---
identifier: iit:postulate/exclusion
title: Exclusion
vetted_by: "William G. P. Mayner"
formalism: iit-4.0-2026
see_also:
  - iit:measure/phi-s
sources:
  - ref: iit:ref/albantakis-2023b
    at: >-
      "Postulates of physical existence" for the postulate; "Exclusion:
      Determining maximal substrates (complexes)", Eqs (24)–(26), for its
      operational form and for maximal unit grains; S1 Text, "Resolving ties in
      the IIT algorithm", for the tie cascade
---

The exclusion postulate requires that a substrate's cause–effect power be
**definite**: it must specify its cause–effect state as *this* whole set of
units. The set that qualifies is the one that is maximally irreducible, as
measured by maximum system integrated information (φ_s\*). That set is called a
maximal substrate, or complex.

Exclusion fixes two things about a substrate. It fixes the **borders**: among
candidate systems competing over overlapping units, the complex is the one with
maximal φ_s, and overlapping candidates with lower φ_s are excluded from
existence. It also fixes the **grain**, since the units constituting a system
must themselves be definite. Across the possible micro- and macroscopic levels
at which units could be defined, the winning grain is the one that maximizes
φ_s for the entity whose units they are.

What exclusion does *not* fix is which cause–effect state a system specifies.
That falls under the information postulate, which requires the substrate's
cause–effect power to be specific, resolved by maximal intrinsic information.
Exclusion does reach state at the level of a mechanism: mechanisms within a
complex must specify a definite cause and effect, and the purview selected is
the one over which integrated information is maximal.

Applied recursively, exclusion condenses a universe into a disjoint and
exhaustive set of complexes. The substrate with maximum φ_s is identified as a
complex, its units are excluded from further consideration, and the remaining
units are searched for the next maximal substrate.

Ties are resolved by a cascade, and the terminal case disqualifies rather than
decides. If overlapping candidate systems tie for maximal φ_s, the one with
maximal structure integrated information Φ is chosen. If two or more also tie in
Φ, those systems are held **not to comply with the exclusion postulate**: they
do not qualify as complexes at all, and the next best system by φ_s that is
unique is chosen instead.

The postulate is why consciousness on IIT's account has definite borders. The
substrate that attains the maximum excludes the overlapping candidates that do
not.