Abstract
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.
Highlights
Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators [5, 45,46,47], has emerged as one of the leading scientific theories of consciousness
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
While we do not think that our particular definitions are satisfying as a general definition of IIT, these results show that the disentanglement of the essential mathematical structure of IIT from auxiliary tools can help to overcome fundamental mathematical or conceptual problems
Summary
Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators [5, 45,46,47], has emerged as one of the leading scientific theories of consciousness. The current definition of the theory can only be applied to comparably simple classical physical systems [1], which is problematic if the theory is taken to be a fundamental theory of consciousness, and should eventually be reconciled with our present theories of physics To resolve these problems, we examine the essentials of the IIT algorithm and formally define a generalized notion of Integrated Information Theory. This notion captures the inherent mathematical structure of IIT and offers a rigorous mathematical definition of the theory which has ‘classical’ IIT 3.0 of Tononi et al [25, 26, 31] as well as the more recently introduced Quantum Integrated Information Theory of Zanardi, Tomka and Venuti [50] as special cases. As such it is part of a number of recent contributions which seek to explore the role and prospects of mathematical theories of consciousness [11, 15, 18, 30, 49], to help overcome problems of existing models [17, 18, 34] and to eventually develop new proposals [6, 13, 16, 20, 22, 29, 39]
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