Interacting Conceptual Spaces I : Grammatical Composition of Concepts
This provides a foundational approach for cognitive modeling and natural language processing, though it appears incremental as it builds on existing categorical methods.
The paper tackles the problem of systematically combining concepts to derive meanings of composite phrases by generalizing the categorical compositional approach to conceptual space models of cognition, resulting in a new mathematical framework for compositional cognition.
The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first 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 then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.