  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.
