The calculus of language: explicit representation of emergent linguistic structure through type-theoretical paradigms

Abstract

The recent success of deep neural network techniques in natural language processing rely heavily on the so-called distributional hypothesis. We suggest that the latter can be understood as a simplified version of the classic structuralist hypothesis, at the core of a programme aiming at reconstructing grammatical structures from first principles and corpus analysis. Then, we propose to reinterpret the structuralist programme with insights from proof theory, especially associating paradigmatic relations and units with formal types defined through an appropriate notion of interaction. In this way, we intend to build original conceptual bridges between computational logic and classic structuralism, which can contribute to understanding the recent advances in NLP.

An Enriched Category Theory of Language: From Syntax to Semantics

“…The authors thank Olivia Caramello, Shawn Henry, Maxim Kontsevich, Laurent Lafforgue, Jacob Miller, David Jaz Myers, David Spivak, and Simon Willerton for helpful mathematical discussions. The authors thank Juan Gastaldi and Luc Pellissier for discussions about their philosophical work [11,12] and the anonymous referees who made suggestions that greatly improved this article.…”