The Mathematics of Text Structure

TL;DR

This paper extends the DisCoCat framework to DisCoCirc, modeling how sentences interact within texts to produce overall meaning, with a quantum-inspired formalism adaptable to quantum computing implementations.

Contribution

It introduces DisCoCirc, a novel mathematical foundation for text-level meaning, building on and generalizing the DisCoCat model to include evolving word meanings within texts.

Findings

DisCoCirc models text as a string diagram of evolving word meanings.

The formalism is highly quantum-inspired and suitable for quantum computer implementation.

It generalizes previous models to handle dynamic, context-dependent meanings.

Abstract

In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and categories of meaning spaces. Here, we give a mathematical foundation, referred to as DisCoCirc, for how sentences interact in texts in order to produce the meaning of that text. First we revisit DisCoCat. While in DisCoCat all meanings are fixed as states (i.e. have no input), in DisCoCirc word meanings correspond to a type, or system, and the states of this system can evolve. Sentences are gates within a circuit which update the variable meanings of those words. Like in DisCoCat, word meanings can live in a variety of spaces e.g. propositional, vectorial, or cognitive. The compositional structure are string diagrams representing information flows, and an entire text yields a single string diagram in which word meanings lift to the meaning of an entire text. While the developments in this paper are independent of a physical embodiment (cf. classical vs. quantum computing), both the compositional formalism and suggested meaning model are highly quantum-inspired, and implementation on a quantum computer would come with a range of benefits. We also praise Jim Lambek for his role in mathematical linguistics in general, and the development of the DisCo program more specifically.