Compositionality as we see it, everywhere around us

by   Bob Coecke, et al.

There are different meanings of the term "compositionality" within science: what one researcher would call compositional, is not at all compositional for another researcher. The most established conception is usually attributed to Frege, and is characterised by a bottom-up flow of meanings: the meaning of the whole can be derived from the meanings of the parts, and how these parts are structured together. Inspired by work on compositionality in quantum theory, and categorical quantum mechanics in particular, we propose the notions of Schrodinger, Whitehead, and complete compositionality. Accounting for recent important developments in quantum technology and artificial intelligence, these do not have the bottom-up meaning flow as part of their definitions. Schrodinger compositionality accommodates quantum theory, and also meaning-as-context. Complete compositionality further strengthens Schrodinger compositionality in order to single out theories like ZX-calculus, that are complete with regard to the intended model. All together, our new notions 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'. At this point we only put forward the intuitive and/or restricted formal definitions, and leave a fully comprehensive definition to future collaborative work.



There are no comments yet.


page 3

page 4

page 14


Moral Dilemmas for Artificial Intelligence: a position paper on an application of Compositional Quantum Cognition

Traditionally, the way one evaluates the performance of an Artificial In...

Open System Categorical Quantum Semantics in Natural Language Processing

Originally inspired by categorical quantum mechanics (Abramsky and Coeck...

Quantum and Concept Combination, Entangled Measurements and Prototype Theory

We analyze the meaning of the violation of the marginal probability law ...

A Unified Dissertation on Bearing Rigidity Theory

Accounting for the current state-of-the-art, this work aims at summarizi...

Minimum Description Length and Compositionality

We present a non-vacuous definition of compositionality. It is based on ...

Measuring non-trivial compositionality in emergent communication

Compositionality is an important explanatory target in emergent communic...

How to make qubits speak

This is a story about making quantum computers speak, and doing so in a ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.