# The Mathematical Structure of Integrated Information Theory

arXiv: https://arxiv.org/abs/2002.07655 · HTML: https://mlsanity.com/paper/2002.07655/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [Dissociating Artificial Intelligence from Artificial Consciousness](https://mlsanity.com/paper/2412.04571/) (2024)
- [A Disproof of Large Language Model Consciousness: The Necessity of Continual Learning for Consciousness](https://mlsanity.com/paper/2512.12802/) (2025)
- [Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy](https://mlsanity.com/paper/2308.00861/) (2023)
- [If consciousness is dynamically relevant, artificial intelligence isn't conscious](https://mlsanity.com/paper/2304.05077/) (2023)
- [Influence of the Geometry of the world model on Curiosity Based Exploration](https://mlsanity.com/paper/2304.00188/) (2023)

## Abstract (arXiv)

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et. al., as well as the Quantum IIT introduced by Zanardi et. al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background.