The Influence of Linear Shapes on Solving Interval-Based Configuration Problems

Abstract

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 well-known 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.