Markus Knauff

Spatial imagery in deductive reasoning: a functional MRI study

Various cognitive theories aim to explain human deductive reasoning: (1) mental logic theories claim syntactic language-based proofs of derivation, (2) the mental model theory proposes cognitive processes of constructing and manipulating spatially organized mental models, and (3) imagery theories postulate that such abilities are based on visual mental images. To explore the neural substrates of human deductive reasoning, we examined BOLD (blood oxygen level dependent) contrasts of twelve healthy participants during relational and conditional reasoning with whole-brain functional magnetic resonance imaging (fMRI). The results indicate that, in the absence of any correlated visual input, reasoning activated an occipitoparietal-frontal network, including parts of the prefrontal cortex (Brodmanns area, BA, 6, 9) and the cingulate gyrus (BA 32), the superior and inferior parietal cortex (BA 7, 40), the precuneus (BA 7), and the visual association cortex (BA 19). In the discussion, we first focus on the activated occipito-parietal pathway that is well known to be involved in spatial perception and spatial working memory. Second, we briefly relate the activation in the prefrontal cortical areas and in the anterior cingulate gyrus to other imaging studies on higher cognitive functions. Finally, we draw some general conclusions and argue that reasoners envisage and inspect spatially organized mental models to solve deductive inference problems.

Reasoning, Models, and Images: Behavioral Measures and Cortical Activity

The goal of this study was to investigate the neurocognitive processes of mental imagery in deductive reasoning. Behavioral studies yielded four sorts of verbal relations: (1) visuospatial relations that are easy to envisage both visually and spatially; (2) visual relations that are easy to envisage visually but hard to envisage spatially; (3) spatial relations that are hard to envisage visually but easy to envisage spatially; and (4) control relations that are hard to envisage both visually and spatially. In three experiments, visual relations slowed the process of reasoning in comparison with control relations, whereas visuospatial and spatial relations yielded inferences comparable to those of control relations. An experiment using functional magnetic resonance imaging showed that in the absence of any correlated visual input (problems were presented acoustically via headphones), all types of reasoning problems evoked activity in the left middle temporal gyrus, in the right superior parietal cortex, and bilaterally in the precuneus. In the prefrontal cortex, increased activity was found in the middle and inferior frontal gyri. However, only the problems based on visual relations also activated areas of the visual association cortex corresponding to V2. The results indicate that cortical activity during reasoning depends on the nature of verbal relations. All relations elicit mental models that underlie reasoning, but visual relations in addition elicit visual images. This account resolves inconsistencies in the previous literature.

Visual imagery can impede reasoning

Although it is natural to suppose that visual mental imagery is important in human deductive reasoning, the evidence is equivocal. This article argues that reasoning studies have not distinguished between ease of visualization and ease of constructing spatial models. Rating studies show that these factors can be separated. Their results yielded four sorts of relations: (1)visuospatial relations that are easy to envisage visually and spatially, (2)visual relations that are easy to envisage visually but hard to envisage spatially, (3)spatial relations that are hard to envisage visually but easy to envisage spatially, and (4)control relations that are hard to envisage both visually and spatially. Three experiments showed that visual relations slow down the process of reasoning in comparison with control relations, whereas visuospatial and spatial relations yield inferences comparable with those of control relations. We conclude that irrelevant visual detail can be a nuisance in reasoning and can impede the process.

Fmri evidence for a three-stage model of deductive reasoning

Deductive reasoning is fundamental to science, human culture, and the solution of problems in daily life. It starts with premises and yields a logically necessary conclusion that is not explicit in the premises. Here we investigated the neurocognitive processes underlying logical thinking with event-related functional magnetic resonance imaging. We specifically focused on three temporally separable phases: (1) the premise processing phase, (2) the premise integration phase, and (3) the validation phase in which reasoners decide whether a conclusion logically follows from the premises. We found distinct patterns of cortical activity during these phases, with initial temporo-occipital activation shifting to the prefrontal cortex and then to the parietal cortex during the reasoning process. Activity in these latter regions was specific to reasoning, as it was significantly decreased during matched working memory problems with identical premises and equal working memory load.

Cortical activation evoked by visual mental imagery as measured by fMRI.

One of the major controversies in cognitive neuroscience is whether the primary visual cortex and nearby areas are involved in visual mental imagery. In an fMRI study we examined the brain activity of 10 healthy subjects under different task conditions: in the perception condition subjects saw complex geometrical shapes and had to decide whether other highlighted stimuli fell inside or outside the figure. In the imagery condition subjects saw only the highlighted stimuli and were instructed to imagine the previously studied geometrical shapes to solve the same task. Although the behavioral data show a distance effect that would be expected based on topographically organized mental images, the functional imaging data do not show increased activity in the primary visual cortex in the imagery condition. In the occipital cortex a slightly increased activity was found only in the visual association cortex (BA 19), whereas the highest activation was observed in the parietal cortex (BA 7 and 40). The results of the study do not support the assumption that the primary visual cortex is involved in visual mental imagery, but rather that a network of spatial subsystems and higher visual areas appears to be involved.

The Neural Correlates of Logical Thinking: An Event-Related fMRI Study

Deductive reasoning is fundamental to science, human culture, and the solution of problems in daily life. It starts with premises and yields a logically necessary conclusion that is not explicit in the premises. Here we investigated the neurocognitive processes underlying logical thinking with event-related functional magnetic resonance imaging. We specifically focused on three temporally separable phases: (1) the premise processing phase, (2) the premise integration phase, and (3) the validation phase in which reasoners decide whether a conclusion logically follows from the premises. We found distinct patterns of cortical activity during these phases, with initial temporo-occipital activation shifting to the prefrontal cortex and then to the parietal cortex during the reasoning process. Activity in these latter regions was specific to reasoning, as it was significantly decreased during matched working memory problems with identical premises and equal working memory load.

A Cognitive Assessment of Topological Spatial Relations: Results from an Empirical Investigation

Whether or not a formal approach to spatial relations is a cognitively adequate (the term will be explicated in this paper) model of human spatial knowledge is more often based on the intuition of the researchers than on empirical data In contrast, the research reported here is concerned with an empirical assessment of one of the three general classes of spatial relations, namely topological knowledge. In the reported empirical investigation, subjects had to group numerous spatial configurations consisting of two circles with respect to their similarity. As is well known, such tasks are solved on the basis of underlying spatial concepts. The results were compared with the RCC-theory and Egenhofers approach to topological relations and support the assumption that both theories are cognitively adequate in a number of important aspects.

Preferred and Alternative Mental Models in Spatial Reasoning

The mental model theory postulates that spatial reasoning relies on the construction, inspection, and the variation of mental models. Experiment 1 shows that in reasoning problems with multiple solutions, reasoners construct only a single model that is preferred over others. Experiment 2 shows that inferences conforming to these preferred mental models (PMM) are easier than inferences that are valid for alternatives. Experiments 3 and 4 support the idea that model variation consists of a model revision process. The process usually starts with the PMM and then constructs alternative models by local transformations. Models which are difficult to reach are more likely to be neglected than models which are only minor revisions of the PMM.

Preferred mental models in reasoning about spatial relations

The theory of mental models postulates that individuals infer that a spatial description is consistent only if they can construct a model in which all the assertions in the description are true. Individuals prefer a parsimonious representation, and so, when a description is consistent with more than one possible layout of entities on the left—right dimension, individuals in our culture prefer to construct models working from left to right. They also prefer to locate entities referred to in the same assertion as adjacent to one another in a model. And, if possible, they tend to chunk entities into a single unit in order to capture several possibilities in a single model. We report four experiments corroborating these predictions. The results shed light on the integration of relational assertions, and they show that participants exploit implicit constraints in building models of spatial relations.

The cognitive adequacy of Allen's interval calculus for qualitative spatial representation and reasoning

Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental results concerning the cognitive adequacy of an important approach used in QSR, namely the spatial interpretation of the interval calculus introduced by Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and inferential cognitive adequacy of Allens interval calculus. The former refers to the thirteen base relations as a representational system and the latter to the compositions of these relations as a tool for reasoning. The results of two memory experiments on conceptual adequacy show that people use ordinal information similar to the interval relations when representing and remembering spatial arrangements. Furthermore, symmetry transformations on the interval relations were found to be responsible for most of the errors, whereas conceptualneighborhood theory did not appear to correspond to cognitively relevant concepts. Inferential adequacy was investigated by two reasoning experiments and the results show that in inference tasks where the number of possible interval relations for the composition is more than one, subjects ignore numerous possibilities and interindividually prefer the same relations. Reorientations and transpositions operating on the relations seem to be important for reasoning performance as well, whereas conceptual neighborhood did not appear to affect the difficulty of reasoning tasks based on the interval relations.