# IIT 4.0

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This page lists the changes and ingredients introduced in IIT 4.0 relative to IIT 3.x.

For a complete mathematical account of IIT 3.x, cf. *Kleiner & Tull, The Mathematical Structrue of IIT, 2021*. For brevity, we will also use the terminology introduced in this paper.

## Contents

# What is IIT 3.x?

IIT 3.0 refers to IIT as introduced in *Oizumi & Albantakis &Tononi, From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0, 2014*.

IIT 3.x refers to the same version of the theory, but with *all* changes that have been proposed by the group in published papers before the 4.0 version taken into account. A mathematical introduction to and definition of IIT 3.x is available in the paper mentioned in the introduction.

# Terminological changes

There are a number of purely terminological changes:

- Distinctions
- Distinctions are what has previously been called
*concepts*.

- -Structure
- -Structure refers to what has previously been called
*Maximally Irreducible Conceptual Structures*, but with new things, such as the relations, added in.

- Causal Relations
- Causal relations are a new ingredient introduced in IIT 4.0. They give rise to a relational structure on the space of conscious experiences.

- Most informative
- Whereas in IIT 3.x, the the term "core" was used in characterizing cause-effect structures and the like of particular interest, in IIT 4.0 these are referred to as "most informative". For example the "most informative effect state".

# New stuff

The following is trying to be (become) a complete list of changes and additions in IIT 4.0 relative to IIT 3.x. Please extend in case there are further updates not already listed.

## New distance function

IIT 3.x makes use of a distance function on a space probability distributions. The theory uses this space of probability distributions in order to construct a space which it claims is identical to conscious experiences. Both the individual spaces as well as the prodcts are instantiations of what is called an *experience space* in Kleiner & Tull, which includes the said distance function.

Whereas in IIT 3.x the distance function is an adaptation of the first Wasserstein metric over probability distributions (also, known as Earth Mover's Distace; cf. Kleiner & Tull for details), IIT introduces a new distance measure, called **Intrinsic Difference**. It is similar to the KL-divergence, but extends to product spaces by use of the 'maximum' of the distances of the component spaces.
For details and a conceptual justification of this new measures, cf. Barbosa et al., A measure for intrinsic information, 2020, Theorem 1 in the *Supplementary Material (!)*.

## More constrained partitions

In IIT 3.x, every choice of subsystems gave a partition of the system. In IIT 4.0, partitions are more constrained, they have to destroy the mechanism.

## Introduction of relations

The most significant change in IIT 4.0 is the introduction of relations.

Relations are introduced on what is called the 'mechanism level' in Kleiner & Tull, once the mechanisms (now called distinctions) are determined, roughly as follows:

- For any two of the core causes and core effects of a mechanism (old terminology), one determines the maximal overlap between them. Here, overlap defers to subsystems: A cause overlaps with another cause or effect if they both comprise the same subsystem.
- For every such maximal overlap, one defines a relational small phi values in a specific way.
- A relation is then a tripe of the core effect/cause, the maximal overlap and the -value. As with mechanisms aka distinctions, they only count if .

The result of this is, for every candidate system, something similar to the concept defined in Eq. (8) in Kleiner & Tull, but now for relations. This relational structure is being added (in the sense of a directional product) to the concept. Extending the distance from concept spaces to relation sapces conceived in this way, the system level algorithm is then applied as before.

## Some change in picking a state differently when partitioning

TBA (Johannes didn't understand the comment ;-) )

TBA

## How to identify conscious systems

TBA