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.

介绍了一种扩展基于范畴的表示意义的方法，将其应用于概念空间模型，提出了凸关系范畴，构建了名词、形容词和动词类型的概念空间，通过例子说明了复合短语的构成方式，建立了一种新的认知复合方法。