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Keywords = integrated information theory (IIT)

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34 pages, 1302 KiB  
Article
Integrated Information in Relational Quantum Dynamics (RQD)
by Arash Zaghi
Appl. Sci. 2025, 15(13), 7521; https://doi.org/10.3390/app15137521 - 4 Jul 2025
Viewed by 308
Abstract
We introduce a quantum integrated-information measure Φ for multipartite states within the Relational Quantum Dynamics (RQD) framework. Φ(ρ) is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator ρ and any product state over a bipartition of [...] Read more.
We introduce a quantum integrated-information measure Φ for multipartite states within the Relational Quantum Dynamics (RQD) framework. Φ(ρ) is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator ρ and any product state over a bipartition of its subsystems. We prove that its square root induces a genuine metric on state space and that Φ is monotonic under all completely positive trace-preserving maps. Restricting the search to bipartitions yields a unique optimal split and a unique closest product state. From this geometric picture, we derive a canonical entanglement witness directly tied to Φ and construct an integration dendrogram that reveals the full hierarchical correlation structure of ρ. We further show that there always exists an “optimal observer”—a channel or basis—that preserves Φ better than any alternative. Finally, we propose a quantum Markov blanket theorem: the boundary of the optimal bipartition isolates subsystems most effectively. Our framework unites categorical enrichment, convex-geometric methods, and operational tools, forging a concrete bridge between integrated information theory and quantum information science. Full article
(This article belongs to the Special Issue Quantum Communication and Quantum Information)
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24 pages, 1187 KiB  
Article
Integrated Information Theory and the Phenomenal Binding Problem: Challenges and Solutions in a Dynamic Framework
by Chris Percy and Andrés Gómez-Emilsson
Entropy 2025, 27(4), 338; https://doi.org/10.3390/e27040338 - 25 Mar 2025
Viewed by 1919
Abstract
Theories of consciousness grounded in neuroscience must explain the phenomenal binding problem, e.g., how micro-units of information are combined to create the macro-scale conscious experience common to human phenomenology. An example is how single ‘pixels’ of a visual scene are experienced as a [...] Read more.
Theories of consciousness grounded in neuroscience must explain the phenomenal binding problem, e.g., how micro-units of information are combined to create the macro-scale conscious experience common to human phenomenology. An example is how single ‘pixels’ of a visual scene are experienced as a single holistic image in the ‘mind’s eye’, rather than as individual, separate, and massively parallel experiences, corresponding perhaps to individual neuron activations, neural ensembles, or foveal saccades, any of which could conceivably deliver identical functionality from an information processing point of view. There are multiple contested candidate solutions to the phenomenal binding problem. This paper explores how the metaphysical infrastructure of Integrated Information Theory (IIT) v4.0 can provide a distinctive solution. The solution—that particular entities aggregable from multiple units (‘complexes’) define existence—might work in a static picture, but introduces issues in a dynamic system. We ask what happens to our phenomenal self as the main complex moves around a biological neural network. Our account of conscious entities developing through time leads to an apparent dilemma for IIT theorists between non-local entity transitions and contiguous selves: the ‘dynamic entity evolution problem’. As well as specifying the dilemma, we describe three ways IIT might dissolve the dilemma before it gains traction. Clarifying IIT’s position on the phenomenal binding problem, potentially underpinned with novel empirical or theoretical research, helps researchers understand IIT and assess its plausibility. We see our paper as contributing to IIT’s current research emphasis on the shift from static to dynamic analysis. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
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15 pages, 942 KiB  
Article
Two Levels of Integrated Information Theory: From Autonomous Systems to Conscious Life
by Zenan Ruan and Hengwei Li
Entropy 2024, 26(9), 761; https://doi.org/10.3390/e26090761 - 5 Sep 2024
Viewed by 5167
Abstract
Integrated Information Theory (IIT) is one of the most prominent candidates for a theory of consciousness, although it has received much criticism for trying to live up to expectations. Based on the relevance of three issues generalized from the developments of IITs, we [...] Read more.
Integrated Information Theory (IIT) is one of the most prominent candidates for a theory of consciousness, although it has received much criticism for trying to live up to expectations. Based on the relevance of three issues generalized from the developments of IITs, we have summarized the main ideas of IIT into two levels. At the second level, IIT claims to be strictly anchoring consciousness, but the first level on which it is based is more about autonomous systems or systems that have reached some other critical complexity. In this paper, we argue that the clear gap between the two levels of explanation of IIT has led to these criticisms and that its panpsychist tendency plays a crucial role in this. We suggest that the problems of IIT are far from being “pseudoscience”, and by adding more necessary elements, when the first level is combined with the second level, IIT can genuinely move toward an appropriate theory of consciousness that can provide necessary and sufficient interpretations. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
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14 pages, 260 KiB  
Article
Conscious Causality, Observer–Observed Simultaneity, and the Problem of Time for Integrated Information Theory
by John Sanfey
Entropy 2024, 26(8), 647; https://doi.org/10.3390/e26080647 - 30 Jul 2024
Cited by 1 | Viewed by 2618
Abstract
Without proven causal power, consciousness cannot be integrated with physics except as an epiphenomenon, hence the term ‘hard problem’. Integrated Information Theory (IIT) side-steps the issue by stating that subjective experience must be identical to informational physical structures whose cause-and-effect power is greater [...] Read more.
Without proven causal power, consciousness cannot be integrated with physics except as an epiphenomenon, hence the term ‘hard problem’. Integrated Information Theory (IIT) side-steps the issue by stating that subjective experience must be identical to informational physical structures whose cause-and-effect power is greater than the sum of their parts. But the focus on spatially oriented structures rather than events in time introduces a deep conceptual flaw throughout its entire structure, including the measure of integrated information, known as Φ (phi). However, the problem can be corrected by incorporating the temporal feature of consciousness responsible for the hard problem, which can ultimately resolve it, namely, that experiencer and experienced are not separated in time but exist simultaneously. Simultaneous causation is not possible in physics, hence the hard problem, and yet it can be proven deductively that consciousness does have causal power because of this phenomenological simultaneity. Experiencing presence makes some facts logically possible that would otherwise be illogical. Bypassing the hard problem has caused much of the criticism that IIT has attracted, but by returning to its roots in complexity theory, it can repurpose its model to measure causal connections that are temporally rather than spatially related. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
17 pages, 321 KiB  
Opinion
Carving Nature at Its Joints: A Comparison of CEMI Field Theory with Integrated Information Theory and Global Workspace Theory
by Johnjoe McFadden
Entropy 2023, 25(12), 1635; https://doi.org/10.3390/e25121635 - 8 Dec 2023
Cited by 5 | Viewed by 2956
Abstract
The quest to comprehend the nature of consciousness has spurred the development of many theories that seek to explain its underlying mechanisms and account for its neural correlates. In this paper, I compare my own conscious electromagnetic information field (cemi field) theory with [...] Read more.
The quest to comprehend the nature of consciousness has spurred the development of many theories that seek to explain its underlying mechanisms and account for its neural correlates. In this paper, I compare my own conscious electromagnetic information field (cemi field) theory with integrated information theory (IIT) and global workspace theory (GWT) for their ability to ‘carve nature at its joints’ in the sense of predicting the entities, structures, states and dynamics that are conventionally recognized as being conscious or nonconscious. I go on to argue that, though the cemi field theory shares features of both integrated information theory and global workspace theory, it is more successful at carving nature at its conventionally accepted joints between conscious and nonconscious systems, and is thereby a more successful theory of consciousness. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
14 pages, 317 KiB  
Article
The Fundamental Tension in Integrated Information Theory 4.0’s Realist Idealism
by Ignacio Cea, Niccolo Negro and Camilo Miguel Signorelli
Entropy 2023, 25(10), 1453; https://doi.org/10.3390/e25101453 - 16 Oct 2023
Cited by 7 | Viewed by 5286
Abstract
Integrated Information Theory (IIT) is currently one of the most influential scientific theories of consciousness. Here, we focus specifically on a metaphysical aspect of the theory’s most recent version (IIT 4.0), what we may call its idealistic ontology, and its tension with [...] Read more.
Integrated Information Theory (IIT) is currently one of the most influential scientific theories of consciousness. Here, we focus specifically on a metaphysical aspect of the theory’s most recent version (IIT 4.0), what we may call its idealistic ontology, and its tension with a kind of realism about the external world that IIT also endorses. IIT 4.0 openly rejects the mainstream view that consciousness is generated by the brain, positing instead that consciousness is ontologically primary while the physical domain is just “operational”. However, this philosophical position is presently underdeveloped and is not rigorously formulated in IIT, potentially leading to many misinterpretations and undermining its overall explanatory power. In the present paper we aim to address this issue. We argue that IIT’s idealistic ontology should be understood as a specific combination of phenomenal primitivism, reductionism regarding Φ-structures and complexes, and eliminativism about non-conscious physical entities. Having clarified this, we then focus on the problematic tension between IIT’s idealistic ontology and its simultaneous endorsement of realism, according to which there is some kind of external reality independent of our minds. After refuting three potential solutions to this theoretical tension, we propose the most plausible alternative: understanding IIT’s realism as an assertion of the existence of other experiences beyond one’s own, what we call a non-solipsistic idealist realism. We end with concluding remarks and future research avenues. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
2 pages, 175 KiB  
Reply
Reply to Rourk, C. Comment on “Albantakis et al. Computing the Integrated Information of a Quantum Mechanism. Entropy 2023, 25, 449”
by Larissa Albantakis, Robert Prentner and Ian Durham
Entropy 2023, 25(10), 1442; https://doi.org/10.3390/e25101442 - 12 Oct 2023
Cited by 6 | Viewed by 1008
Abstract
In response to a comment by Chris Rourk on our article Computing the Integrated Information of a Quantum Mechanism, we briefly (1) consider the role of potential hybrid/classical mechanisms from the perspective of integrated information theory (IIT), (2) discuss whether the (Q)IIT [...] Read more.
In response to a comment by Chris Rourk on our article Computing the Integrated Information of a Quantum Mechanism, we briefly (1) consider the role of potential hybrid/classical mechanisms from the perspective of integrated information theory (IIT), (2) discuss whether the (Q)IIT formalism needs to be extended to capture the hypothesized hybrid mechanism, and (3) clarify our motivation for developing a QIIT formalism and its scope of applicability. Full article
(This article belongs to the Collection Advances in Integrated Information Theory)
6 pages, 1249 KiB  
Comment
Comment on Albantakis et al. Computing the Integrated Information of a Quantum Mechanism. Entropy 2023, 25, 449
by Christopher Rourk
Entropy 2023, 25(10), 1436; https://doi.org/10.3390/e25101436 - 11 Oct 2023
Cited by 1 | Viewed by 1554
Abstract
Integrated information theory (IIT) is a powerful tool that provides a framework for evaluating consciousness, whether in the human brain or in other systems. In Computing the Integrated Information of a Quantum Mechanism, the authors extend IIT from digital gates to a quantum [...] Read more.
Integrated information theory (IIT) is a powerful tool that provides a framework for evaluating consciousness, whether in the human brain or in other systems. In Computing the Integrated Information of a Quantum Mechanism, the authors extend IIT from digital gates to a quantum CNOT logic gate, and while they explicitly distinguish the analysis from quantum theories of consciousness, they nonetheless provide an analytical road map for extending IIT not only to other quantum mechanisms but also to hybrid computing structures like the brain. This comment provides additional information relating to an adiabatic quantum mechanical energy routing mechanism that is part of a hybrid biological computer that provides an action selection mechanism, which has been hypothesized to exist in the human brain and for which predicted evidence has been subsequently observed, and it hopes to motivate the further evaluation and extension of IIT not only to that hypothesized mechanism but also to other hybrid biological computers. Full article
(This article belongs to the Collection Advances in Integrated Information Theory)
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9 pages, 236 KiB  
Communication
What Is It like to Be a Brain Organoid? Phenomenal Consciousness in a Biological Neural Network
by Ivanna Montoya and Daniel Montoya
Entropy 2023, 25(9), 1328; https://doi.org/10.3390/e25091328 - 13 Sep 2023
Cited by 5 | Viewed by 3051
Abstract
It has been shown that three-dimensional self-assembled multicellular structures derived from human pluripotent stem cells show electrical activity similar to EEG. More recently, neurons were successfully embedded in digital game worlds. The biologically inspired neural network (BNN), expressing human cortical cells, was able [...] Read more.
It has been shown that three-dimensional self-assembled multicellular structures derived from human pluripotent stem cells show electrical activity similar to EEG. More recently, neurons were successfully embedded in digital game worlds. The biologically inspired neural network (BNN), expressing human cortical cells, was able to show internal modification and learn the task at hand (predicting the trajectory of a digital ball while moving a digital paddle). In other words, the system allowed to read motor information and write sensory data into cell cultures. In this article, we discuss Neural Correlates of Consciousness (NCC) theories, and their capacity to predict or even allow for consciousness in a BNN. We found that Information Integration Theory (IIT) is the only NCC that offers the possibility for a BNN to show consciousness, since the Φ value in the BNN is >0. In other words, the recording of real-time neural activity responding to environmental stimuli. IIT argues that any system capable of integrating information will have some degree of phenomenal consciousness. We argue that the pattern of activity appearing in the BNN, with increased density of sensory information leading to better performance, implies that the BNN could be conscious. This may have profound implications from a psychological, philosophical, and ethical perspective. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness II)
23 pages, 746 KiB  
Article
Computing the Integrated Information of a Quantum Mechanism
by Larissa Albantakis, Robert Prentner and Ian Durham
Entropy 2023, 25(3), 449; https://doi.org/10.3390/e25030449 - 3 Mar 2023
Cited by 13 | Viewed by 5215
Abstract
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory [...] Read more.
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT’s latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum. Full article
(This article belongs to the Collection Advances in Integrated Information Theory)
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15 pages, 2368 KiB  
Article
System Integrated Information
by William Marshall, Matteo Grasso, William G. P. Mayner, Alireza Zaeemzadeh, Leonardo S. Barbosa, Erick Chastain, Graham Findlay, Shuntaro Sasai, Larissa Albantakis and Giulio Tononi
Entropy 2023, 25(2), 334; https://doi.org/10.3390/e25020334 - 11 Feb 2023
Cited by 10 | Viewed by 4482
Abstract
Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used [...] Read more.
Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause–effect structure unfolded from a maximally irreducible substrate (a Φ-structure). In this work we introduce a definition for the integrated information of a system (φs) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the φs of which is greater than the φs of any overlapping candidate systems. Full article
(This article belongs to the Collection Advances in Integrated Information Theory)
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13 pages, 2168 KiB  
Article
Different Approximation Methods for Calculation of Integrated Information Coefficient in the Brain during Instrumental Learning
by Ivan Nazhestkin and Olga Svarnik
Brain Sci. 2022, 12(5), 596; https://doi.org/10.3390/brainsci12050596 - 3 May 2022
Cited by 1 | Viewed by 1799
Abstract
The amount of integrated information, Φ, proposed in an integrated information theory (IIT) is useful to describe the degree of brain adaptation to the environment. However, its computation cannot be precisely performed for a reasonable time for time-series spike data collected from [...] Read more.
The amount of integrated information, Φ, proposed in an integrated information theory (IIT) is useful to describe the degree of brain adaptation to the environment. However, its computation cannot be precisely performed for a reasonable time for time-series spike data collected from a large count of neurons.. Therefore, Φ was only used to describe averaged activity of a big group of neurons, and the behavior of small non-brain systems. In this study, we reported on ways for fast and precise Φ calculation using different approximation methods for Φ calculation in neural spike data, and checked the capability of Φ to describe a degree of adaptation in brain neural networks. We show that during instrumental learning sessions, all applied approximation methods reflect temporal trends of Φ in the rat hippocampus. The value of Φ is positively correlated with the number of successful acts performed by a rat. We also show that only one subgroup of neurons modulates their Φ during learning. The obtained results pave the way for application of Φ to investigate plasticity in the brain during the acquisition of new tasks. Full article
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15 pages, 2007 KiB  
Article
Emergence of Integrated Information at Macro Timescales in Real Neural Recordings
by Angus Leung and Naotsugu Tsuchiya
Entropy 2022, 24(5), 625; https://doi.org/10.3390/e24050625 - 29 Apr 2022
Cited by 4 | Viewed by 2854
Abstract
How a system generates conscious experience remains an elusive question. One approach towards answering this is to consider the information available in the system from the perspective of the system itself. Integrated information theory (IIT) proposes a measure to capture this integrated information [...] Read more.
How a system generates conscious experience remains an elusive question. One approach towards answering this is to consider the information available in the system from the perspective of the system itself. Integrated information theory (IIT) proposes a measure to capture this integrated information (Φ). While Φ can be computed at any spatiotemporal scale, IIT posits that it be applied at the scale at which the measure is maximised. Importantly, Φ in conscious systems should emerge to be maximal not at the smallest spatiotemporal scale, but at some macro scale where system elements or timesteps are grouped into larger elements or timesteps. Emergence in this sense has been demonstrated in simple example systems composed of logic gates, but it remains unclear whether it occurs in real neural recordings which are generally continuous and noisy. Here we first utilise a computational model to confirm that Φ becomes maximal at the temporal scales underlying its generative mechanisms. Second, we search for emergence in local field potentials from the fly brain recorded during wakefulness and anaesthesia, finding that normalised Φ (wake/anaesthesia), but not raw Φ values, peaks at 5 ms. Lastly, we extend our model to investigate why raw Φ values themselves did not peak. This work extends the application of Φ to simple artificial systems consisting of logic gates towards searching for emergence of a macro spatiotemporal scale in real neural systems. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness)
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19 pages, 2177 KiB  
Article
From Shorter to Longer Timescales: Converging Integrated Information Theory (IIT) with the Temporo-Spatial Theory of Consciousness (TTC)
by Georg Northoff and Federico Zilio
Entropy 2022, 24(2), 270; https://doi.org/10.3390/e24020270 - 13 Feb 2022
Cited by 31 | Viewed by 5669
Abstract
Time is a key element of consciousness as it includes multiple timescales from shorter to longer ones. This is reflected in our experience of various short-term phenomenal contents at discrete points in time as part of an ongoing, more continuous, and long-term ‘stream [...] Read more.
Time is a key element of consciousness as it includes multiple timescales from shorter to longer ones. This is reflected in our experience of various short-term phenomenal contents at discrete points in time as part of an ongoing, more continuous, and long-term ‘stream of consciousness’. Can Integrated Information Theory (IIT) account for this multitude of timescales of consciousness? According to the theory, the relevant spatiotemporal scale for consciousness is the one in which the system reaches the maximum cause-effect power; IIT currently predicts that experience occurs on the order of short timescales, namely, between 100 and 300 ms (theta and alpha frequency range). This can well account for the integration of single inputs into a particular phenomenal content. However, such short timescales leave open the temporal relation of specific phenomenal contents to others during the course of the ongoing time, that is, the stream of consciousness. For that purpose, we converge the IIT with the Temporo-spatial Theory of Consciousness (TTC), which, assuming a multitude of different timescales, can take into view the temporal integration of specific phenomenal contents with other phenomenal contents over time. On the neuronal side, this is detailed by considering those neuronal mechanisms driving the non-additive interaction of pre-stimulus activity with the input resulting in stimulus-related activity. Due to their non-additive interaction, the single input is not only integrated with others in the short-term timescales of 100–300 ms (alpha and theta frequencies) (as predicted by IIT) but, at the same time, also virtually expanded in its temporal (and spatial) features; this is related to the longer timescales (delta and slower frequencies) that are carried over from pre-stimulus to stimulus-related activity. Such a non-additive pre-stimulus-input interaction amounts to temporo-spatial expansion as a key mechanism of TTC for the constitution of phenomenal contents including their embedding or nesting within the ongoing temporal dynamic, i.e., the stream of consciousness. In conclusion, we propose converging the short-term integration of inputs postulated in IIT (100–300 ms as in the alpha and theta frequency range) with the longer timescales (in delta and slower frequencies) of temporo-spatial expansion in TTC. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness)
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18 pages, 1365 KiB  
Article
Application of the Catecholaminergic Neuron Electron Transport (CNET) Physical Substrate for Consciousness and Action Selection to Integrated Information Theory
by Chris Rourk
Entropy 2022, 24(1), 91; https://doi.org/10.3390/e24010091 - 6 Jan 2022
Cited by 2 | Viewed by 3789
Abstract
A newly discovered physical mechanism involving incoherent electron tunneling in layers of the protein ferritin that are found in catecholaminergic neurons (catecholaminergic neuron electron transport or CNET) is hypothesized to support communication between neurons. Recent tests further confirm that these ferritin layers can [...] Read more.
A newly discovered physical mechanism involving incoherent electron tunneling in layers of the protein ferritin that are found in catecholaminergic neurons (catecholaminergic neuron electron transport or CNET) is hypothesized to support communication between neurons. Recent tests further confirm that these ferritin layers can also perform a switching function (in addition to providing an electron tunneling mechanism) that could be associated with action selection in those neurons, consistent with earlier predictions based on CNET. While further testing would be needed to confirm the hypothesis that CNET allows groups of neurons to communicate and act as a switch for selecting one of the neurons in the group to assist in reaching action potential, this paper explains how that hypothesized behavior would be consistent with Integrated Information Theory (IIT), one of a number of consciousness theories (CTs). While the sheer number of CTs suggest that any one of them alone is not sufficient to explain consciousness, this paper demonstrates that CNET can provide a physical substrate and action selection mechanism that is consistent with IIT and which can also be applied to other CTs, such as to conform them into a single explanation of consciousness. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness)
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