Fig 1. Identifying substrates of consciousness through the postulates of existence, intrinsicality, information, integration, and exclusion.

(A) The substrate S = aBC in state (−1, 1, 1) (lowercase letters for units indicated state “−1,” uppercase letters state “+1”) is the starting point for applying the postulates. The substrate updates its state according to the depicted transition probability matrix (TPM) (gray shading indicates probability value from white (p = 0) to black (p = 1); each unit follows a logistic equation (see “Results” for definition) with k = 4.0 and connection weights as indicated in the causal model). Existence requires that the substrate must have cause–effect power, meaning that the TPM among substrate states must differ from chance. (B) Intrinsicality requires that a candidate substrate, for example, units aB, has cause–effect power over itself. Units outside the candidate substrate (in this case, unit C) are treated as background conditions. The corresponding cause and effect TPMs (T_c and T_e) of system aB are depicted on the right. (C) Information requires that the candidate substrate aB selects a specific cause–effect state (s′). This is the cause state (red) and effect state (green) for which intrinsic information (ii) is maximal. Bar plots on the right indicate the three probability terms relevant for computing ii_c (7) and ii_e (5): the selectivity (light colored bar), as well as the constrained (dark colored bar) and unconstrained (gray bar) effect probabilities in the informativeness term. (D) Integration requires that the substrate specifies its cause–effect state irreducibly (“as one”). This is established by identifying the minimum partition (MIP; θ′) and measuring the integrated information of the system (φ_s)—the minimum between cause integrated information (φ_c) and effect integrated information (φ_e). Here, gray bars represent the partitioned probability required for computing φ_c (20) and φ_e (19). (E) Exclusion requires that the substrate of consciousness is definite, including some units and excluding others. This is established by identifying the candidate substrate with the maximum value of system integrated information (${\phi }_s^{*}$)—the maximal substrate, or complex. In this case, aB is a complex since its system integrated information (φ_s = 0.17) is higher than that of all other overlapping systems (for example, subset a with φ_s = 0.04 and superset aBC with φ_s = 0.13).