[2311.17813] Higher-Order DisCoCat (Peirce-Lambek-Montague semantics)
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Computer Science > Computation and Language

arXiv:2311.17813 (cs)
[Submitted on 29 Nov 2023]

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

Authors: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 theoretical definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.
Comments: 19 pages, 11 figures
Subjects: Computation and Language (cs.CL); Category Theory (math.CT)
Cite as: arXiv:2311.17813 [cs.CL]
  (or arXiv:2311.17813v1 [cs.CL] for this version)
  https://doi.org/10.48550/arXiv.2311.17813

Submission history

From: Alexis Toumi [view email]
[v1] Wed, 29 Nov 2023 17:04:15 UTC (301 KB)
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