The Mathematical Structure of Integrated Information Theory
This work addresses the need for a rigorous mathematical foundation in consciousness research, making it accessible to formal researchers, though it is incremental in building on prior theories.
The paper tackles the challenge of formalizing Integrated Information Theory (IIT) by providing a generalized mathematical structure that unifies existing versions like IIT 3.0 and Quantum IIT, offering an axiomatic definition for future research.
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.