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Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms

Larissa Albantakis, Leonardo Barbosa, Graham Findlay, Matteo Grasso, Andrew M Haun, William Marshall, William GP Mayner, Alireza Zaeemzadeh, Melanie Boly, Bjørn E Juel, Shuntaro Sasai, Keiko Fujii, Isaac David, Jeremiah Hendren, Jonathan P Lang, Giulio Tononi

arXiv:2212.14787v1q-bio.NC

TL;DR

Consciousness remains difficult to formulate in objective physical terms while explaining why experience depends on particular substrates and states. IIT 4.0 translates phenomenal axioms into physical postulates and concludes that each experience corresponds to an irreducible, structured Φ-structure rather than merely a set of functions.

  • Problem

    A scientific theory must explain subjective experience in objective terms and account for its dependence on particular portions of the world and their states.

    Source: Introduction · p. 2

  • Method

    IIT infers physical postulates from phenomenal axioms, requiring cause–effect power to be intrinsic, informative, integrated, definite, and structured.

    Source: Introduction · p. 2

  • Results

    Each experience corresponds to a Φ-structure rather than a set of functions, so functionally equivalent systems need not be phenomenally equivalent.

    Source: Conclusions · p. 38

  • Takeaways & Limitations

    Consciousness is characterized by a substrate’s unfolded, irreducible cause–effect structure, which IIT uses to relate physical distinctions and relations to experiential quality.

    Source: Conclusions · p. 37

    IIT’s axiomatic basis, translation into postulates, discrete atomic-unit assumptions, and brain-substrate predictions remain open to empirical and physical scrutiny.

    Source: Conclusions · p. 40

Abstract

from arXiv · show

This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate translation of axioms into postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system's irreducible cause-effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

Author summary · Introduction

IIT 4.0 explains phenomenal properties in strictly operational physical terms, beginning from experience and deriving substrate requirements through axioms, postulates, and mathematical formalism. It identifies experience with the cause–effect structure unfolded from a maximal substrate and refines the theory with new measures, causal assessment, and testable predictions.

Introduction

  • IIT begins from experience itself—immediate and irrefutable—and identifies five phenomenal axioms: intrinsicality, information, integration, exclusion, and composition.Source: Introduction · p. 2
  • Physical existence is treated as an operational postulate: something exists physically when it has cause–effect power, taking and making a difference for a conscious observer or manipulator.Source: Introduction · p. 2
  • IIT maps each phenomenal axiom onto a corresponding physical requirement, so a conscious substrate must have cause–effect power that is intrinsic, specific, unitary, definite, and structured.Source: Introduction · p. 2
  • IIT’s fundamental explanatory identity equates an experience with the cause–effect structure unfolded from a maximal substrate, without additional ingredients.Source: Introduction · p. 2
  • The mathematical framework applies in principle to general models of interacting units, enabling consistency checks, predictions about experience and its brain substrate, and inferences about consciousness in other beings.Source: Introduction · p. 2
  • IIT aims to explain why consciousness depends on particular brain regions and states, fades during dreamless sleep, and has specific qualitative features; several predictions have been or are being tested empirically.Source: Introduction · pp. 2–3
  • IIT 4.0 presents a more complete and self-consistent formulation, with more accurate axiom-to-postulate translations, the Intrinsic Difference measure, and explicit assessment of causal relations.Source: Introduction · p. 3
  • The paper updates IIT’s mathematical formalism, demonstrates internal consistency through representative examples, and computationally unfolds substrates’ cause–effect structures, while situating motivation and predictions in related works.Source: Introduction · p. 3

From phenomenal axioms to physical postulates

IIT 4.0 derives physical postulates from five essential properties of experience, treating cause–effect power as the necessary and sufficient basis of consciousness. It identifies the resulting Φ-structure of a maximal substrate with the experience’s phenomenal properties.

Axioms of phenomenal existence

  • Experience begins as IIT’s immediate and irrefutable zeroth axiom and has five essential properties: intrinsicality, information, integration, exclusion, and composition.These specify experience as existing for itself, being specific, forming an irreducible whole, being definite, and comprising distinctions and relations; candidate properties such as space, time, intentionality, and affect are not essential because experiences lacking them are conceivable and achievable.Source: Axioms of phenomenal existence · p. 3

Postulates of physical existence

  • IIT’s physical postulates are necessary and sufficient for consciousness because they translate every essential phenomenal property into requirements on a substrate’s cause–effect power.Existence requires cause–effect power; intrinsicality, information, integration, exclusion, and composition require intrinsic, specific, unitary, definite, and structured cause–effect power, respectively.Source: Postulates of physical existence · pp. 4–5

The explanatory identity between experiences and Φ-structures

  • The Φ-structure unfolded from a maximal substrate accounts one-to-one for every property of experience through its objectively characterized cause–effect power, without ad hoc ingredients.The identity is explanatory rather than a correspondence between separate things: subjective feeling is explained operationally or physically by cause–effect power.Source: The explanatory identity between… · pp. 5–6

Box 1. Methodological guidelines of IIT

  • IIT grounds physical existence in reliable cause–effect power and operational reductionism, evaluating systems intrinsically and, ideally, down to the smallest observable and manipulable units.A substrate must be able to take and make a difference; its transition probability matrix should capture this power, while intrinsic evaluation makes information state-specific and treats external units as fixed background conditions.Source: Box 1. Methodological guidelines of IIT · pp. 6–7

Overview of IIT’s framework

IIT 4.0 formalizes a substrate’s cause–effect structure from its transition probabilities, identifying consciousness substrates through intrinsic, specific, integrated, and exclusive cause–effect power. It then unfolds each maximal substrate’s Φ-structure into distinctions and relations whose integrated information specifies experience’s quality and quantity.

Overview of IIT’s framework

  • IIT 4.0 characterizes a substrate in a given state through its transition probability function and mathematically identifies candidate systems satisfying the postulates of consciousness.The formalism selects a maximal cause–effect state using intrinsic information (ii), then selects a maximal substrate using integrated information (ϕs) relative to overlapping candidates.Source: Overview of IIT’s framework · p. 7, Implementing the postulates · p. 8
  • IIT 4.0 is the first formulation that aims to characterize Φ-structures completely using measures that uniquely satisfy the postulates, while remaining a work in progress.The paper applies the formalism to extremely simple simulated networks as illustrations of how hypothetical substrates’ cause–effect power can be unfolded.Source: Overview of IIT’s framework · p. 7, Substrates, transition probabilities,… · p. 8

Substrates, transition probabilities, and cause–effect power

  • The TPM represents a stochastic system’s cause–effect power as intervention-defined transition probabilities over a finite, discretely updating state space with conditionally independent units.IIT operationally treats physical existence as the ability to take and make a difference, while practical causal models need capture only relevant explanatory and predictive features.Source: Substrates, transition probabilities,… · p. 8

Existence

  • Existence requires causal informativeness, while intrinsicality requires that an open system exert cause–effect power within itself rather than through its external background.Cause and effect informativeness compare probability changes against chance; conditioning external units fixes them as causally inert background conditions.Source: Existence · p. 8, Intrinsicality · p. 9

Information

  • The information postulate selects a specific maximal cause–effect state by maximizing intrinsic information, the product of informativeness and selectivity.This creates a tradeoff between expansion and dilution: larger systems may diverge more from chance while concentrating less power on a specific state.Source: Information · p. 9

Integration

  • Integration requires the maximal cause–effect state to be irreducible, measured by integrated information (ϕs) under the minimum partition that makes the least difference.Integrated information is sensitive to fault lines separating weakly or directionally interacting system parts.Source: Integration · p. 9

Exclusion

  • Exclusion selects a definite grain and maximal substrate—the unit set maximizing integrated information over itself—among overlapping candidate systems.Over a universal substrate, complexes can be identified recursively by repeatedly selecting maxima among competing overlapping sets.Source: Exclusion · p. 9

Composition

  • Composition unfolds a complex by evaluating mechanisms over subsets, binding congruently overlapping distinctions through causal relations, and summing their integrated information into structured information (Φ).The resulting Φ-structure comprises distinctions and relations congruent with the complex’s whole-system cause–effect state and corresponds to the quality of experience, while their summed ϕd/r values determine its quantity.Source: Composition · p. 10

Box 2. Ontological principles of IIT

This section formalizes IIT’s procedure for identifying maximal complexes and unit grains and unfolding their irreducible cause–effect structure. It defines the resulting distinctions, relations, and Φ-structure in terms of intrinsic causal powers and experience.

Box 2. Ontological principles of IIT

  • IIT defines being as having physical cause–effect power—taking and making a difference—and maximal existence selects the complex with greatest system integrated information ϕs.The maximal-existence principle also determines the system state, mechanisms, distinctions, relations, and grain; overlapping candidates with lower ϕs are excluded.Source: Box 2. Ontological principles of IIT · p. 11
  • Minimal existence evaluates irreducibility at the least irreducible partition and takes the minimum of cause- and effect-side irreducibility.A system or distinction exists only to the extent that it specifies both an irreducible cause and an irreducible effect.Source: Box 2. Ontological principles of IIT · p. 11

Existence, intrinsicality, and information: Determining the maximal cause–effect state of a candidate system

Exclusion: Determining maximal substrates (complexes)

Informativeness (over chance)

  • Informativeness requires cause and effect probabilities to exceed chance, whereas selectivity measures how concentrated that deviation is on one selected state.Their product creates a tension between larger systems’ higher informativeness and lower selectivity; indeterminism and degeneracy reduce intrinsic information, measured in ibits.Source: Informativeness (over chance) · p. 14, Selectivity (over states) · pp. 14–15

The maximal cause–effect state

  • The maximal cause–effect state is the state that maximizes intrinsic information, whose formal measure uniquely satisfies causality, specificity, and intrinsicality aligned with IIT’s postulates.Intrinsic information is formally equivalent to a measure of intrinsic difference.Source: The maximal cause–effect state · p. 15

Integration: Determining the irreducibility of a candidate system

  • Integration requires a candidate substrate to specify its cause–effect state irreducibly as one system rather than as separately existing subsets.Directional partitions cut inputs, outputs, or both by replacing affected causal connections with independent noise; valid parts must interact with the rest in both causal directions.Source: Integration: Determining the… · p. 16, Directional system partitions · pp. 16–17

System integrated information ϕs

  • System integrated information ϕs quantifies irreducible existence as the minimum cause–effect irreducibility across the minimum partition.The MIP identifies the least irreducible fault line, and normalization assesses integration relative to each partition’s maximum possible value.Source: System integrated information ϕs · pp. 17–18

Determining maximal substrates recursively

  • Recursive substrate search condenses the universe into a disjoint, exhaustive set of complexes, excluding overlapping substrates that specify less integrated information.Tied maximal systems are resolved by selecting the next unique system when necessary.Source: Determining maximal substrates… · p. 18

Determining maximal unit grains

  • Across possible spatial, temporal, and state grains, the winning grain maximizes the complex’s irreducible existence, while candidate units must themselves be maximally irreducible within.Among candidate unit sets, the existing macro-unit set maximizes the existence of the complex to which the units belong.Source: Determining maximal unit grains · pp. 18–19

Unfolding the cause–effect structure of a complex through composition

Composition and causal distinctions

  • A causal distinction comprises a mechanism, a maximal cause–effect state over linked purviews, and positive irreducibility, with purviews selected by intrinsic information and integrated information.The updated formalism additionally requires causal distinctions to be congruent with the system’s maximal cause–effect state.Source: Composition and causal distinctions · pp. 19–20

Existence, intrinsicality, and information: Determining the cause and effect state specified by a mechanism over candidate purviews

  • Mechanism-specific cause and effect states are computed from interventional probabilities after causal marginalization, using product distributions that impose conditional independence and distinguish IIT’s analysis from standard information-theoretic flow.Intrinsic information combines informativeness with selectivity, balancing deviation from chance against concentration on particular purview states.Source: Existence, intrinsicality, and… · pp. 20–21

Integration: Determining the irreducibility of a candidate distinction

  • Integration measures whether a mechanism’s specified cause or effect is irreducible by testing disintegrating partitions and evaluating the minimum partition; ϕ(m, Z) therefore quantifies irreducible existence.A partition can cut a multi-unit mechanism into independent parts or sever all mechanism–purview connections.Source: Integration: Determining the… · pp. 22–23

Exclusion: Determining causal distinctions

  • Exclusion selects the cause and effect purviews with maximum integrated information, and a mechanism’s distinction irreducibility is the minimum of its integrated cause and effect information.This makes each mechanism select definite causal purviews rather than contributing across all candidate purviews.Source: Exclusion: Determining causal… · p. 23

Composition and causal relations

  • Causal relations bind distinctions when their causes or effects overlap congruently over shared units, with relation irreducibility measuring the integrated binding of their cause–effect power.Relations contain sets of distinctions, faces representing shared cause–effect aspects, and an associated ϕr > 0; relations binding h distinctions are h-degree relations.Source: Composition and causal relations · pp. 24–25
  • Relations bind distinctions whose cause–effect purviews overlap congruently, with relation integrated information limited by the weakest distinction’s integrated information.A maximal relation fully overlaps each distinction’s cause and effect, and distinctions plus their relations compose a cause–effect structure.Source: Composition and causal relations · pp. 26–27

Cause–effect structures and Φ-structures

  • A complex is a substrate whose intrinsic, specific, irreducible, definite, and structured causal powers are unfolded into a Φ-structure existing for itself.The Φ-structure is the union of the substrate’s distinctions and binding relations, rather than the substrate as observed operationally.Source: Cause–effect structures and Φ-structures · p. 28
  • An experience is identical to an intrinsic entity’s Φ-structure: its structure specifies experiential quality, while its Φ value specifies the quantity of intrinsic content.This follows IIT’s explanatory identity, which requires each property of experience to correspond to a property of the Φ-structure without additional ingredients.Source: Cause–effect structures and Φ-structures · p. 28

Results and discussion

The results and discussion apply IIT 4.0 to simple binary networks to examine how intrinsic causal organization gives rise to complexes, Φ-structures, and consciousness. They also clarify IIT’s identification of consciousness with Φ-structures, its testable predictions and theoretical implications, and the computational and empirical limitations of analyzing realistic systems.

Degenerate systems, indeterminism, and specificity

  • Degeneracy and indeterminism limit maximal substrates: bottleneck connectivity produces small complexes and low Φ by reducing selectivity, intrinsic information, and ϕs.The authors suggest that large, high-Φ substrates require specialized units with low degeneracy and highly effective, low-indeterminism interactions.Source: Degenerate systems, indeterminism, and… · p. 31

Modular systems, fault lines, and irreducibility

  • Modular fault lines split a six-unit network into three small complexes with low Φ, paralleling the proposed effects of cerebellar modularity and slow-wave-sleep disconnection.Fault lines may arise anatomically or physiologically; bistability can make cortical interactions causally ineffective and is associated with loss of consciousness.Source: Modular systems, fault lines, and… · pp. 31–32

Directed cycles, structural sparseness, and composition

  • A six-unit directed cycle forms a complex with ϕs = 1.74 ibits but Φ = 7.65, because sparse first-order structure lacks cross-connected relations.By contrast, a specialized six-unit lattice has 24 distinctions among 63 possible and many more causal relations than the copy loop.Source: Directed cycles, structural… · p. 32

Near-maximal substrates, extrinsic entities, and exclusion

  • A slightly less irreducible six-unit whole excludes its integrated four-unit subset from the main complex, showing that intrinsic maximal irreducibility overrides extrinsic unity.The remaining units become a lower-ϕs background complex, while connectivity determines which units constitute complexes and the structured information they specify.Source: Near-maximal substrates, extrinsic… · p. 33

Consciousness and activity: active, inactive, and inactivated units

  • Changing one unit’s state can reorganize an entire Φ-fold: turning E OFF changes purviews and irreducibility and increases relations, while inactivation shrinks the complex to four units with 14 distinctions and Φ = 3.31.An inactive unit can contribute to experience, whereas an inactivated unit ceases to contribute altogether.Source: Consciousness and activity: active,… · pp. 33–35

Consciousness and functional equivalence: being is not doing

  • Functionally equivalent systems can differ phenomenally: one has Φ = 21.01 ibits, another Φ = 3.64 ibits, and a feed-forward system has ϕs = 0 ibits.Although the three systems share coin-counting behavior and global dynamics, their differing internal architectures specify different cause–effect structures; recurrent behavior can therefore be implemented without consciousness.Source: Figure 8 · p. 36, Consciousness and functional… · pp. 36–37

Conclusions

  • IIT defines a complex through an unfolded Φ-structure whose subset causal powers specify informative, irreducible, definite, and composed cause–effect distinctions and relations.The postulates constrain substrates: nonspecific, weakly integrated, or structurally sparse systems may fail to form large or maximally irreducible complexes, and a universal substrate condenses into disjoint complexes.Source: Conclusions · p. 37
  • Consciousness corresponds to the Φ-structure specified by a substrate in its current state, so small state changes can produce major experiential changes.The physical correspondent is not the substrate as such; changing one unit can alter an entire Φ-fold, and inactivating a unit can collapse its associated fold (Fig. 7).Source: Conclusions · p. 38
  • Because consciousness concerns being rather than doing, functionally equivalent architectures need not be phenomenally equivalent; feed-forward systems cannot constitute complexes, unlike suitable recurrent systems.This implies that behaviorally human-like artificial systems may experience nothing or nearly nothing if their physical architecture lacks maximal irreducibility.Source: Conclusions · p. 38
  • Exhaustively unfolding realistic systems is infeasible because observations, manipulations, partitions, distinctions, relations, grains, and maximizations create nested combinatorial explosions.Full analyses are currently limited to idealized systems of a few units, while approximations and bounded estimates of Φ remain active research areas.Source: Conclusions · p. 38
  • IIT predicts high Φ in wakefulness and dreaming and low Φ in dreamless sleep and anesthesia, with crude Φ approximations already classifying humans as conscious or unconscious.It also predicts where the brain’s main complex lies, how inactive constituents support consciousness, and that complete inactivation causes absolute agnosia.Source: Conclusions · pp. 38–39
  • The composition of a Φ-structure should account for experiential quality, including spatial extendedness in 2D-grid substrates and changes caused by connection strength even without altered neural activity.Further validation requires systematic exchange among phenomenology, theoretical inference, and neuroscientific evidence.Source: Conclusions · p. 39
  • IIT’s intrinsic ontology extends its postulates toward actual causation, a unified causal account of information, and inferences about consciousness, agency, and nonhuman minds, while remaining vulnerable to theoretical and empirical failure.Open questions concern the compatibility of discrete atomic units with physics, the uniqueness of the axioms-to-postulates translation, and whether brain studies support IIT’s quantity–quality relationship.Source: Conclusions · pp. 39–40

A Appendix · A.1 Ties

IIT 4.0 resolves ties caused by architectural or functional symmetries by applying maximal-existence principles to substrates, system states, and mechanisms. Selection proceeds through intrinsic information, integrated information, and structured information, with some residual ties treated as extrinsic or resolved by relational support.

A.1 Ties

  • Symmetric architectures or unit input–output functions can produce ties among unit sets or cause–effect states for maximal intrinsic information or cause–effect power.The appendix outlines tie resolution in accordance with IIT’s postulates and principles.Source: §A.1 · p. 40
  • Maximal substrates are identified iteratively, with each maximal substrate excluding overlapping systems having lower ϕs from existing as complexes.If overlapping systems tie for maximality, the next unique best system is selected; see and.Source: §A.1 · p. 40
  • For tied system states, IIT first maximizes intrinsic cause and effect information and then selects the state with maximal integrated information ϕs over its minimum partition.Remaining equal-ϕs states do not affect system selection but must be resolved to determine the cause–effect structure.Source: §A.1 · p. 40
  • Remaining system-state ties are resolved by choosing the cause–effect state with maximal structured information Φ.In highly symmetrical systems, tied Φ values may specify intrinsically identical cause–effect structures, making the tie extrinsic rather than a violation of the information postulate.Source: §A.1 · pp. 40–41
  • Mechanism cause or effect states are first selected by intrinsic information ii(m, z), then compared across maximal states and purviews using integrated information ϕ.This identifies the mechanism’s maximally irreducible cause or effect state z∗c/e.Source: §A.1 · p. 41
  • Ties in a mechanism’s maximal ϕd and cause–effect state can be resolved at the cause–effect-structure level by selecting the state that maximizes system structured information Φ.This applies the maximum existence postulate to tied distinctions.Source: §A.1 · p. 41
  • For mechanism-state ties within one purview, IIT selects the state congruent with the system’s cause–effect state, whereas ties across purviews generally favor the state supporting more relations, typically involving larger purviews.These rules preserve specific cause–effect states for mechanisms and systems as required by the information and exclusion postulates.Source: §A.1 · pp. 40–41

A.2 Comparison to IIT 1.0–3.0 and subsequent publications

IIT 4.0 presents a more complete, self-consistent formulation while retaining IIT’s core theory and refining its formal framework. Its main advances are a uniquely postulate-consistent Intrinsic Difference measure, explicit causal-relation assessment, and more exact axiom-to-postulate translation.

Comparison to IIT 1.0–3.0 and subsequent publications

  • IIT 4.0 presents a more complete, self-consistent formulation than IIT 1.0–3.0 while retaining the theory’s core and progressively refining its formal framework.The section focuses mainly on developments subsequent to IIT 3.0, which already compared earlier versions.Source: §A.2 · p. 41
  • IIT 4.0 introduces an Intrinsic Difference measure uniquely consistent with IIT’s postulates, explicitly assesses causal relations, and translates axioms into postulates more exactly.Source: §A.2 · p. 41

Axioms and postulates

IIT 4.0 distinguishes phenomenal existence from intrinsicality by introducing existence as a foundational zeroth axiom, followed by five axioms describing experience’s essential properties. Its revised postulates more closely track these axioms, grounding specific cause–effect states and phenomenal distinctions and relations in physical causal terms.

Axioms

  • IIT 4.0 defines existence of experience as a foundational zeroth axiom and identifies intrinsicality, information, integration, exclusion, and composition as five essential properties of every conceivable experience.This exposition separates phenomenal existence, which is not itself a property, from intrinsicality, which is an essential property of phenomenal existence.Source: Axioms and postulates · p. 41

Postulates

  • The revised postulates are designed to track the refined axioms more closely than in IIT 3.0, avoiding misunderstandings and emphasizing their immediacy and irrefutability.The postulates were updated correspondingly to improve the translation from phenomenal axioms into physical terms.Source: Axioms and postulates · p. 41
  • The information postulate now requires a system to select a specific cause–effect state over its units, conforming more closely to the information axiom.This refinement makes the physical requirement more directly match the axiom’s emphasis on specificity.Source: Axioms and postulates · p. 41
  • The composition postulate accounts for phenomenal distinctions and relations through causal distinctions and relations, and therefore comes last because structured experience must be intrinsic, specific, irreducible, and definite.Composition captures both the distinctions and their relations that constitute experiential structure.Source: Axioms and postulates · p. 41

Identifying maximal substrates

IIT 4.0 identifies maximal substrates (complexes) using state-dependent system integrated information, with directional minimum partitions normalized to detect candidate systems’ fault lines. A system exists only when it has positive cause and effect power.

Identifying maximal substrates

  • Maximal substrates, or complexes, are identified using system integrated information ϕs, with directional system partitions retained from IIT 3.0.This approach differs from IIT 3.0 by evaluating integration at the system level rather than after composition.Source: Identifying maximal substrates · p. 42
  • The minimum partition is the partition with minimal ϕs normalized by the maximum possible ϕs for an arbitrary TPM of matching dimensions, making it sensitive to candidate systems’ fault lines.This normalization prevents the analysis from defaulting to partitions of individual system units.Source: Identifying maximal substrates · p. 42
  • The IIT 4.0 analysis is state-dependent, and a system exists only if it has positive cause and effect power.These conditions continue features associated with earlier IIT formulations.Source: Identifying maximal substrates · p. 42

Measuring intrinsic information

IIT 4.0 introduces a new Intrinsic Difference measure that uniquely complies with IIT’s postulates and evaluates intrinsic information as the product of informativeness and selectivity.

Measuring intrinsic information

  • IIT 4.0 replaces prior Kullback-Leibler divergence and extended Earth Mover’s Distance measures with Intrinsic Difference (ID), which uniquely complies with IIT’s postulates.Intrinsic information is evaluated over specific cause or effect states, and its maximum across a state distribution identifies the state selected by the system or mechanism.Source: Measuring intrinsic information · p. 42
  • Intrinsic information is the product of informativeness and selectivity and is subadditive when p < 1, indicating cause–effect power spread across multiple states.The measure evaluates information over specific cause or effect states in accordance with the information postulate.Source: Measuring intrinsic information · p. 42

Causal distinctions

IIT 4.0 reformulates causal distinctions as irreducible mechanisms selecting specific cause and effect states, extending earlier formalisms. Its updates determine these states independently of partitions and retain only system-congruent distinctions.

Causal distinctions

  • IIT 4.0 replaces IIT 3.0’s “concepts” terminology with causal distinctions that specify system subsets as causes and effects, requiring irreducibility (ϕd > 0).The formalism identifies distinctions within the system and preserves the irreducibility requirement from IIT 3.0.Source: Causal distinctions · p. 42
  • Mechanisms select specific cause and effect states using Intrinsic Difference, while updated permissible partitions ensure that partitions are always disintegrating.The cause and effect probability definitions remain unchanged but are expressed formally through product probabilities rather than “virtual elements”.Source: Causal distinctions · p. 42
  • Cause–effect states are selected by intrinsic information before integrated information is evaluated, ensuring mechanism-level selection independent of partitioning and satisfying the existence postulate.The formulation also removes the absolute value, uses effect probabilities on the cause side, and resolves ties by maximal existence.Source: Causal distinctions · p. 42
  • A candidate distinction contributes to the system’s cause–effect structure only when its maximal cause–effect state is congruent with the system’s maximal state.This congruence condition limits distinctions to those compatible with the system-level cause–effect state.Source: Causal distinctions · p. 43

Relations

IIT 4.0 explicitly formalizes phenomenal relations as causal relations among distinctions with overlapping causes and/or effects, and defines experience through the resulting Φ-structure. It also provides an analytical method for summing relation integrated information without evaluating relations individually, while treating self-relations separately.

Relations

  • IIT 4.0 distinguishes relations from their faces: relations bind distinctions with overlapping causes and/or effects, while faces specify maximal purview overlap and the relation type.Each distinction contributes its full ϕd, weighted by the extent of its joint overlap; its irreducible information is not recomputed over the candidate overlap.Source: Relations · p. 43
  • A conscious complex is a maximum of system integrated information ϕs under information, integration, and exclusion, with experience quality given by its unfolded distinctions and relations.The quantity of consciousness is the Φ value, summing integrated information across all distinctions and relations in the Φ-structure.Source: Relations · p. 43

Analytical solution

  • The analytical solution computes the total relation integrated information and relation count from the set of causal distinctions by constructing congruently overlapping relation faces and overlaps.Any subset of at least two distinctions whose purviews overlap congruently defines a relation face, and the relation overlap is the union of the face overlaps.Source: Relations · pp. 43–44
  • The final computation sums integrated information for all non-self-relations without combinatorial explosion, while self-relations are assessed individually.The summation is organized through distinctions containing each node in their cause or effect purviews, then factored over subsets of those node-associated distinctions.Source: Relations · pp. 44–45

Analytical count of the number of relations · A.4 IIT Algorithm

The section develops an analytical method for counting causal relations among distinctions in D(TS, s). It generalizes Z(n), applies inclusion–exclusion, and excludes self-relations from the resulting count.

Analytical count of the number of relations

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