Abstract
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.