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arXiv · 2311.17813

Higher-Order DisCoCat (Peirce-Lambek-Montague semantics)

Alexis Toumi·Giovanni de Felice
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Abstract

We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague semantics based on a lambda calculus where the primitives act on string diagrams rather than logical formulae. As a special case, we show how to translate from the Lambek calculus into Peirce's system beta for first-order logic. This allows us to give a purely diagrammatic treatment of higher-order and non-linear processes in natural language semantics: adverbs, prepositions, negation and quantifiers. The definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.

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Alexis Toumi, Giovanni de Felice. 2023-11-29. Higher-Order DisCoCat (Peirce-Lambek-Montague semantics). https://doi.org/10.4204/eptcs.429.7

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