Mental models: towards a cognitive science of language, inference, and consciousness
Mental models: towards a cognitive science of language, inference, and consciousness
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Mental Models in Spatial Reasoning
Spatial Cognition, An Interdisciplinary Approach to Representing and Processing Spatial Knowledge
Shape Nouns and Shape Concepts: A Geometry for 'Corner'
Spatial Cognition, An Interdisciplinary Approach to Representing and Processing Spatial Knowledge
Abstract Structures in Spatial Cognition
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
An Axiomatic Approach to the Spatial Relations Underlying Left-Right and in Front of-Behind
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Learning and Interpretation of the Layout of Structured Documents
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Using sonification and haptics to represent overlapping spatial objects: effects on accuracy
UAHCI'13 Proceedings of the 7th international conference on Universal Access in Human-Computer Interaction: design methods, tools, and interaction techniques for eInclusion - Volume Part I
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Spatial configuration problems can be considered as a special kind of inference tasks, and can therefore be investigated within the framework of the well-established mental model theory of human reasoning. Since it is a wellknown fact that content and context affects human inference, we are interested to know to what extent abstract properties of linear shape curves conform to previous findings of interval-based reasoning. This investigation is done on a formally grounded basis. The main issue of this paper concerns the question whether the shape of linear curves in general and salient points on the curves in particular have an influence on solving interval-based configuration problems. It has been shown in previous experiments that there are preferred mental models if the linear structure consists of a straight line segment. The reported experiment demonstrates under which conditions arbitrary shaped curves reveal similar and different effects. To distinguish different types of points on a curve a classification of points based on ordering geometry is introduced. It turns out that only those shape features are employed in solving configuration-based problems that can be characterized on the basis of ordering geometry. Curves supplied with salient points also lead to strongly preferred configurations corroborating the notion of preferred mental models. Differences to the obtained types of preferred solutions in comparison to former investigations are discussed and possible explanations are given.