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.     

Individual differences in strategies for syllogistic reasoning

Current theories of reasoning such as mental models or mental logic assume a universal cognitive mechanism that underlies human reasoning performance. However, there is evidence that this is not the case, for example, the work of Ford (1995), who found that some people adopted predominantly spatial and some verbal strategies in a syllogistic reasoning task. Using written and think-aloud protocols, the present study confirmed the existence of these individual differences. However, in sharp contrast to Ford, the present study found few differences in reasoning performance between the two groups, in terms of accuracy or type of conclusion generated. Hence, reasoners present an outward appearance of ubiquity, despite underlying differences in reasoning processes. These findings have implications for theoretical accounts of reasoning, and for attempts to model reasoning data. Any comprehensive account needs to account for strategic differences and how these may develop in logically untrained individuals.     

Effects of belief and logic on syllogistic reasoning: Eye-movement evidence for selective processing models

Studies of syllogistic reasoning have demonstrated a nonlogical tendency for people to endorse more believable conclusions than unbelievable ones. This belief bias effect is more dominant on invalid syllogisms than valid ones, giving rise to a logic by belief interaction. We report an experiment in which participants' eye movements were recorded in order to provide insights into the nature and time course of the reasoning processes associated with manipulations of conclusion validity and believability. Our main dependent measure was people's inspection times for syllogistic premises, and we tested predictions deriving from three contemporary mental-models accounts of the logic by belief interaction. Results supported recent "selective processing" theories of belief bias (e.g., Evans, 2000; Klauer, Musch, & Naumer, 2000), which assume that the believability of a conclusion biases model construction processes, rather than biasing the search for falsifying models (e.g., Oakhill & Johnson-Laird, 1985) or a response stage of reasoning arising from subjective uncertainty (e.g., Quayle & Ball, 2000). We conclude by suggesting that the eye-movement analyses in reasoning research may provide a useful adjunct to other process-tracing techniques such as verbal protocol analysis.     

The source of belief bias effects in syllogistic reasoning.

In studies of the belief bias effect in syllogistic reasoning, an interaction between logical validity and the believability of the conclusion has been found; in essence, logic has a larger effect on unbelievable than on believable conclusions. Two main explanations have been proposed for this finding. The selective scrutiny account claims that people focus on the conclusion and only engage in logical processing if this is found to be unbelievable; while the misinterpreted necessity account claims that subjects misunderstand what is meant by logical necessity and respond on the basis of believability when indeterminate syllogisms are presented. Experiments 1 and 2 compared the predictions of these two theories by examining whether the interaction would disappear if only determinate syllogisms were used. It did, thus providing strong support for the misinterpreted necessity explanation. However, the results are also consistent with a version of the mental models theory, and so Experiment 3 was carried out to compare these two explanations. The mental models theory received strong support, as it did also in the follow-up Experiments 4 and 5. It is concluded that people try to construct a mental model of the premises but, if there is a believable conclusion consistent with the first model they produce, then they fail to construct alternative models.     

Phonological and visual working memory in mental addition

The goal of the present research was to examine the role of working memory in mental arithmetic. Adults (n = 96) solved multidigit arithmetic problems (e.g., 52 + 3; 3 + 52) alone and in combination with either a phonological memory load (i.e., nonwords, such as gup) or a visual memory load (i.e., random pattern of asterisks). The participants solved problems presented in a vertical format significantly faster than problems presented in a horizontal format. They also solved double digit first problems (e.g., 52 + 3) more quickly than the reverse (e.g., 3 + 52), but only when the problems were presented horizontally. Performance was worse in the phonological load condition than in the visual load condition for the participants who solved problems presented horizontally, whereas performance was worse in the visual load condition than in the phonological load condition when problems were presented vertically. The present research provides evidence that both phonological and visual aspects of working memory are involved in mental arithmetic but that the role of each working memory component will depend on such factors as presentation format.     

Content and strategy in syllogistic reasoning.

Syllogistic reasoning has been investigated as a general deductive process (Johnson-Laird & Byrne, 1991; Revlis, 1975; Rips, 1994). However, several studies have demonstrated the role of cognitive strategies in this type of reasoning. These strategies focus on the method used by the participants (Ford, 1995; Gilhooly, Logie, Wetherick, & Wynn, 1993) and strategies related to different interpretations of the quantified premises (Roberts, Newstead, & Griggs, 2001). In this paper, we propose that content (as well as individual cognitive differences) is an important factor in inducing a certain strategy or method for syllogistic resolution. Specifically, we suggest that syllogisms with a causal conditional premise that can be extended by an agency premise induce the use of a conditional method. To demonstrate this, we carried out two experiments. Experiment 1 provided evidence that this type of syllogism leads participants to draw the predicted conditional conclusions, in contrast with control content syllogisms. In Experiment 2, we demonstrated that the drawing of conditional conclusions is based on a causal conditional to an agent representation of the syllogism premises. These results support the role of content as inducing a particular strategy for syllogistic resolution. The implications of these results are discussed.     

Updating mental models in predictive reasoning

Abstract

A mental model account for predictive judgement is proposed. According to this view, solving a predictive task involves the foundation ad updating of a mental he work as the relevant data are provided. The final model state determines the subject's predictive outcome. Two experiments examine the temporal course of reasoning in novices (Experiment 1) and experts (Experiment 2). Each task provided in succession a quantitative source (e.g. “Last year, of the vehidts that stopped at the cafe, 80% were cars and 20% were trucks”), a diagnostic source (e.g. “This vehide is mksy”) and a categorical choice (e.g. “What kind of vehicle was it?”). Two factors were manipulated: The order of sources aimed at analysing the contextual dependence of the updating processes, and the between-sources congruence (congruent or incongruent) in order to explore the integrative processes in model building. The pattern of the sources reading times, the choice times and the categorical choices suggested that: (1) the processing of a source depends on the previous one, (2) subjects try to integrste both sources into a single mental framework, and (3) experts and novices have a similar performance, although experts give more importance to the quantitative source in the diagnostic-quantitative order. These results are better accounted for by the mental model framework than both the heuristic and the formal view of prediction.     

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.     

Belief bias and figural bias in syllogistic reasoning

Belief bias is the tendency to be influenced by the believability of the conclusion when attempting to solve a syllogistic reasoning problem. Figural bias is the tendency to be influenced by the order in which the information is presented in the premises when attempting to solve a syllogistic reasoning problem. When studied simultaneously they enable an investigation of whether participants' reasoning on the syllogistic reasoning task is guided by the conclusion (backward reasoning) or the premises (forward reasoning). Experiments 1 and 2 found evidence of belief bias but not figural bias on the syllogistic evaluation task paradigm. Experiments 3 and 4 found evidence of figural bias but not belief bias on the syllogistic production task paradigm. The findings highlight that different task characteristics influence performance dependent upon the nature of task presentation. These findings are discussed in the context of current theories of belief bias in syllogistic reasoning.     

Early and late processes in syllogistic reasoning: evidence from eye-movements

An eye-movement monitoring experiment was carried out to examine the effects of the difficulty of the problem (simple versus complex problems) and the type of figure (figure 1 or figure 4) on the time course of processing categorical syllogisms. The results showed that the course of influence for these two factors is different. We found early processing effects for the figure but not for the difficulty of the syllogism and later processing effects for both the figure and the difficulty. These results lend support to the Model Theory (Johnson-Laird, P. N., Byrne, R. M. J. (1991). Deduction. Hillsdale, New Jersey: LEA.) as opposed to other theories of reasoning (Chater, N., Oaksford, M. (1999). The probability heuristics model of syllogistic reasoning. Cognitive Psychology, 38, 191-258; Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press; Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press).     

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.     

Category typicality effects in episodic memory: Testing models of distinctiveness

Middle Tennessee State University, Murfreesboro, Tennessee Category typicality effects were investigated within the context of three models of distinctiveness: a univariate model, a fixed-multifeature model, and a weighted-multifeature model. High-typical, medium-typical, and atypical targets were embedded in lists containing a background set of mediumto high-typicality items. Atypical items were more poorly recalled than were medium- and high-typical items independently of list structure. In recognition, subjects who studied high-typical items had difficulty discriminating between high-typical items that were and were not presented as part of the list. However, item typicality had little effect on the recognition performance of subjects who did not study high-typical items. These findings were consistent with the weighted-multifeature model of distinctiveness.     

Necessity, possibility and belief: A study of syllogistic reasoning

The present study extended the investigation of the belief bias effect in syllogistic reasoning in two ways: (1) The effect was studied under instructions to decide whether conclusions were possible, as well as necessary, given the premises; and (2) the effect was studied for types of syllogism where people rarely endorse the conclusions as well as those (valid and fallacious) where endorsements are common. Three experiments are reported, which show first that there is a marked tendency to reject unbelievable conclusions relative to abstract or neutral controls on all kinds of syllogism and under both types of instruction. There was also significant evidence of positive belief bias (increased acceptance of believable conclusions) and of interactions between belief bias effects and logical form. The results are discussed with particular respect to accounts of belief bias offered by theorists in the mental-model tradition.     

Phonological similarity and the irrelevant speech effect: Implications for models of short-term verbal memory

Three experiments studied the interaction between irrelevant speech and phonological similarity within both the remembered and the irrelevant auditory material. Phonological similarity within the remembered list impaired performance in both baseline and irrelevant speech conditions, whereas phonological similarity between the remembered and ignored irrelevant items did not influence performance. Although there was a tendency for similarity within the irrelevant items to reduce interference, this proved to be a less robust finding. Implications for the theoretical interpretation of the irrelevant speech effect are discussed.     

A temporal distinctiveness theory of recency and modality effects

A temporal distinctiveness theory of contextually cued retrieval from memory is presented and applied to recency and modality effects. According to this theory, one part of the mnemonic trace of an item is a representation of the item's time of presentation. Time of presentation may be encoded with a coarse grain (so that it is consistent with a wide range of times) or with a fine grain (so that it is consistent with a narrow range of times). Retrieval proceeds by constructing temporally defined search sets that include representations of items consistent with the temporal bounds of the search set. The temporal width of the search set increases as the retention interval increases. Recency effects arise from retrieval of recently presented items from narrow search sets that include representations of few items; within the context of the search set, these items are distinctive and recalled well. Superiority in recall of recently presented auditory information in comparison with recently presented visual information is attributed to differences in the grain of time of presentation representations for aurally (fine grain) and visually (coarse grain) presented information. Four experiments confirm qualitative and quantitative predictions of the theory, including the prediction of auditory superiority at the beginning of the list when the initial items are temporally distinct.     

On the conflict between logic and belief in syllogistic reasoning

Three experiments are reported that investigate the weighting attached to logic and belief in syllogistic reasoning. Substantial belief biases were observed despite controls for possible conversions of the premises. Equally substantial effects of logic were observed despite controls for two possible response biases. A consistent interaction between belief and logic was also recorded; belief bias was more marked on invalid than on valid syllogisms. In all experiments, verbal protocols were recorded and analyzed. These protocols are interpreted in some cases as providing rationalizations for prejudiced decisions and, in other cases, as reflecting a genuine process of premise to conclusion reasoning. In the latter cases, belief bias was minimal but still present. Similarly, even subjects who focus primarily on the conclusion are influenced to an extent by the logic. Thus a conflict between logic and belief is observed throughout, but at several levels of extent.     

Linguistic marking,strategy, and affect in syllogistic reasoning

It has repeatedly been shown that three-term-series problems with unmarked comparatives (e.g., taller, higher) are solved more quickly than otherwise identical problems using their marked opposites (e.g., shorter, lower). Clark's principle of lexical marking accounts for these results in terms of a simpler semantic featural coding of the unmarked comparative with respect to its marked counterpart. Huttenlocher's theory of spatial imagery accounts for these same results via the subjects' mental ordering of the three terms as instructed by the problem statements. The present research demonstrated that while the lower latency of the unmarked adjective is a reliable effect, congruent ordering strategies are necessary for significant results. Subjects who order terms from unmarked to marked produce significant results for Clark's principle of lexical marking. Those who order terms in opposite direction do not. Further, it is shown that the choice of direction of ordering is itself significantly influenced by the affective value of the adjectives in context and to the individual subject.This research is based on a thesis submitted in partial fulfillment of the requirements for the doctoral degree to the University of Illinois.