This paper presents Integrated Information Theory (IIT) of consciousness 3.0, which incorporates several advances over previous formulations. IIT starts from phenomenological axioms: information says that each experience is specific – it is what it is by how it differs from alternative experiences; integration says that it is unified – irreducible to non-interdependent components; exclusion says that it has unique borders and a particular spatio-temporal grain. These axioms are formalized into postulates that prescribe how physical mechanisms, such as neurons or logic gates, must be configured to generate experience (phenomenology). The postulates are used to define intrinsic information as “differences that make a difference” within a system, and integrated information as information specified by a whole that cannot be reduced to that specified by its parts. By applying the postulates both at the level of individual mechanisms and at the level of systems of mechanisms, IIT arrives at an identity: an experience is a maximally irreducible conceptual structure (MICS, a constellation of concepts in qualia space), and the set of elements that generates it constitutes a complex. According to IIT, a MICS specifies the quality of an experience and integrated information Φ^Max its quantity. From the theory follow several results, including: a system of mechanisms may condense into a major complex and non-overlapping minor complexes; the concepts that specify the quality of an experience are always about the complex itself and relate only indirectly to the external environment; anatomical connectivity influences complexes and associated MICS; a complex can generate a MICS even if its elements are inactive; simple systems can be minimally conscious; complicated systems can be unconscious; there can be true “zombies” – unconscious feed-forward systems that are functionally equivalent to conscious complexes. Integrated information theory (IIT) approaches the relationship between consciousness and its physical substrate by first identifying the fundamental properties of experience itself: existence, composition, information, integration, and exclusion. IIT then postulates that the physical substrate of consciousness must satisfy these very properties. We develop a detailed mathematical framework in which composition, information, integration, and exclusion are defined precisely and made operational. This allows us to establish to what extent simple systems of mechanisms, such as logic gates or neuron-like elements, can form complexes that can account for the fundamental properties of consciousness. Based on this principled approach, we show that IIT can explain many known facts about consciousness and the brain, leads to specific predictions, and allows us to infer, at least in principle, both the quantity and quality of consciousness for systems whose causal structure is known. For example, we show that some simple systems can be minimally conscious, some complicated systems can be unconscious, and two different systems can be functionally equivalent, yet one is conscious and the other one is not.

Significance: Properly characterizing emergence requires a causal approach. Here, we construct causal models of simple systems at micro and macro spatiotemporal scales and measure their causal effectiveness using a general measure of causation [effective information ( EI )]. EI is dependent on the size of the system’s state space and reflects key properties of causation (selectivity, determinism, and degeneracy). Although in the example systems the macro mechanisms are completely specified by their underlying micro mechanisms, EI can nevertheless peak at a macro spatiotemporal scale. This approach leads to a straightforward way of quantifying causal emergence as the supersedence of a macro causal model over a micro one.

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 concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as 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.

Causal interactions within complex systems such as the brain can be analyzed at multiple spatiotemporal levels. It is widely assumed that the micro level is causally complete, thus excluding causation at the macro level. However, by measuring effective information—how much a system’s mechanisms constrain its past and future states—we recently showed that causal power can be stronger at macro rather than micro levels. In this work, we go beyond effective information and consider additional requirements of a proper measure of causal power from the intrinsic perspective of a system: composition (the cause–effect power of the parts), state-dependency (the cause–effect power of the system in a specific state); integration (the causal irreducibility of the whole to its parts), and exclusion (the causal borders of the system). A measure satisfying these requirements, called Φ^Max, was developed in the context of integrated information theory. Here, we evaluate Φ^Max systematically at micro and macro levels in space and time using simplified neuronal-like systems. We show that for systems characterized by indeterminism and/or degeneracy, Φ can indeed peak at a macro level. This happens if coarse-graining micro elements produces macro mechanisms with high irreducible causal selectivity. These results are relevant to a theoretical account of consciousness, because for integrated information theory the spatiotemporal maximum of integrated information fixes the spatiotemporal scale of consciousness. More generally, these results show that the notions of macro causal emergence and micro causal exclusion hold when causal power is assessed in full and from the intrinsic perspective of a system.

Natural selection favors the evolution of brains that can capture fitness-relevant features of the environment's causal structure. We investigated the evolution of small, adaptive logic-gate networks (“animats”) in task environments where falling blocks of different sizes have to be caught or avoided in a ‘Tetris-like’ game. Solving these tasks requires the integration of sensor inputs and memory. Evolved networks were evaluated using measures of information integration, including the number of evolved concepts and the total amount of integrated conceptual information. The results show that, over the course of the animats' adaptation, i) the number of concepts grows; ii) integrated conceptual information increases; iii) this increase depends on the complexity of the environment, especially on the requirement for sequential memory. These results suggest that the need to capture the causal structure of a rich environment, given limited sensors and internal mechanisms, is an important driving force for organisms to develop highly integrated networks (“brains”) with many concepts, leading to an increase in their internal complexity. The capacity to integrate information is a prominent feature of biological brains and has been related to cognitive flexibility as well as consciousness. To investigate how environment complexity affects the capacity for information integration, we simulated the evolution of artificial organisms (“animats”) controlled by small, adaptive neuron-like networks (“brains”). Task environments varied in difficulty due primarily to the requirements for internal memory. By applying measures of information integration, we show that, under constraints on the number of available internal elements, the animats evolved brains that were the more integrated the more internal memory was required to solve a given task. Thus, in complex environments with a premium on context-sensitivity and memory, integrated brain architectures have an evolutionary advantage over modular ones.