The Mathematical Structure of Integrated Information Theory
Open accessAbstract
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.
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This is seldom the case for engineered systems, for which simplicity and modularity are favored.
“This is seldom the case for engineered systems, for which simplicity and modularity are favored [109].”
From Dissociating Artificial Intelligence from Artificial Consciousness (2024) · cites this paper as [109]
Sections 5 (Integration) and 9.1 (Systems) describe integrated information and the components of physical systems, but do not compare engineered systems with other systems or discuss engineering preferences. Searches for engineered systems, modularity, and simplicity found no passage supporting the claim that simplicity and modularity are favored in their design. (LLM, conf=0.74)
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- Authors
- Kleiner, J., & Tull, S.
- Affiliations
- Ludwig-Maximilians-Universität München (DE)
- Cambridge Quantum Computing (United Kingdom) (GB)
- Corresponding author
- Kleiner, Johannes
- Tull, Sean
- ORCID
- Kleiner, Johannes
- Venue
- Frontiers in Applied Mathematics and Statistics
- Publisher
- Frontiers Media SA
- Published
- 2021-06-04
- Volume
- 6
- ISSN
- 2297-4687 (ISSN-L)
- OpenAlex
- W3005695434
- Cited by
- 46
- References
- 49
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 12 · 2023: 7 · 2022: 10 · 2021: 4 · 2020: 5
- FWCI
- 7.97
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Frontiers in Applied Mathematics and Statistics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Open access LMU (Ludwid Maxmilian's Universitat Munchen) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- University of Cambridge
- University of Oxford
- Engineering and Physical Sciences Research Council
- Leibniz-Gemeinschaft
- Division of Mathematical Sciences
- Topics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Philosophy and Theoretical Science
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- integrated information theory, consciousness, axiomatic definition, mathematical structures, subjective experience, brain states, information integration
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