Counterexamples in sentential reasoning

How do logically naive individuals determine that an inference is invalid? In logic, there are two ways to proceed: (1) make an exhaustive search but fail to find a proof of the conclusion and (2) use the interpretation of the relevant sentences to construct a counterexample—that is, a possibility consistent with the premises but inconsistent with the conclusion. We report three experiments in which the strategies that individuals use to refute invalid inferences based on sentential connectives were examined. In Experiment 1, the participants’ task was to justify their evaluations, and it showed that they used counterexamples more often than any other strategy. Experiment 2 showed that they were more likely to use counterexamples to refute invalid conclusions consistent with the premises than to refute invalid conclusions inconsistent with the premises. In Experiment 3, no reliable difference was detected in the results between participants who wrote justifications and participants who did not.     

ERP characteristics of sentential inductive reasoning in time and frequency domains

Earlier studies have examined the issues of brain spatial localization in human sentential inductive reasoning using PET/fMRI. However, the temporal characteristics of such reasoning remain unclear. In our present study, we have used ERP (Event-related Potential) to further study human inductive reasoning involving sentential tasks. For congruent induction tasks, in which premises and conclusions are related, participants need to synthesize semantic information from the premises, conclusions, as well as background knowledge, while for incongruent induction tasks (baseline), in which premises and conclusions are unrelated, participants can respond “no” immediately. Behavioral data have been obtained that is consistent with expectations. ERPs imply that participants may integrate semantic information within the time window of 350–650 ms. Statistical analysis in the frequency domain has revealed a significant increase in the power of the gamma band (30–50 Hz) for congruent induction tasks in contrast to incongruent induction tasks.     

Four-dimensional spatial reasoning in humans

Human subjects practiced navigation in a virtual, computer-generated maze that contained 4 spatial dimensions rather than the usual 3. The subjects were able to learn the spatial geometry of the 4-dimensional maze as measured by their ability to perform path integration, a standard test of spatial ability. They were able to travel down a winding corridor to its end and then point back accurately toward the occluded origin. One interpretation is that the brain substrate for spatial navigation is not a built-in map of the 3-dimensional world. Instead it may be better described as a set of general rules for manipulating spatial information that can be applied with practice to a diversity of spatial frameworks.     

Induced strategy shifts in spatial reasoning

Previous research on reasoning about spatial arrangements has revealed two major strategies used by adults: Series Formation and Elimination. It was hypothesized that all adults have both strategies available. An experiment was carried out in which subjects who showed no spontaneous tendency to shift strategy were induced to do so. The strategy shifts by the subjects are simulated by a computer program in the form of a homogeneous production system. The conditions under which homogeneous and hierarchical production system models will yield the same predictions are discussed.     

Power and spatial relations

Embodied views of language hold that perceptual and motor simulations are involved during comprehension. Study 1 investigated power-related language in a picture recognition task wherein participants judged whether the picture presented at either the upper or lower screen position matched the sentence. In Study 2, participants chose the picture that best described the sentence between two (identical) images that were aligned vertically. Results demonstrated that participants responded faster to pictures presented at the implied location and chose that picture more often. Such results suggest that spatial information implicit in power-related language is involved in linguistic comprehension.     

Causal relations and feature similarity in children's inductive reasoning

Four experiments examined the development of property induction on the basis of causal relations. In the first 2 studies, 5-year-olds, 8-year-olds, and adults were presented with triads in which a target instance was equally similar to 2 inductive bases but shared a causal antecedent feature with 1 of them. All 3 age groups used causal relations as a basis for property induction, although the proportion of causal inferences increased with age. Subsequent experiments pitted causal relations against featural similarity in induction. It was found that adults and 8-year-olds, but not 5-year-olds, preferred shared causal relations over strong featural similarity as a basis for induction. The implications for models of inductive reasoning and development are discussed.     

Preferences and illusions in quantified spatial relational reasoning

The following presents the results of an investigation of strategies and preferences in human reasoning about quantified spatial relational assertions. An empirical study revealed a clear preference effect for specific models: The initially constructed model depends on the number of mental model operations. The participants' strategies can be classified as follows: (1) Models with grouped elements are preferred; (2) Models are constructed according to a parsimonious representation strategy. Systematic reasoning errors and illusions can be identified with logical connectors (AND: 86 % valid initial models; XOR: 47 %; Wilcoxon z = 4.6; p < .001). Error rates were smallest when using two universal quantifiers (All-All), they increase significantly when using one (Some-All; All-Some) and again using none (Some-Some) (Page's L = 436; z = 3.40 p < .001). Although the different assertions allowed for multiple situations, the difficulty can be traced back to specific quantifiers and logical connectors.     

Action, verbal response and spatial reasoning

Studies have shown that perception of distance, orientation and size can be dissociated from action tasks. The action system seems to possess more veridical, unbiased information than the perceptual/verbal system. The current study examines the nature of the distinction between action and verbal responses in a spatial reasoning task. Participants imagined themselves facing different orientations and either pointed to where other objects would be, or verbally reported their egocentric directions (e.g., "50 degrees to my left"). When using pointing responses, RT and error increased as a function of the angular disparity between the imagined heading and their actual heading. However, when using verbal responses, performance was not affected by angular disparity, suggesting that participants knew the direction of the targets from the imagined perspective but could not point to them directly. The verbal and action systems have fundamentally different information or processes rather than quantitatively different ones.     

Distortions in judged spatial relations

In three experiments, we explore distortions in subjects' judgments of relative geographical relations. People make large systematic errors in judging the geographical relations between two locations that are in different geographical or political units. There is a strong tendency to distort the judged relation to conform with the relation of the superordinate political unit. To account for this result, we present a model in which spatial information is stored hierarchically. Spatial relations between any two locations are stored explicitly only if those locations are within the same superordinate unit. Spatial relations not stored are inferred by combining the relations from between and within superordinate units.     

Temporal references and temporal relations in sentence comprehension

The author investigated the interpretation of temporal references during comprehension of sentences containing a main and subordinate clause. Experiments 1 and 2 examined state and event subordinate clauses, respectively, and showed that subordinate temporal references overlapping with or close to the time of the main clause event were read faster than nonoverlapping distant references. Experiment 3 examined temporal references in nonsubordinate main clauses and confirmed that temporal relations between main and subordinate clauses were established on-line in the previous experiments. Experiment 4 independently manipulated temporal overlap and distance and suggested that event and state clauses are processed according to distinct temporal parameters. The results are explained by the contingency relations that events and states establish with other discourse events.     

Temporal and spatial effects in luminance discrimination

Luminance difference thresholds (ΔI) were obtained by a successive and a simultaneous method of presenting the stimuli Spatial and temporal separation between the fields was the independent variable while other variables as stimulus size, luminance, retinal area of stimulation and duration were kept constant ΔI was less for simultaneously presented stimuli than for successively presented stimuli This was related to spatial and temporal interaction effects such that the greater the spatial interaction between simultaneously presented fields, the greater the discriminability while the greater the temporal interaction between successively presented fields, the less the sensitivity to luminance differences. It was suggested that the basis of the luminance discrimination may be different under conditions of temporal interaction than under conditions of spatial interaction between the fields.     

Temporal and spatial distance in situation models

In two experiments, we investigated how readers use information about temporal and spatial distance to focus attention on the more important parts of the situation model that they create during narrative comprehension. Effects of spatial distance were measured by testing the accessibility in memory of objects and rooms located at differing distances from the protagonist's current location. Before the test probe, an intervening episode was inserted in the narrative. Story time distance was manipulated by stating that the intervening episode lasted for either minutes or hours. Discourse time--that is, time spent reading from prime to test--was manipulated by describing the intervening episode either briefly or at length. Clear effects of story time distance and spatial distance on accessibility were found, whereas discourse time distance did not affect accessibility. The results are interpreted as supporting constructionist theories of text comprehension.     

Eye movements in a simple spatial reasoning task

We report two experiments in which participants read a question about the spatial relationship between two letters, then viewed a visual display containing the letters and were required to respond to the question. The format of the question influenced the nature of the eye movements generated to the visual display. Participants also had a tendency to make additional eye movements in order to generate a fixation sequence that corresponded to the order of the letters in the question. This demonstrates an influence of stored information on eye movement generation, and suggests that the scanpath plays a role in structuring the visual information to facilitate reasoning.     

The importance of gesture in children's spatial reasoning

On average, men outperform women on mental rotation tasks. Even boys as young as 4 1/2 perform better than girls on simplified spatial transformation tasks. The goal of our study was to explore ways of improving 5-year-olds' performance on a spatial transformation task and to examine the strategies children use to solve this task. We found that boys performed better than girls before training and that both boys and girls improved with training, whether they were given explicit instruction or just practice. Regardless of training condition, the more children gestured about moving the pieces when asked to explain how they solved the spatial transformation task, the better they performed on the task, with boys gesturing about movement significantly more (and performing better) than girls. Gesture thus provides useful information about children's spatial strategies, raising the possibility that gesture training may be particularly effective in improving children's mental rotation skills.     

Turning the tables: language and spatial reasoning

This paper investigates possible influences of the lexical resources of individual languages on the spatial organization and reasoning styles of their users. That there are such powerful and pervasive influences of language on thought is the thesis of the Whorf-Sapir linguistic relativity hypothesis which, after a lengthy period in intellectual limbo, has recently returned to prominence in the anthropological, linguistic, and psycholinguistic literatures. Our point of departure is an influential group of cross-linguistic studies that appear to show that spatial reasoning is strongly affected by the spatial lexicon in everyday use in a community (e.g. Brown, P., & Levinson, S. C. (1993). Linguistic and nonlinguistic coding of spatial arrays: explorations in Mayan cognition (Working Paper No. 24). Nijmegen: Cognitive Anthropology Research Group, Max Planck Institute for Psycholinguistics; Cognitive Linguistics 6 (1995) 33). Specifically, certain groups customarily use an externally referenced spatial-coordinate system to refer to nearby directions and positions ("to the north") whereas English speakers usually employ a viewer-perspective system ("to the left"). Prior findings and interpretations have been to the effect that users of these two types of spatial system solve rotation problems in different ways, reasoning strategies imposed by habitual use of the language-particular lexicons themselves. The present studies reproduce these different problem-solving strategies in speakers of a single language (English) by manipulating landmark cues, suggesting that language itself may not be the key causal factor in choice of spatial perspective. Prior evidence on rotation problem solution from infants (e.g. Acredolo, L.P. (1979). Laboratory versus home: the effect of environment on the 9-month-old infant's choice of spatial reference system. Developmental Psychology, 15 (6), 666-667) and from laboratory animals (e.g. Restle, F. (1975). Discrimination of cues in mazes: a resolution of the place-vs.-response question. Psychological Review, 64, 217-228) suggests a unified interpretation of the findings: creatures approach spatial problems differently depending on the availability and suitability of local landmark cues. The results are discussed in terms of the current debate on the relation of language to thought, with particular emphasis on the question of why different cultural communities favor different perspectives in talking about space.     

Functionality and spatial relations in memory and language

We examined whether the functionality of spatial relations affects the construction and memory of information in situation models. A functional relationship involves the interaction of entities that is implied by either typical use or contextual demands. Previous research has shown that spatial relations are less likely to be encoded during comprehension unless there is extensive prior knowledge, explicit instructions to attend to spatial information, or a clear emphasis on spatial information. If the construction of a situation model is guided by a need to understand the functional structure of a situation, then functional spatial relations should be more likely to be encoded. The results of our study showed that sentences with functional spatial relations were read faster and remembered better in both recall and recognition tests than sentences with nonfunctional spatial relations.