Events can be modeled through a geometric approach, representing event structures in terms of spaces and mappings between spaces. At least two spaces are needed to describe an event, an action space and a result space. In this article, we invoke general mathematical structures in order to develop this geometric perspective. We focus on three cognitive processes that are crucially involved in events: causal thinking, control of action and learning by generalization. These cognitive processes are supported by three corresponding mathematical (...) properties: monotonicity (that we relate to qualitative causal thinking and allows extrapolation); continuity (that plays a key role in our activities of action control); and convexity (that facilitates generalization and the categorization of events, and enables interpolation). We define how such properties constrain events representations and relate them to thinking about events. We discuss the relevance of the three constraints for event segmentation and explore the implications of such constraints for semantics. We conclude by a discussion that relates our approach to other accounts of events. (shrink)

This paper studies the learnability of natural concepts in the context of the conceptual spaces framework. Previous work proposed that natural concepts are represented by the cells of optimally partitioned similarity spaces, where optimality was defined in terms of a number of constraints. Among these is the constraint that optimally partitioned similarity spaces result in easily learnable concepts. While there is evidence that systems of concepts generally regarded as natural satisfy a number of the proposed optimality constraints, the connection between (...) naturalness and learnability has been less well studied. To fill this gap, we conduct a computational study employing two standard models of concept learning. Applying these models to the learning of color concepts, we examine whether natural color concepts are more readily learned than nonnatural ones. Our findings warrant a positive answer to this question for both models employed, thus lending empirical support to the notion that learnability is a distinctive characteristic of natural concepts. (shrink)