The Mathematics of Text Structure

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