The Mathematics of Text Structure

Bob Coecke (University of Oxford)

In previous work we provided a mathematical foundation for how words interact in a sentence in order to produce the meaning of that sentence, referred to as DisCoCat. Here we provide a mathematical foundation for how sentences interact in texts, named DisCoCirc, by first revisiting our previous work on word interaction in sentences: while in DisCoCat all meanings were states, now meanings can also be I/O-processes. The result is a circuit in which sentences play the role of gates and update the meanings of words. In order to accommodate updating in a concrete model meanings would be represented as density matrices, and the need for an update mechanism aligns this research program with that of quantum Bayesian updating.