Year: 2025
Type: article
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.
DOI: 10.4204/eptcs.429.7
Authors: Alexis Toumi, Giovanni de Felice
Institutions: Quantinuum (United Kingdom), Quantinuum (United States)
Language: English
Subfield: Language and Linguistics
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4414402233