# Meaning updating of density matrices

@article{Coecke2020MeaningUO, title={Meaning updating of density matrices}, author={Bob Coecke and Konstantinos Meichanetzidis}, journal={FLAP}, year={2020}, volume={7}, pages={745-770} }

The DisCoCat model of natural language meaning assigns meaning to a sentence given: (i) the meanings of its words, and, (ii) its grammatical structure. The recently introduced DisCoCirc model extends this to text consisting of multiple sentences. While in DisCoCat all meanings are fixed, in DisCoCirc each sentence updates meanings of words. In this paper we explore different update mechanisms for DisCoCirc, in the case where meaning is encoded in density matrices---which come with several…

## 18 Citations

### The Mathematics of Text Structure

- LinguisticsJoachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
- 2021

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.

### Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
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This work extends the interpretation of the type system with an extra spin density matrix space and introduces a way of simultaneously representing co-existing interpretations of ambiguous utterances, and provides a uniform framework for the integration of lexical and derivational ambiguity.

### Cats climb entails mammals move: preserving hyponymy in compositional distributional semantics

- Computer ScienceArXiv
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This paper proposes that psd matrices for verbs, adjectives, and other functional words be lifted to completely positive maps that match their grammatical type, and gives a number of proposals for the structure of Compr, based on spiders, cups and caps, and generates a range of composition rules.

### Foundations for Near-Term Quantum Natural Language Processing

- Computer ScienceArXiv
- 2020

The encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

### Talking Space: inference from spatial linguistic meanings

- PhilosophyArXiv
- 2021

A mechanism for how space and linguistic structure can be made to interact in a matching compositional fashion and how linguistic model of space can interact with other such models related to the authors' senses and/or embodiment, such as the conceptual spaces of colour, taste and smell are proposed.

### Compositionality as we see it, everywhere around us

- PhilosophyArXiv
- 2021

Inspired by work on compositionality in quantum theory, and categorical quantum mechanics in particular, the notions of Schrödinger, Whitehead, and complete compositionality are proposed, which aim to capture the fact that compositionality is at its best when it is ‘real’, ‘non-trivial’ and even more when it also is “complete’.

### The Safari of Update Structures: Visiting the Lens and Quantum Enclosures

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- 2020

It is shown that update structures survive decoherence and are sufficiently general to capture quantum observables, pinpointing the additional assumptions required to make the two coincide.

### Modelling Lexical Ambiguity with Density Matrices

- Computer ScienceCONLL
- 2020

Three new neural models for learning density matrices from a corpus are presented and their ability to discriminate between word senses on a range of compositional datasets is tested, and the best model outperforms existing vector-based compositional models as well as strong sentence encoders.

### Parsing conjunctions in DisCoCirc

- PhilosophySEMSPACE
- 2021

In distributional compositional models of meaning logical words require special interpretations, that specify the way in which other words in the sentence interact with each other. So far within the…

### Fibrational linguistics: First concepts

- Linguistics
- 2022

We deﬁne a general mathematical framework for linguistics based on the theory of ﬁbrations, called FibLang. We start by modelling the interaction between linguistics and cognition in the most general…

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