and visual distinctiveness effects in syllogistic reasoning: Implications for mental models theory

Two experiments are reported in which the representational distinctiveness of terms within categorical syllogisms was manipulated in order to examine the assumption of mental models theory that abstract, spatially based representations underpin deduction. In Experiment 1, participants evaluated conclusion validity for syllogisms containing either phonologically distinctive terms (e.g., harks, paps, and fids) or phonologically nondistinctive terms (e.g., fuds, fods, and feds). Logical performance was enhanced with the distinctive contents, suggesting that the phonological properties of syllogism terms can play an important role in deduction. In Experiment 2, participants received either the phonological materials from Experiment 1 or syllogisms involving distinctive or nondistinctive visual contents. Logical inference was again enhanced for the distinctive contents, whether phonological or visual in nature. Our findings suggest a broad involvement of multimodal information in syllogistic reasoning and question the assumed primacy of abstract, spatially organized representations in deduction, as is claimed by mental models theorists.     

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.     

Generating initial models for reasoning

Much of the knowledge that children and adults have about the world resides in intuitive models. Previous work shows that intuitive models allow for computation of specific outcomes given information about the system, but little is known about how such models are acquired. The current study tested three hypotheses about how children and adults construct intuitive models when they encounter a new property: (1) intuitive models are constructed by transferring principles from familiar properties; (2) with development, children shift from applying a default model to constructing specialized models; and (3) younger children's model construction is constrained by the domain, but becomes increasingly domain independent with development. Participants from three age groups (10, 13, and 19 years) made a series of judgments about two familiar properties and one novel property. Causal models showed that all age groups transferred principles from the familiar properties to the novel property. None of the age groups used a default model. There was developmental change in the effect of domain; younger, but not older, children's models were affected by domain. These findings suggest that the transfer process is developmentally invariant but that constraints on the process (i.e., domain dependence and understanding of base models) change with development.     

Individual differences in mental animation during mechanical reasoning

In three experiments we tested the effects of spatial visualization ability on performance of a motion-verification task, in which subjects were shown a diagram of a mechanical system and were asked to verify a sentence stating the motion of one of the system components. We propose that this task involves component processes of (1) sentence comprehension, (2) diagram comprehension, (3) text-diagram integration, and (4) mental animation. Subjects with law spatial ability made more errors than did subjects with high spatial ability on this task, and they made more errors on items in which more system components had to be animated to solve the problem. In contrast, the high-spatial subjects were relatively accurate on all trials. These results indicate that spatial visualization is correlated with accuracy on the motion-verification task and suggest that this correlation is primarily due to the mental animation component of the task. Reaction time and eye-fixation data revealed no differences in how the high- and low-spatial subjects decomposed the task. The data of the two groups of subjects were equally consistent with a piecemeal model of mental animation, in which components are animated one by one in order of the causal chain of events in the system.     

Differences in mental representations spontaneously adopted for reasoning

Retrospective reporting was used to show that people spontaneously adopt different mental representations for reasoning. In two experiments, subjects solved a large number of threeterm series reasoning problems and then gave retrospective reports (verbal protocols, drawings, and forced-choice strategy selections) about their solutions. A majority of subjects’ reports could be classified reliably into two groups. One group (abstract directional thinkers) claimed to construct a mental ordering of the three geometric figures used as the terms in the problems. A second group (concrete properties thinkers) claimed to attribute physical properties to mental geometric objects. In both experiments, abstract directional thinkers made few errors and were sensitive to the number of pivot-first premises in a problem. Concrete properties thinkers made more errors and were sensitive to the use of inverse relations and the number of alternations between a relation and its inverse as a problem was read. Quantitative models of the two kinds of reasoning are presented. Implications are discussed concerning theories of reasoning, tests of reasoning, and the usefulness of retrospective reporting as a general method.     

Understanding children's and adults' limitations in mental state reasoning

Young children exhibit several deficits in reasoning about their own and other people's mental states. We propose that these deficits, along with more subtle limitations in adults' social-cognitive reasoning, are all manifestations of the same cognitive bias. This is the 'curse of knowledge' - a tendency to be biased by one's own knowledge when attempting to appreciate a more na?ve or uninformed perspective. We suggest the developmental differences in mental state reasoning exist because the strength of this bias diminishes with age, not because of a conceptual change in how young children understand mental states. By pointing out the common denominator in children's and adults' limitations in mental state reasoning we hope to provide a unified framework for understanding the nature and development of social cognition.     

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.     

Formulation and experimental verification of models in propositional reasoning

In Evans (1977) an experiment of Evans and Lynch (1973) based on Wason's selection task is re-analysed. We reformulated the model proposed by Evans as a state model and extended it to a new model by means of which the data of Evans and Lynch (1973), of Manktelow and Evans (1979), and of our own experiments can be explained. The new model is based on a falsification state, a verification state and a matching state.     

Mental models and logical reasoning problems in the GRE

The Graduate Record Examination (GRE) contains a class of complex reasoning tests known as logical reasoning problems. These problems are demanding for human reasoners and beyond the competence of any existing computer program. This article applies the mental model theory of reasoning to the analysis of these problems. It predicts 3 main causes of difficulty, which were corroborated by the results of 4 experiments: the nature of the logical task (Experiment 1), the set of foils (Experiment 2), and the nature of the conclusions (Experiments 3 and 4). This article shows how these factors can be applied to the design of new problems.