Interacting Conceptual Spaces

TL;DR

This paper introduces a categorical compositional framework for conceptual space models of cognition, emphasizing convex structures and demonstrating how to construct composite types like adjectives and verbs with detailed examples.

Contribution

It presents a novel category of convex relations for semantic modeling and applies categorical compositional schemes to conceptual spaces, enabling complex type constructions.

Findings

Convex relations form a new setting for compositional semantics.

Composite types like adjectives and verbs can be systematically constructed.

The model is illustrated with detailed examples.

Abstract

We propose applying the categorical compositional scheme of [6] to conceptual space models of cognition. In order to do this we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We show how conceptual spaces for composite types such as adjectives and verbs can be constructed. We illustrate this new model on detailed examples.