Interacting Conceptual Spaces I: Grammatical Composition of Concepts

Abstract

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.

Moral Dilemmas for Artificial Intelligence: A Position Paper on an Application of Compositional Quantum Cognition

“…Therefore, in this section and in order to maintain simplicity, the main concepts of CCMM framework will be presented together with a preliminary framework, which expects to integrate QC and CCMM in a common approach. For a more complete mathematical background and description about CCMM and QC, please refer to [8,29] and [9,15,30] respectively.…”

“…Computing the meaning of a sentence. Diagrammatically, the final meaning of one sentence will be the meaning of individual words interacting according to the grammatical structure, defined as a process [8,29].…”

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“…The categorical model has proved successful in a number of natural language processing tasks [9,14], and is flexible enough that it can be extended to include ambiguity [22] and changes of the semantic category [5,1]. These formalisms have allowed for connections between semantic meanings.…”

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“…The categorical compositional approach was introduced in the context of distributional semantics by [6], and further elucidated in [3]. The approach was outlined in [3] as follows:…”