Higher-Order DisCoCat (Peirce-Lambek-Montague semantics)
This work addresses the challenge of representing complex linguistic phenomena like quantifiers and negation in categorical compositional semantics, though it appears incremental as it builds on existing DisCoCat frameworks.
The authors tackled the problem of modeling higher-order and non-linear processes in natural language semantics by proposing a new definition of higher-order DisCoCat models where word meanings are diagram-valued higher-order functions. They demonstrated this with a proof-of-concept implementation in DisCoPy, enabling a purely diagrammatic treatment of adverbs, prepositions, negation, and quantifiers.
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.