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2007 | Buch

Spatial Cognition V Reasoning, Action, Interaction

International Conference Spatial Cognition 2006, Bremen, Germany, September 24-28, 2006, Revised Selected Papers

herausgegeben von: Thomas Barkowsky, Markus Knauff, Gérard Ligozat, Daniel R. Montello

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Computer Science

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SUCHEN

Über dieses Buch

This is the fifth volume in a series of book publications featuring basic interdisciplinary research in spatial cognition. The study of spatial cognition is the study of knowledge about spatial properties of objects and events in the world. Spatial properties include location, size, distance, direction, separation and connection, shape, pattern, and so on. Cognition is about the structures and processes of knowledge: its acquisition, storage, retrieval, manipulation, and use by humans, nonhuman animals, and machines. Broadly construed, cognitive activities include sensation and perception, thinking, attention, imagery, attitudes, memory, learning, language, and reasoning and problem-solving; the interaction of these activities with motoric (body movement) and affective (emotional) processing is recognized as critically important, as well. Cognition is typically considered to make up much of the activity of the mind. But though the mind is an expression of the structures and processes of the brain and nervous system, it is also an expression of an organism or agent with a physical body that typically exists in a physical and socio-cultural world. Researchers study spatial cognition for several reasons. Spatial cognition plays important roles in most of the domains of knowledge and behavior of sentient beings, including activities associated with biological survival, social interaction, cultural practice, and economic exchange. Attempts to describe, predict, and explain the basic components of spatial cognition and their interrelationships stimulate a host of interesting basic questions about how important parts of reality work.

Inhaltsverzeichnis

Frontmatter

Spatial Reasoning, Human-Robot Interaction, and Assistance

Reachability and Dependency Calculi: Reasoning in Network Algebras
Abstract
Reasoning in complex systems of dependencies is important in our highly connected world, e. g. for logistics planning, and for the analysis of communication schemes and social networks. Directed graphs are often used to describe scenarios with links or dependencies. However, they do not reflect uncertainties. Further, hardly any formal method for reasoning about such systems is in use. As it is hard to quantify dependencies, calculi for qualitative reasoning (QR) are a natural choice to fill this gap. However, QR is so far concentrated on spatial and temporal issues. A first approach is the dependency calculus \(\mathfrak{DC}\)  for causal relations [15], but it cannot describe situations in which cycles might occur within a graph. In this paper, refinements of \(\mathfrak{DC}\)  meeting all requirements to describe dependencies on networks are investigated with respect to satisfiability problems, construction problems, and tractable subclassses.
Alexander Scivos
The Qualitative Trajectory Calculus on Networks
Abstract
Moving objects are commonly handled using quantitative methods and information. However, in many cases, qualitative information can be more efficient and more meaningful than quantitative information. A lot of research has been done in generating, indexing, modelling and querying network-based moving objects, but little work has been done in building a calculus of relations between these objects in a qualitative way. In this paper, we introduce a formal definition of how to represent and reason about the relative trajectories of pairs of objects moving along a network.
Peter Bogaert, Nico Van de Weghe, Anthony G. Cohn, Frank Witlox, Philippe De Maeyer
Qualitative Spatial Representation and Reasoning in the SparQ-Toolbox
Abstract
A multitude of calculi for qualitative spatial reasoning (QSR) have been proposed during the last two decades. The number of practical applications that make use of QSR techniques is, however, comparatively small. One reason for this may be seen in the difficulty for people from outside the field to incorporate the required reasoning techniques into their software. Sometimes, proposed calculi are only partially specified and implementations are rarely available. With the SparQ toolbox presented in this text, we seek to improve this situation by making common calculi and standard reasoning techniques accessible in a way that allows for easy integration into applications. We hope to turn this into a community effort and encourage researchers to incorporate their calculi into SparQ. This text is intended to present SparQ to potential users and contributors and to provide an overview on its features and utilization.
Jan Oliver Wallgrün, Lutz Frommberger, Diedrich Wolter, Frank Dylla, Christian Freksa
Remembering Places in Space: A Human Analog Study of the Morris Water Maze
Abstract
We conducted a human analog study of the Morris Water Maze, with individuals indicating a remembered location in a 3 m diameter arena over different intervals of time and with different memory loads. The primary focus of the study was to test a theory of how varying cue location and number of cues affects memory for spatial location. As expected, memory performance, as measured by proximity to the actual location, was negatively affected by increasing memory load, increasing delay interval, and decreasing the number of cues. As memory performance decremented, bias effects increased and were in accordance with the cue-based memory model described by Fitting, Wedell and Allen (2005). Specifically, remembered locations were biased toward the nearest cue and error decreased with more cues. These results demonstrate that localization processes that apply to small two-dimensional task fields may generalize to a larger traversable task field.
Sylvia Fitting, Gary L. Allen, Douglas H. Wedell
The Role of Users’ Concepts of the Robot in Human-Robot Spatial Instruction
Abstract
Spatial instructions are always delivered for a particular communication partner. In this paper I investigate the the role of users’ concepts of their communication partner in human-robot interaction by analysing the spatial language choices speakers make in three comparable corpora with three different robots. I show that the users’ concepts of their artificial communication partner is only mildly shaped by the appearance of the robot, and thus that users do not mindlessly use all clues they can get about their communication partner in order to formulate their spatial instructions. Instead, spatial instruction in human-robot interaction also depends on the users’ models of the communication situation, as well as on external variables, such as gender.
Kerstin Fischer
Collaborative Assistance with Spatio-temporal Planning Problems
Abstract
The paper describes a collaborative assistance approach with spatio-temporal planning, which requires user’s active participation in the problem solving task. The proposed collaborative assistance system operates on a region-based representation structure, which allows for partial specification of constraints at different levels of granularity. Weakly specified constraints contribute on the one hand to high computational complexity when generating alternative solutions and on the other hand to large solution spaces. The paper introduces Partial Order, Neighboring Regions and Partial Order of Neighboring Regions heuristics, which allow for pruning of significant parts of the search space, and produce hierarchical structuring of the solution space. Resulting hierarchical organization of the solution space reflects human mental processing of geographic information. To reduce cognitive load during observation of solution space, filtering of certain aspects, set-oriented structuring and case-based reasoning approaches are introduced.
Inessa Seifert

Visuo-Spatial Reasoning and Spatial Dynamics

Dialog-Based 3D-Image Recognition Using a Domain Ontology
Abstract
The combination of vision and speech, together with the resulting necessity for formal representations, builds a central component of an autonomous system. A robot that is supposed to navigate autonomously through space must be able to perceive its environment as automatically as possible. But each recognition system has its own inherent limits. Especially a robot whose task is to navigate through unknown terrain has to deal with unidentified or even unknown objects, thus compounding the recognition problem still further. The system described in this paper takes this into account by trying to identify objects based on their functionality where possible. To handle cases where recognition is insufficient, we examine here two further strategies: on the one hand, the linguistic reference and labeling of the unidentified objects and, on the other hand, ontological deduction. This approach then connects the probabilistic area of object recognition with the logical area of formal reasoning. In order to support formal reasoning, additional relational scene information has to be supplied by the recognition system. Moreover, for a sound ontological basis for these reasoning tasks, it is necessary to define a domain ontology that provides for the representation of real-world objects and their corresponding spatial relations in linguistic and physical respects. Physical spatial relations and objects are measured by the visual system, whereas linguistic spatial relations and objects are required for interactions with a user.
Joana Hois, Michael Wünstel, John A. Bateman, Thomas Röfer
Protein Structure Prediction with Visuospatial Analogy
Abstract
We show that visuospatial representations and reasoning techniques can be used as a similarity metric for analogical protein structure prediction. Our system retrieves pairs of α-helices based on contact map similarity, then transfers and adapts the structure information to an unknown helix pair, showing that similar protein contact maps predict similar 3D protein structure. The success of this method provides support for the notion that changing representations can enable similarity metrics in analogy.
Jim Davies, Janice Glasgow, Tony Kuo
The Spatial Representation of Dynamic Scenes – An Integrative Approach
Abstract
This paper addresses the spatial representation of dynamic scenes, particularly the question whether recognition performance is viewpoint dependent or viewpoint invariant. Beginning with the delimitation of static and dynamic scene recognition, the viewpoint dependency of visual recognition performance and the structure of the underlying mental representation are discussed. In the following, two parameters (an easy to identify event model and salient static features) are identified which appeared to be accountable for viewpoint dependency or viewpoint invariance of visual recognition performance for dynamic scenes.
Markus Huff, Stephan Schwan, Bärbel Garsoffky
Modeling Geospatial Events and Impacts Through Qualitative Change
Abstract
This paper presents a qualitative formal framework to model the impact of an event. An event could be a forest fire or a flood, for example, that results in a discernable change such as a reduced vegetation height. This framework provides a qualitative classification of impacts in order to reason about events and their impacts. The underlying conceptual model distinguishes between immediate and delayed impacts. Based on this distinction, a set of basic types of impacts are differentiated, in particular abrupt and gradual impacts. We analyze how the temporal relation between an event and an impact can be used to capture combinations of impact types, called evolving impacts. To link event-impact relations spatially, this work introduces the concept of qualitative impact maps that represent the extent of an impact type. The combination of qualitative impact maps with event-impact inference rules enables the identification of events that are likely to underlie these impacts. The application potential of this approach is demonstrated via a case study based on vegetation change and event data for a nature reserve near Melbourne, Australia. This study shows how the model can support decision making for planning and management in nature reserves.
Inga Mau, Kathleen Stewart Hornsby, Ian D. Bishop

Spatial Concepts, Human Memory, and Mental Reasoning

Preferred Mental Models: How and Why They Are So Important in Human Reasoning with Spatial Relations
Abstract
According to the mental models theory, humans reason by constructing, inspecting, and validating mental models of the state of affairs described in the premises. We present a formal framework describing all three phases and testing new predictions about the construction principle humans normally use and about the deduction process itself – the model variation phase. Finally, empirical findings in support of these principles are reported.
Marco Ragni, Thomas Fangmeier, Lara Webber, Markus Knauff
The Spatial and the Visual in Mental Spatial Reasoning: An Ill-Posed Distinction
Abstract
It is an ongoing and controversial debate in cognitive science which aspects of knowledge humans process visually and which ones they process spatially. Similarly, artificial intelligence (AI) and cognitive science research, in building computational cognitive systems, tended to use strictly spatial or strictly visual representations. The resulting systems, however, were suboptimal both with respect to computational efficiency and cognitive plau sibility. In this paper, we propose that the problems in both research strands stem from a mis conception of the visual and the spatial in mental spatial knowl edge pro cessing. Instead of viewing the visual and the spatial as two clearly separable categories, they should be conceptualized as the extremes of a con tinuous dimension of representation. Regarding psychology, a continuous di mension avoids the need to exclusively assign processes and representations to either one of the cate gories and, thus, facilitates a more unambiguous rating of processes and rep resentations. Regarding AI and cognitive science, the con cept of a continuous spatial / visual dimension provides the possibility of rep re sentation structures which can vary continuously along the spatial / visual di mension. As a first step in exploiting these potential advantages of the pro posed conception we (a) introduce criteria allowing for a non-dichotomic judgment of processes and representations and (b) present an approach towards rep re sentation structures that can flexibly vary along the spatial / visual dimension.
Holger Schultheis, Sven Bertel, Thomas Barkowsky, Inessa Seifert
Grounded Perceptual Schemas: Developmental Acquisition of Spatial Concepts
Abstract
Hand-engineered definitions of spatial categories are increasingly seen as brittle and spatial concepts in human interactions may need to learn these in terms of perceptually grounded “image schemas”. Here, we present a developmental approach for the acquisition of grounded spatial schemas in a perceptual agent. We assume a capability for dynamic visual attention, and perceptual notions of wholeness and proximity. We first learn perceptual-object to linguisticname mappings from simple 2D multi-agent visual streams co-occurring with word-separated utterances. Mutual information based statistical measures are seen to be sufficient to identify nominal participants in a simple discourse, based on a synthetic model of dynamic visual attention. Next, we use this knowledge of nominals to ground the semantics of spatial relations in language.We show that a notion of proximity between perceptual objects is sufficient to obtain a pre-verbal notion of graded spatial poses. Once linguistic data is superimposed on this, simple associative structures lead to distinctions such as “in” or “out”. Finally we also show how this can lead to a model of actions, where verbs are learned along with the associated argument structures.
Amitabha Mukerjee, Mausoom Sarkar
Modeling Human Spatial Memory Within a Symbolic Architecture of Cognition
Abstract
This paper presents a study on the integration of spatial cognition into a symbolic theory. The concepts of encoding object-locations in local allocentric reference systems and noisy representations of locations have been integrated into the ACT-R architecture of cognition. The intrinsic reference axis of the local reference systems automatically result from the sequence of attended locations. The first part of the paper describes experiments we performed to test hypotheses on the usage of local allocentric reference systems in the context of object-location memory in graphical layout structures. The second part describes in more detail the theory and its integration into ACT-R. Based on the theory a model has been developed for the task in the experiments. The parameters for the noise in the representation of locations and the parameters for the recall of symbolic memory chunks were set to values in the magnitude quoted in literature. The model satisfyingly reproduces the data from user studies with 30 subjects.
Carsten Winkelholz, Christopher M. Schlick
Updating in Models of Spatial Memory
Abstract
This chapter discusses a new model of spatial memory and updating. The model includes an egocentric subsystem that computes and represents transient self-to-object spatial relations and an environmental subsystem that forms enduring representations of environments using intrinsic reference systems. Updating occurs in both subsystems, but only the egocentric subsystem readily provides object locations relative to any adopted orientation. In the absence of visual support, updating in the egocentric subsystem is limited, and object locations may have to be retrieved from the orientation dependent environmental subsystem. The model is evaluated in light of the results of numerous studies from the areas of spatial memory and spatial updating and contrasted with two alternative models. Furthermore, results are presented that suggest that interobject spatial relations are preferentially represented when they are aligned with intrinsic reference directions in the environmental subsystem.
Björn Rump, Timothy P. McNamara
Sensorimotor Interference When Reasoning About Described Environments
Abstract
The influence of sensorimotor interference was examined in two experiments that compared pointing with iconic arrows and verbal responding in a task that entailed locating target-objects from imagined perspectives. Participants studied text narratives describing objects at locations around them in a remote environment and then responded to targets from memory. Results revealed only minor differences between the two response modes suggesting that bodily cues do not exert severe detrimental interference on spatial reasoning from imagined perspective when non-immediate described environments are used. The implications of the findings are discussed.
Marios N. Avraamides, Melina-Nicole Kyranidou
Mechanisms for Human Spatial Competence
Abstract
Research spanning decades has generated a long list of phenomena associated with human spatial information processing. Additionally, a number of theories have been proposed about the representation, organization and processing of spatial information by humans. This paper presents a broad account of human spatial competence, integrated with the ACT-R cognitive architecture. Using a cognitive architecture grounds the research in a validated theory of human cognition, enhancing the plausibility of the overall account. This work posits a close link of aspects of spatial information processing to vision and motor planning, and integrates theoretical perspectives that have been proposed over the history of research in this area. In addition, the account is supported by evidence from neuropsychological investigations of human spatial ability. The mechanisms provide a means of accounting for a broad range of phenomena described in the experimental literature.
Glenn Gunzelmann, Don R. Lyon

Navigation, Wayfinding, and Route Instructions

Algorithms for Reliable Navigation and Wayfinding
Abstract
Wayfinding research has inspired several algorithms that compute the shortest, fastest, or even simplest paths between two locations. Current navigation systems, however, do not take into account the navigational complexity of certain intersections. A short route might involve a number of intersections that are difficult to navigate, because they offer more than one alternative to turn left or right. The navigational complexity of such an intersection may require modified instructions such as veer right. This paper, therefore, presents a reliable path algorithm that minimizes the number of complex intersections with turn ambiguities between two locations along a route. Our algorithm computes the (shortest) most reliable path, i.e., the one with the least turn ambiguities. Furthermore, we develop a variation of this algorithm that balances travel distance and navigational complexity. Simulation results show that traversing a reliable path leads to less navigational errors, which in turn reduces the average travel distance. A further advantage is that reliable paths require simpler instructions.
Shazia Haque, Lars Kulik, Alexander Klippel
Interpreting Route Instructions as Qualitative Spatial Actions
Abstract
In this paper we motivate the use of qualitative spatial actions as the fundamental unit in processing user route instructions. The spatial action model has been motivated by an analysis of empirical studies in human-robot interaction on the navigation task, and can be interpreted as a conceptual representation of the spatial action to be performed by the agent in their navigation space. Furthermore, we sketch out two distinct models of interpretation for these actions in cognitive robotics. In the first, the actions are related to a formalized conceptual user modeling of navigation space, while in the second the actions are interpreted as fuzzy operations on a voronoi graph. Moreover, we show how this action model allows us to better capture the points at which user route instructions become out of alignment with a robot’s knowledge of the environment through a number of examples.
Hui Shi, Christian Mandel, Robert J. Ross
Knowledge Based Schematization of Route Directions
Abstract
It is common for a wayfinding task to involve travel across a familiar and an unfamiliar region that encompass different parts of the same route. Routes of this kind would entail schematized descriptions and the schematization would directly depend on the familiarity of the region being described. This paper presents a new formalization that identifies key conceptual elements of such routes and introduces a principle of “knowledge chunking” that enables their schematization. This is followed by empirical evidence that supports this schematization of route directions for wayfinder’s who may perform such a task. The evidence suggests the need for future wayfinding systems to produce schematized route descriptions based on the user’s prior knowledge of a route. The formal approach presented is useful in implementing such a system and possible methods for its implementation are discussed.
Samvith Srinivas, Stephen C. Hirtle
Map Use and Wayfinding Strategies in a Multi-building Ensemble
Abstract
This experiment investigated the role of familiarity, map usage and instruction on wayfinding strategies and performance. 32 participants had to find eight goals in a multilevel building ensemble consisting of two distinctive vertical segments. Generally users who were familiar with the building ensemble outperformed first-time visitors of the setting. We tested if the standard wall-mounted floor maps found in the majority of public buildings can help navigation in a complex unknown environment. Unfamiliar users tried to make use of these plans more frequently, but were not able to compensate for spatial knowledge deficits through them. Two strategies of across-level wayfinding are compared with respect to a region-based hierarchical planning approach. Strategy selection relied largely on task and instruction characteristics. Overall, the strategy of moving horizontally into the target section of the building prior to vertical travel was shown to be more effective in this multi-building setting.
Christoph Hölscher, Simon J. Büchner, Tobias Meilinger, Gerhard Strube
How Much Information Do You Need? Schematic Maps in Wayfinding and Self Localisation
Abstract
The paper is concerned with the empirical investigation of different types of schematised maps. In two experiments a standard floor plan was compared to three strongly schematised maps providing only route knowledge. With the help of one of the maps, the participants had to localise themselves in two tasks and performed two wayfinding tasks in a multi-level building they didn’t know before. We recorded map usage time and a range of task performance measures. Although the map provided much less information, participants performed better in wayfinding with an unambiguous schematic map than with a floor plan. In the self localisation tasks, participants performed equally well with the detailed floor plan and with the schematised map versions. Like the users of a schematic map, users of a floor map presumably oriented on the network structure rather than on local geometric features. This allows them to limit the otherwise potentially very large search space in map-based self localisation. In both types of tasks participants looked at the schematised maps for a shorter time. Providing less than standard information like in a highly schematised map can lead to better performance. We conclude that providing unambiguous turning information (route knowledge) rather than survey knowledge is most crucial for wayfinding in unknown environments.
Tobias Meilinger, Christoph Hölscher, Simon J. Büchner, Martin Brösamle
Wayfinding Strategies in Behavior and Language: A Symmetric and Interdisciplinary Approach to Cognitive Processes
Abstract
We present an interdisciplinary approach to the investigation of strategies and heuristics reflecting the cognitive processes underlying human wayfinding. To achieve this, we symmetrically investigate navigation behavior and associated language. This novel approach combines two completely different and independent directions of research that complement each other naturally and necessarily, but which have seldom been directly combined so far. The current focus on wayfinding strategies and heuristics is a fairly new scientific goal both in behavioral and linguistic research areas; also, the methods of discourse analysis have rarely been directly adopted to systematically investigate parallels between natural discourse and navigation behavior. In this paper, we outline and motivate our approach and present first results gained in combined empirical investigation.
Thora Tenbrink, Jan M. Wiener
A Spatial Cognitive Map and a Human-Like Memory Model Dedicated to Pedestrian Navigation in Virtual Urban Environments
Abstract
Many articles dealing with agent navigation in an urban environment involve the use of various heuristics. Among them, one is prevalent: the search of the shortest path between two points. This strategy impairs the realism of the resulting behaviour. Indeed, psychological studies state that such a navigation behaviour is conditioned by the knowledge the subject has of its environment. Furthermore, the path a city dweller can follow may be influenced by many factors like his daily habits, or the path simplicity in term of minimum of direction changes. It appeared interesting to us to investigate how to mimic human navigation behavior with an autonomous agent. The solution we propose relies on an architecture based on a generic model of informed environment, a spatial cognitive map model merged with a human-like memory model, representing the agent’s temporal knowledge of the environment, it gained along its experiences of navigation.
Romain Thomas, Stéphane Donikian

Linguistic and Social Issues in Spatial Knowledge Processing

The Influence of Scale, Context and Spatial Preposition in Linguistic Topology
Abstract
Following a similar method to that of Mark and Egenhofer (1994), a questionnaire-based experiment tested for possible effects of scale, context and spatial relation type on the acceptability of spatial prepositions. The results suggest that the previous assumption of scale invariance in spatial language is incorrect. The physical world as experienced by humans, and described by human language, is not a fractal: scale appears to change its very physical nature, and hence the meaning of its spatial relations. The experiment demonstrated how scale influences preposition use, and how different preposit-ions appeared to evoke different levels of acceptability in themselves. Context, in terms of object type (solid or liquid), interacted with these factors to demonstrate specific constraints upon spatial language use. The results are discussed in terms of figure-ground relations, as well as the role of human experience and the classification of the world into ’objects’ in different ways at different scales. Since this was a preliminary and artificially-constrained experiment, the need for further research is emphasized.
Anna-Katharina Lautenschütz, Clare Davies, Martin Raubal, Angela Schwering, Eric Pederson
Before or After: Prepositions in Spatially Constrained Systems
Abstract
Cognitive agents use different strategies to identify relevant spatial information in communication. The chosen strategy depends on the agents’ conceptualization of the spatial situation at hand. This situation is determined by structural and functional aspects that are induced by the environment and the actions performed or intended therein. In this paper, we are interested in conceptualizations in the context of route directions. We focus on the meaning of prepositions used to characterize movements (actions) in spatially constrained systems such as street networks. We report on different strategies employed by people to disambiguate turning actions at intersections and demonstrate how these can be reflected in automatically generated route directions, again concentrating on the assignment of prepositions for anchoring movement. Including methods that focus on the most successful strategies people use in computational systems is a prerequisite for route directions that respect for human conceptualizations of spatial situations and that become, thus, cognitively ergonomic route directions.
Kai-Florian Richter, Alexander Klippel
Discourse Factors Influencing Spatial Descriptions in English and German
Abstract
The ways in which objects are referred to by using spatial language depend on many factors, including the spatial configuration and the discourse context. We present the results of a web experiment in which speakers were asked to either describe where a specified item was located in a picture containing several items, or which item was specified. Furthermore, conditions differed as to whether the first six configurations were specifically simple or specifically complex. Results show that speakers’ spatial descriptions are more detailed if the question is where rather than which, mirroring the fact that contrasting the target item from the others in which tasks may not always require an equally detailed spatial description as in where tasks. Furthermore, speakers are influenced by the complexity of initial configurations in intricate ways: on the one hand, individual speakers tend to self-align with respect to their earlier linguistic strategies; however, also a contrast effect could be identified with respect to the usage of combined projective terms.
Constanze Vorwerg, Thora Tenbrink
Autobahn People: Distance Estimations Between German Cities Biased by Social Factors and the Autobahn
Abstract
Re-analyses of a study on distance estimations between German cities [1] revealed that conclusions drawn from aggregated data sets can also be found on the individuals’ data level. It could be shown that mental barriers, here the former iron curtain which has been physically absent for 15 years, while still assuming a significant role in social interactions, are powerful predictors for psychological distance estimations. Moreover, by integrating new demographical information about the participants, evidence can be found that social attitudes are often much stronger predictions for distance estimations than implicit or explicit geographical knowledge. For instance, it was revealed that the attitude towards German reunification plays a crucial role in estimating distances between cities crossing the former iron curtain: the more negative the attitude the more pronounced was the overestimation of distances. This trend was impenetrable by higher route knowledge measured implicitly by the extent of traveling experience and explicitly by ratings of geographical knowledge about Germany. Furthermore, participants appeared to base their estimations of direct (air) distances between German cities on distances resulting from their experience with the German Autobahn system.
Claus-Christian Carbon
Backmatter
Metadaten
Titel
Spatial Cognition V Reasoning, Action, Interaction
herausgegeben von
Thomas Barkowsky
Markus Knauff
Gérard Ligozat
Daniel R. Montello
Copyright-Jahr
2007
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-75666-8
Print ISBN
978-3-540-75665-1
DOI
https://doi.org/10.1007/978-3-540-75666-8

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