A Neuro-Cognitive Theory of Deductive Relational Reasoning with Mental Models and Visual Images

Abstract

Many neuro-imaging studies have provided evidence that the parietal cortex plays a key role in reasoning based on mental models, which are supposed to be of abstract spatial nature. However, these studies have also shown concurrent activation in vision-related cortical areas which have often been interpreted as evidence for the role of visual mental imagery in reasoning. The aim of the paper is to resolve the inconsistencies in the previous literature on reasoning and imagery and to develop a neurally and cognitively plausible theory of human relational reasoning. The main assumption is that visual brain areas are only involved if the problem information is easy to visualize and when this information must be processed and maintained in visual working memory. A regular reasoning process, however, does not involve visual images but more abstract spatial representations—spatial mental models—held in parietal cortices. Only these spatial representations are crucial for the genuine reasoning processes.     

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 Allen's 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.     

Spatial updating and common misinterpretations of spatial reference frames

Spatial memory plays an important role in everyday life, and a large amount of research has been devoted to understanding spatial coding and reference frames across many areas. The popular research paradigms to study spatial reference frames include novel shortcut, perspective change, and landmark control tests. However, the growing research on spatial updating challenges the logical foundation of these classical paradigms, and suggests that the experimental findings using these paradigms have usually been misinterpreted. That is, performance in these tasks is generally unrelated to whether the spatial representations themselves are egocentric or allocentric. This article reviews the traditional paradigms and their logic, summarizes the theories of spatial updating, analyzes the logical flaws in these popular paradigms, and discusses their implications.     

Learning to Reach to Locations Encoded from Imaging Displays

We examined the use of hand gestures while people solved spatial reasoning problem in which they had to infer motion from static diagrams (mental animation problems). In Experiment 1, participants were asked to think aloud while solving mental animation problems. They gestured on more than 90% of problems, and most gestures expressed information about the component motions that was not stated in words. Two further experiments examined whether the gestures functioned in the mechanical inference process, or whether they merely served functions of expressing or communicating the results of this process. In these experiments, we examined the effects of instructions to think aloud, restricting participants' hand motions, and secondary tasks on mental animation performance. Although participants who were instructed to think aloud gestured more than control groups, some gestures occurred even in control conditions. A concurrent spatial tapping task impaired performance on mechanical reasoning, whereas a simple tapping task and restricting hand motions did not. These results indicate that gestures are a natural way of expressing the results of mental animation processes and suggest that spatial working memory and premotor representations are involved in mental animation. They provide no direct evidence that gestures are functional in the thought process itself, but do not rule out a role for overt gestures in this type of spatial thinking.     

Expert Algorithmic and Imagistic Problem Solving Strategies in Advanced Chemistry

Abstract

Visualization and imagistic reasoning appear central to expert practice in science; however, expert use of these strategies on authentic tasks has not been examined in detail. This study documents how science experts use both algorithms and imagistic reasoning to solve problems. Using protocol analysis, we report expert chemists' preferential use of algorithms for solving spatial problems and imagistic reasoning for deducing spatial transformations. We observed experts employ algorithms to solve the majority of spatial tasks while reserving imagistic strategies to solve a class of tasks that required translating between representations. Strategy used varied widely among experts and tasks.     

Qualitative Spatial Reasoning in Interpreting Text and Narrative

Abstract

Simple natural language texts and narratives often raise problems in commonsense spatial knowledge and reasoning of surprising logical complexity and geometric richness. In this article, I consider a dozen short texts—five taken from literature, the remainder contrived as illustrations—and discuss the spatial reasoning involved in understanding them. I conclude by summarizing their common features, and by tentatively drawing some morals for research in this area.     

Special issue introduction: Approaching spatial uncertainty visualization to support reasoning and decision making

While research on uncertainty and decision-making has a long history across several disciplines, recent technological developments compel researchers to rethink how to best address and advance the understanding of how humans reason and make decisions under spatial uncertainty. This introduction presents a visual summary graphic to provide an overview of each article in this special issue. Upon viewing these visual summaries, the reader will find that each of these articles covers different topics in the uncertainty visualization domain, offering complementary research in this field. Extending this body of research and finding new ways to explore how these visualizations may help or hinder the analytical and reasoning process of humans continues to be a necessary step towards designing more effective uncertainty visualizations to support reasoning and decision-making.     

Human Four-Dimensional Spatial Judgments of Hyper-Volume

The dimensionality limitation of human spatial representations has been a long-lasting, unsolved issue in psychology, mathematics, and philosophy. The present study examined the possibility of human four-dimensional spatial representations using a spatial judgment task on hyper-volume, a novel property unique to higher dimensional space. Observers studied visual simulations of random wireframe hyper-tetrahedrons (4-simplexes) rotating around the y-z plane and judged their hyper-volume by adjusting the size of a 4-D block. Multiple regression analyses showed a significant correlation between the responses and the actual hyper-volume but not the definition-based, lower-dimensional cues such as the mean 3-D volume, providing empirical evidence of human 4-D spatial representations that can support judgments of certain novel, high-dimensional properties.     

Space,Language and Ontology: A Response to Davis

Abstract

Ernest Davis' article “Qualititative Spatial Reasoning in Interpreting Text and Narrative” discusses challenges that the interpretation of natural language appears to raise for the formalization of commonsense spatial reasoning. Davis finds these to be of “surprising logical complexity,” but also “erratic” in that they do not show a logical structuring of the problem space that could guide productive research. In this response I argue that much of the apparent lack of structure Davis laments is due to the very style of formal modeling he pursues. By augmenting logical considerations with substantial input from other disciplines and by adopting a heterogeneous and modular approach to formalization, I suggest that the problem space is by no means as ill-structured as Davis presents it.     

Gesture in Spatial Cognition: Expressing,Communicating, and Thinking About Spatial Information

Do hand gestures play a role in spatial cognition? This paper reviews literature addressing the roles of gestures in (1) expressing spatial information, (2) communicating about spatial information, and (3) thinking about spatial information. Speakers tend to produce gestures when they produce linguistic units that contain spatial information, and they gesture more when talking about spatial topics than when talking about abstract or verbal ones. Thus, gestures are commonly used to express spatial information. Speakers use gestures more in situations when those gestures could contribute to communication, suggesting that they intend those gestures to communicate. Further, gestures influence addressees' comprehension of the speech they accompany, and addressees also detect information that is conveyed uniquely in gestures. Thus, gestures contribute to effective communication of spatial information. Gestures also play multiple roles in thinking about spatial information. There is evidence that gestures activate lexical and spatial representations, promote a focus on spatial information, and facilitate the packaging of spatial information in speech. Finally, some of the observed variation across tasks in gesture production is associated with task differences in demands on spatial cognitive processes, and individual differences in gesture production are associated with individual differences in spatial and verbal abilities. In sum, gestures appear to play multiple roles in spatial cognition. Central challenges for future research include: (1) better specification of the mental representations that give rise to gestures, (2) deeper understanding of the mechanisms by which gestures play a role in spatial thinking, and (3) greater knowledge of the sources of task and individual differences in gesture production.     

Effects of Communication Methods on Communication Patterns and Performance in a Remote Spatial Orientation Task

Abstract

An experiment was conducted to examine the impact of communication methods (text-only, audio-only, and audio-plus-video) on communication patterns and effectiveness in a 2-person remote spatial orientation task. The task required a pair of participants to figure out the cardinal direction of a target object by communicating spatial information and perspectives. Results showed that overall effectiveness in the audio-only condition was better than the text-only and audio-plus-video conditions, and communication patterns were more predictive of errors than individual differences in spatial abilities. Discourse analysis showed that participants in the audio-plus-video condition performed less mental transformation of spatial information when communicating, which led to more interpretation errors by the listener. Participants in the text-only conditions performed less confirmation and made more errors by misreading their own display. Results suggested that speakers in the audio-plus-video condition minimized effort by communicating spatial information based on their own perspective but speakers in the audio-only and text-only conditions would more likely communicate transformed spatial information. Analysis of gestures in the audio-plus-video condition confirmed that iconic gestures tended to co-occur with spatial transformation. Iconic gesture rates were negatively correlated with transformation errors, indicating that iconic gestures more likely co-occurred with successful communication of spatial transformation. Results show that when visual interactive feedback is available, speakers tend to adopt egocentric spatial perspectives to minimize effort in mental transformation and rely on the feedback to ensure that the hearer correctly interprets the information. When visual interactive feedback is not available, speakers will put more effort in transforming spatial information to help the hearer to understand the information. The current result demonstrated that allowing two persons to see and communicate with each other during a remote spatial reasoning task can lead to more errors because of the use of a suboptimal communication strategy.     

Spatial Thinking in Undergraduate Science Education

Spatial thinking is central to many scientific domains and professions spatial ability predicts success and participation in science. However spatial thinking is not is not emphasized in our educational system. This paper presents a selective review of four types of studies regarding spatial thinking in undergraduate science curricula; (1) correlational studies examining the relations between measures of spatial ability and performance in science disciplines, (2) studies that attempt to train aspects of spatial thinking, (3) studies of how students understand specific spatial representations in sciences (4) studies that use dynamic spatial representations to promote scientific understanding. For each type of study, the evidence is critically evaluated and conclusions are drawn about how to nurture spatial thinking in science.     

Spatial Thinking Across the College Curriculum: A Report on a Specialist Meeting

This report presents findings from a specialist meeting of spatially-minded researchers and administrators from education and industry to consider prospects for introducing courses and curricula on spatial thinking in higher education. More than 40 participants explored the rationale for expanding student exposure to concepts, tools, and applications of spatial reasoning across a range of science, engineering, and humanities disciplines. The focus was on what we know and what we need to know to make the case for space, underscoring basic research on what is meant by spatial thinking and on variations in the spatial reasoning skills required in different domains of knowledge. The need for rigorous assessments of learning outcomes associated with different approaches to teaching spatial thinking was emphasized.     

Young Children's Perception of Diagrammatic Representations

Diagrams and pictorial representations are common in children's lives and require abstraction away from visual perception. In three experiments, we investigated 4- to 8-year-olds’ comprehension of such representations. In Experiment 1 (N = 80), children were shown photographs of geometric objects and asked to choose the corresponding line drawing from among sets of four, or vice versa. Results showed considerable developmental progression, especially around age 6. Experiment 2 (N = 16) ruled out that 4-year-olds’ difficulties were due to problems with the visual matching task itself. Experiment 3 (N = 32) showed comparable performance for matching diagrams to 3D objects rather than to photographs. Findings suggest increasing understanding of diagrammatic representations around the time of school entry.     

Virtual to Real Transfer of Spatial Learning in a Complex Environment: The Role of Path Network and Additional Features

The effects of the amount and type of spatial information on the orientation accuracy and metric properties of mental representations of a large-scale built environment were evaluated in a virtual-real transfer study. Four groups of participants explored different virtual versions of a campus before being tested in the real environment. Learning with or without additional features and with or without a network of pathways led to different patterns of data. Although direction measures and straight-line and route distance estimates were least accurate in the absence of either type of information, the combination of both types of information did not produce more accurate knowledge than either did alone. In particular, the presence of additional features had a facilitating effect only on the direction estimates. The results highlight the respective importance of amount and type of spatial information in the acquisition and use of mental spatial representations.     

Qualitative Spatial Reasoning for Topological Map Learning

Abstract

In this paper we investigate the application of qualitative spatial reasoning methods for learning the topological map of an unknown environment. We develop a topological mapping framework that achieves robustness against ambiguity in the available information by tracking all possible graph hypotheses simultaneously. We then exploit spatial reasoning to reduce the space of possible hypotheses. The considered constraints are qualitative direction information and the assumption that the map is planar. We investigate the effects of absolute and relative direction information using two different spatial calculi and combine the approach with a real mapping system based on Voronoi graphs.     

Analyzing Qualitative Spatio-Temporal Calculi using Algebraic Geometry

Abstract

Qualitative spatial reasoning is based on calculi which comprise relations and operation tables that encode operations like relation composition. Designing a calculus involves determining these tables and analyzing reasoning properties—a demanding task that is susceptible to errors if performed manually. This paper is concerned with automating computation of operation tables and analysis of qualitative calculi over real-valued domains like the plane ². We present an approach to specify qualitative relations using polynomial equations that allows methods from algebraic geometry to be applied. This paper shows how reasoning with qualitative relations can be posed algebraically and demonstrates algebraic reasoning using Gröbner base analysis. We evaluate this approach and describe our implementation, which is freely available as part of the spatial reasoning toolbox SparQ.     

Modelling Dynamic Spatial Systems in the Situation Calculus

Abstract

We propose and systematically formalise a dynamical spatial systems approach for the modelling of changing spatial environments. The formalisation adheres to the semantics of the situation calculus and includes a systematic account of key aspects that are necessary to realize a domain-independent qualitative spatial theory that may be utilised across diverse application domains. The spatial theory is primarily derivable from the all-pervasive generic notion of “qualitative spatial calculi” that are representative of differing aspects of space. In addition, the theory also includes aspects, both ontological and phenomenal in nature, that are considered inherent in dynamic spatial systems. Foundational to the formalisation is a causal theory that adheres to the representational and computational semantics of the situation calculus. This foundational theory provides the necessary (general) mechanism required to represent and reason about changing spatial environments and also includes an account of the key fundamental epistemological issues concerning the frame and the ramification problems that arise whilst modelling change within such domains. The main advantage of the proposed approach is that based on the structure and semantics of the proposed framework, fundamental reasoning tasks such as projection and explanation directly follow. Within the specialised spatial reasoning domain, these translate to spatial planning/re-configuration, causal explanation and spatial simulation. Our approach is based on the hypothesis that alternate formalisations of existing qualitative spatial calculi using high-level tools such as the situation calculus are essential for their utilisation in diverse application domains such as intelligent systems, cognitive robotics and event-based GIS.