Abstract We present a mathematical model for the cognitive operation of conceptual blending that aims at being uniform across different representation formalisms, while capturing the relevant structure of this operation. The model takes its inspiration from amalgams as applied in case-based reasoning, but lifts them into category theory so as to follow Joseph Goguen’s intuition for a mathematically precise characterisation of conceptual blending at a representation-independent level of abstraction. We prove that our amalgam-based category-theoretical model of conceptual blending is essentially equivalent to the pushout model in the ordered category of partial maps as put forward by Goguen. But unlike Goguen’s approach, our model is more suitable to capture computational realisations of conceptual blending, and we exemplify this by concretising our model to computational conceptual blends for various representation formalisms and application domains.

中文翻译：

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计算概念融合的统一模型

摘要 我们提出了一个概念混合认知操作的数学模型，旨在在不同的表示形式中保持一致，同时捕获该操作的相关结构。该模型从基于案例推理中应用的汞合金中汲取灵感，但将它们提升到类别理论中，以便遵循 Joseph Goguen 的直觉，即在独立于表示的抽象级别上对概念混合进行数学精确表征。我们证明了我们的基于汞合金的概念混合类别理论模型本质上等同于 Goguen 提出的局部地图有序类别中的推出模型。但与 Goguen 的方法不同，我们的模型更适合捕捉概念混合的计算实现，