Error processes in syllogistic reasoning

In recent years, a number of proposals have been advanced to account for the errors that subjects make in deductive inferences from invalid syllogisms. Principles such as erroneous conversion of premises, probabilistic inference, feature selection, and various other interpretation and combination processes have been suggested. The present paper focuses on the 32 invalid categorical syllogisms for which conversion of premises does not provide an explanation of subject error. An explanation is presented in terms of three error processes: the erroneous conversion of conclusions resulting from backward processing, the erroneous integration of information from the two premises, and the failure to consider hypothetical possibilities. Empirical predictions regarding the differential difficulty of the various premise combinations as well as the pattern of correlations between premise combinations are derived from this formulation, and data are presented that support these predictions.     

Figural effects in a syllogistic evaluation paradigm: an inspection-time analysis

Robust biases have been found in syllogistic reasoning that relate to the figure of premises and to the directionality of terms in given conclusions. Mental models theorists (e.g., Johnson-Laird & Byrne, 1991) have explained figural bias by assuming that reasoners can more readily form integrated models of premises when their middle terms are contiguous than when they are not. Biases associated with the direction of conclusion terms have been interpreted as reflecting a natural mode of reading off conclusions from models according to a "first-in, first-out principle." We report an experiment investigating the impact of systematic figural and conclusion-direction manipulations on the processing effort directed at syllogistic components, as indexed through a novel inspection-time method. The study yielded reliable support for mental-models predictions concerning the nature and locus of figural and directionality effects in syllogistic reasoning. We argue that other accounts of syllogistic reasoning seem less able to accommodate the full breadth of inspection-time findings observed.     

Syllogistic inference

This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises (the ‘figure’ of the premises) affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental models of the premises, formulate informative conclusions about the relations in the model, and search for alternative models that are counterexamples to these conclusions. This theory, which has been implemented in several computer programs, predicts that two principal factors should affect performance: the figure of the premises, and the number of models that they call for. These predictions were confirmed by a third experiment.     

The Role of Negation in Conditional Inference

This paper addresses the issue of how negative components affect people's ability to draw conditional inferences. The study was motivated by an attempt to resolve a difficulty for the mental models theory of Johnson-Laird and Byrne, whose account of matching bias in the selection task is apparently inconsistent with Johnson-Laird's explanation of the double negation effects in conditional inference reported by Evans, Clibbens, and Rood (1995). Two experiments are reported, which investigate frequencies of conditional inferences with task presentation similar to that of the selection task in two respects: the presence of a picture of four cards and the use of implicit negations in the premises. The latter variable was shown to be critical and demonstrated a new phenomenon: Conditional inferences of all kinds are substantially suppressed when based on implicitly negative premises. This phenomenon was shown to operate independently of and in addition to the double negation effect. A third experiment showed that the implicit negation effect could be extended to the paradigm in which people are asked to produce their own conclusions. It is argued that these two effects can be explained within either the mental models theory or the inference rule theory, of propositional reasoning, but that each will require some revision in order to offer a convincing account.     

Reasoning with contrary-to-fact propositions

In the initial study, the ability of subjects at four age levels (10, 13, 15, 18 years) (1) to accept if-then premises as a basis for reasoning and (2) to reason correctly with if-then premises was examined. Half the subjects were assessed with four reasoning problems involving factually accurate premises. The other half received factually inaccurate premises which were derived from the preceding ones by altering a single term. Both tests included an abstract problem which preceded the concrete propositions. Results indicate that the 10 year olds, and to a lesser extent the 13 year olds, did have difficulty in accepting contrary-to-fact premises as a basis for reasoning. The 15 and 18 year olds did not, but did find reasoning correctly more difficult with contrary-to-fact premises. The second study examined the ability of 5 and 7 year olds to accept contrary-to-fact premises. Subjects were given factually false premises either alone or within a fantasy context. Results indicate that the fantasy context decreases the extent to which empirical knowledge interferes with accepting contrary-to-fact premises. This result supports the notion that a representational process may be involved in accepting contrary-to-fact premises.     

Retracted: Correction or comparison? The effects of prime awareness on social judgments

In previous research on the effects of accessible information on social judgments, divergent explanations have been offered for contrast effects that occur as a consequence of prime awareness. Some authors favor a comparison explanation, whereas others favor a correction explanation. In two studies, we successfully disentangled comparison and correction contrast by demonstrating that whereas correction for unwanted influences is a general process that leads to contrast on various dimensions on which a target is judged, comparison effects are prime specific and occur mainly on comparison relevant dimensions. In addition, our findings indicate that for correction attempts to occur and succeed, respondents must have the feeling that these primes contaminate their target judgments and should be removed from their “true” reaction to the target. When people are not suspicious of the potential contaminating influences of priming stimuli, prime awareness is more likely to lead to prime‐target comparisons than to correction efforts. Copyright © 2009 John Wiley & Sons, Ltd.     

Structural factors in figure perception

In this report, we examine tachistoscopic perception of lines in structured figures. Previous research has shown that perception of lines is facilitated when the lines occur as parts of coherent three-dimensional figures. Experiment 1 demonstrates that it is not necessary for the figure to be three-dimensional to obtain facilitation. Experiments 2 and 3 show that three-dimensionality is not sufficient either. What is important is that the target lines be structurally relevant to the figure. However, structural relevance of a target segment to the figure as perceived with unlimited viewing time is not perfectly correlated with perceptibility under tachistoscopic conditions; it appears that the targets which fall on the external contour of a figure may be facilitated even without a high degree of structural relevance. In view of this, we suggest a model in which perceivers use processing heuristics to direct processing to aspects of the input that are potentially important for determining the structure of the final figure, working primarily from the outside in.     

Judgments of discrete and continuous quantity: an illusory Stroop effect

Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship between judgments of discrete and continuous quantity remains controversial. Some researchers have suggested that both continuous and discrete quantity may be automatically extracted from a scene and represented internally, and that competition between these representations leads to Stroop interference. Here, four experiments provide evidence for a different explanation of adults’ performance on the types of tasks that have been said to demonstrate Stroop interference between representations of discrete and continuous quantity. Our well-established tendency to underestimate individual two-dimensional areas can provide an alternative explanation (introduced here as the “illusory-Stroop” hypothesis). Though these experiments were constructed like Stroop tasks, and they produce patterns of performance that initially appear consistent with Stroop interference, Stroop interference effects are not involved. Implications for models of the construction of cumulative area representations and for theories of discrete and continuous quantity processing in large sets are discussed.     

Cognitive control in belief‐laden reasoning during conclusion processing: An ERP study

Belief bias is the tendency to accept conclusions that are compatible with existing beliefs more frequently than those that contradict beliefs. It is one of the most replicated behavioral findings in the reasoning literature. Recently, neuroimaging studies using functional magnetic resonance imaging (fMRI) and event‐related potentials (ERPs) have provided a new perspective and have demonstrated neural correlates of belief bias that have been viewed as supportive of dual‐process theories of belief bias. However, fMRI studies have tended to focus on conclusion processing, while ERPs studies have been concerned with the processing of premises. In the present research, the electrophysiological correlates of cognitive control were studied among 12 subjects using high‐density ERPs. The analysis was focused on the conclusion presentation phase and was limited to normatively sanctioned responses to valid–believable and valid–unbelievable problems. Results showed that when participants gave normatively sanctioned responses to problems where belief and logic conflicted, a more positive ERP deflection was elicited than for normatively sanctioned responses to nonconflict problems. This was observed from ?400 to ?200 ms prior to the correct response being given. The positive component is argued to be analogous to the late positive component (LPC) involved in cognitive control processes. This is consistent with the inhibition of empirically anomalous information when conclusions are unbelievable. These data are important in elucidating the neural correlates of belief bias by providing evidence for electrophysiological correlates of conflict resolution during conclusion processing. Moreover, they are supportive of dual‐process theories of belief bias that propose conflict detection and resolution processes as central to the explanation of belief bias.     

A review of conceptual models explaining the effects of child sexual abuse

Based on clinical experience and empirical literature demonstrating that child sexual abuse (CSA) often results in initial and long-term adverse outcomes, researchers have explored why such problems occur. Specifically, starting in the mid 1980s and continuing into the 1990s, several authors proposed conceptual models to explain the negative effects of CSA. Such models have been based on diverse theoretical premises. The purpose of the present article is to provide a general summary review of various conceptual models. Following the review, the current state of the literature on this topic is discussed, as are suggested future directions for research.     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.     

Exploring Message Framing Outcomes When Systematic,Heuristic, or Both Types of Processing Occur

Mixed findings have emerged in message framing studies, even when such studies employ the same general type of framing, such as goal framing. This article attempts to show that by extending the heuristic–systematic model‐based explanation of message framing effects to incorporate conditions that may prompt both systematic and heuristic processing, this theory may accommodate some of the aberrant findings. The research reported shows that by varying a message issue's risky implications and its personal relevance, 2 factors that potentially influence the type of processing people employ, systematic, heuristic, or concurrently both types of processing were evoked and influenced people's judgments, causing alternative patterns of message framing effects to occur. The results offer insight into how each of these types of processing can affect message framing outcomes, and they imply that certain seemingly aberrant findings in the literature can be reconciled with this extended theory.     

Interfering with inferential, but not associative, processes underlying spontaneous trait inference

Three studies explore mental processes underlying spontaneous trait inferences about self-informants and the spontaneous trait transference characterizing third-party informants. Process differences are suggested in that instructions prompting a nontrait inference (truth or lie?) reduce self-informant trait-savings effects and lower self-informant trait judgments. For third-party informants, such instructions have no effect on these outcome variables. Results of a third study are inconsistent with cognitive load as an explanation for these effects. Taken together, these results indicate that inferences, and not merely associations, spontaneously form when processing information about self-informants. The results also show that the inferences and judgments that occur in spontaneous trait transference are not caused by the misidentification of third-party informants as self-informants.     

Amodal completion, depth stratification, and illusory figures: a test of Kanizsa's explanation.

Subjective contours have been explained by Kanizsa as being a consequence of amodal completion of incomplete figures. According to the theory of amodal completion, figural incompleteness triggers the emergence of an illusory object superimposed on the gaps in the inducers, which in turn hide parts of the pattern, thus suggesting that the plane of the illusory object must always be seen to be above the plane of the inducers. A figure was created in which subjective contours are seen despite the fact that the perceived depth relationships run counter to that required by the theory of amodal completion. In four experiments, this depth relationship is confirmed by using direct and indirect measures which assess both registered and apprehended depth. By emphasizing a logical inconsistency in the explanation based on amodal completion, the results show that amodal completion, at least in Kanizsa-like patterns, cannot be considered as a causal factor for subjective contour figures.     

Effects of directionality in deductive reasoning: II. Premise integration and conclusion evaluation

Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given-new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model.     

Practice effects in backward masking

In two experiments we demonstrate that much larger practice effects occur in a backward masking paradigm where patterned masks are used than in similar visual processing paradigms, such as lateral masking and whole report. In additional experiments we examine four possible explanations for the large practice effects: increased familiarity with the paradigm in general, learning about the targets, learning about the masks, and enhanced sensory processing. Because of failure to observe similar practice effects in related paradigms not involving backward masking and because of the sustained nature of the improvement, we reject the first explanation as a source of practice effect. Experiment 3 allowed us to reject target learning as a source of improvement as well; target sets were switched at the end of training, but no decrement in performance was observed. In Experiment 4, mask sets were switched at the end of training, revealing a significant decrement in performance. Learning about the specific masks, then, does contribute to the observed improvement. However, it is responsible for only about one third of the overall improvement in performance. The final experiment provides evidence that the residual improvement is due to enhanced sensory processing. In that experiment, training on backward masking led to a lowered threshold in a two-flash paradigm but not to a significant change in whole-report performance.     

Age of acquisition and the cumulative-frequency hypothesis: a review of the literature and a new multi-task investigation

Early-acquired words are processed faster than late-acquired words. This is a well-accepted effect within the word recognition literature. Different explanations have been proposed, either localizing the effect of age of acquisition (AoA) in a particular substage of word processing or seeing it as the result of the way in which information is stored and accessed in the brain in general. The cumulative-frequency hypothesis is an example of the latter type of explanation: it states that the total number of times a system has come across a particular stimulus will determine the speed with which the stimulus can be recognized. The present multi-task investigation provides a critical test of the different explanations. Results show that in a variety of word processing tasks the effects of frequency and AoA are highly correlated, and that the impact of AoA is consistently higher than would be expected on the basis of the cumulative-frequency hypothesis. The findings are interpreted as evidence for recent demonstrations of a loss of plasticity in neural networks due to training and/or for mathematical models that describe the growth of the lexico-semantic network as the attachment of new nodes to existing nodes.     

An erotetic approach to explanation by specification

In earlier publications of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by subsumption under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically valid (elementary) arguments.Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined.In the present paper it is shown that all four kinds of erotetic argumentative steps occurring in the train of thought of explanation by specification are valid arguments in the sense of inferential erotetic logic. Hence, in view of the fact that the other argumentative steps were already shown to be valid, it may be concluded that the logical structure of explanation by specification can be as well-established as that of explanation by nomological subsumption. Moreover, explanation by specification provides some illustrations of the applicability of erotetic logic in everyday life and some empirical sciences.     

Three-dimensional Müller-Lyer illusion

Three-dimensional (3-D) variants of the Müller-Lyer pattern were created to address the question of where along the path of information flow in the visual system the illusion might occur. These variants, which yielded a robust illusion, included dihedral angles in place of the arrowheads of the classical pattern. The enormous difference in the shape of the resulting retinal image, compared with that of the classical pattern, makes it difficult to explain the present illusion by resorting to image-processing theories such as selective filtering (Ginsburg, 1984, 1986) or depth processing (Gregory, 1963, 1966, 1968). It was also shown that this 3-D illusion is homologous with the classical illusion, and that the two may thus share a common causal mechanism. A new type of 3-D figure, which yielded the same retinal image as did the classical pattern, was then employed. However, since the figure was 3-D, its shape in spatial coordinates was very different compared to that of the classical pattern. The magnitude of the illusion obtained with this figure was half that of the classical pattern. This finding suggests that the illusion might be caused by processes that occur after the computation of depth. All three experiments indicated that the illusion may be produced later in the processing stream than has previously been suggested.     

Left-right holistic integration of human bodies

Holistic integration of faces has been widely studied. More recently, investigations have explored whether similar processing is used for human bodies. Here we show that holistic processing, as measured by the composite task, does occur for bodies but is stronger for left and right halves than for top and bottom halves. We also found composite effects for left-right halves of inverted bodies. Standard composite effects were found for top halves of faces, tested as a control. We argue that our results suggest that holistic processing of faces and bodies might not exclusively occur for identification, but instead may also have evolved to aid communication and/or decisions about mate choice (through judging symmetry).