Strategies in sentential reasoning

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagrams corresponding to mental models, and the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e., the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams.     

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.     

Structure mapping in spatial reasoning

Four experiments examined whether spatial reasoning about non-spatial concepts is based on mapping concepts to space according to similarities in relational structure. Six- and 7-year-old children without any prior graphing experience were asked to reason with graph-like diagrams. In Experiments 1 and 2, children were taught to map time and quantity to vertical and horizontal lines, and then were asked to judge the relative value of a second-order variable (rate) or a first-order variable (quantity) represented in a function line. Children’s judgments indicated that they mapped concepts to space by aligning similar relational structures: quantity judgments corresponded to line height, and rate judgments corresponded to line slope. These correspondences entail a mapping of first-order concepts to first-order spatial dimensions and second-order concepts to second-order spatial dimensions. Experiments 3 and 4 investigated the role of context in establishing relational structure. Children were taught to map age and rate (Experiment 3) or age and size (Experiment 4) to vertical and horizontal lines, and were then asked to judge the rate or the size represented by a function line. In this context, both rate and size were first-order variables, and children’s judgments corresponded to line height, also a first-order variable. The results indicate that spatial reasoning involves a structure-sensitive mapping between concepts and space.     

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.     

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.     

Mapping relational structure in spatial reasoning

Three experiments investigated whether the similarity of relational structures influences the interpretation of spatial representations. Adults were shown diagrams of hand gestures paired with simple statements and asked to judge the meaning of new gestures. In Experiment 1 the gestures were paired with active declarative statements. In Experiment 2, the gestures were paired with conjunctive and disjunctive relations. Experiment 3 used statements similar to those used in Experiment 1, but eliminated the initial object-to-object mapping provided in Experiments 1 and 2. In all three experiments, most participants chose an interpretation that set up a parallel relational structure between the gesture and its meaning: spatial elements were paired with conceptual elements and spatial relations were paired with conceptual relations. These results are consistent with the hypothesis that similarity of relational structures influences spatial reasoning, and have implications for analogical reasoning, diagrammatic reasoning, and language processing.     

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.     

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.     

Temporal order relations in language comprehension

The role of temporal orientation (chronological or reverse) and chronological distance (close, intermediate, or distant) in general event knowledge on language comprehension was examined. Experiment 1 used a relation-recognition paradigm in which the comprehension of a target event could be facilitated or disrupted by the temporal orientation implied by the prior information. Experiments 2 and 3 used a sentence-probe-recognition paradigm in which the temporal orientation, the stimulus onset asynchrony, and the chronological distance between the sentence event and the probe event were manipulated. The results demonstrated that readers used temporal information conveyed by their knowledge to construct situation models while comprehending sentences. The internal temporal dimension appeared to be directional and reflected the chronological distance between everyday events.     

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.     

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.     

The relevance of selecting what's relevant: A dual process approach to transitive reasoning with spatial relations

The present paper focuses on the heuristic selection process preceding the actual transitive reasoning process. A part of the difficulty of transitive reasoning lies in the selection of the relevant problem aspects. Two experiments are presented using the paradigm introduced by Markovits, Dumas, and Malfait (1995 Markovits, H., Dumas, C. and Malfait, N. 1995. Understanding transitivity of a spatial relationship: A developmental analysis. Journal of Experimental Child Psychology, 59: 124–141.  [Google Scholar]), in which children were asked to make “higher than” inferences about arrays of coloured blocks. In order to discriminate between genuine transitive inference and a simple strategy of relative position, Markovits et al. interspersed white blocks with the coloured blocks, such that the relative position strategy leads to erroneous responses. However, we argue that the white blocks cause confusion due to their ambiguity, which interferes with the heuristic selection process. Two methodological adaptations were introduced, which are hypothesised to facilitate the selection process and improve transitive reasoning: (1) the white blocks were replaced by coloured blocks, and (2) a less abstract context was added to the experimental design. The colour manipulation leads to a clear increase in the use of a transitive strategy by 9-year-old children; 8-year-old children mainly used the relative position strategy. When adding a context story, 9-year-old children used the transitive strategy regardless of the colour of the interspersed blocks. The overall performance of 8-year-olds improved slightly. These results are interpreted as support for a dual-process model of transitive reasoning.     

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.     

What's what: talkers help listeners hear and understand by clarifying sentential relations

It was predicted that a talker would clarify the sentential relations of an utterance if a listener indicated difficulty in hearing and understanding. Subjects read syntactically clear and distorted sentences to a listener (experimenter) in an adjoining room. The experimenter often asked “What?” Subjects changed distorted versions to clear versions, while repeating clear versions essentially as first read. Other subjects were asked to make the sentences clear and simple to understand. The same basic results were obtained. Talkers thus seem to interpret a “What?” partly as a request for clearer sentential relations and respond accordingly. The results indicate that talkers have knowledge of underlying structure. Several alternate explanations can be rejected. A relative derivational theory of complexity is presented.