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The Mathematics of Text Structure | | Bob Coecke
; | | Date: |
6 Apr 2019 | | 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. We revisit DisCoCat: while in the latter all meanings are
states (i.e. have no input), in DisCoCirc word meanings are types of which the
state can evolve, and sentences are gates within a circuit which update the
meaning of 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. | | Source: | arXiv, 1904.3478 | | Services: | Forum | Review | PDF | Favorites | |
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