Integrated information theory (IIT) proposes that consciousness is identical to maximally integrated conceptual information, measured by Φmax, and that experience corresponds to a set of maximally irreducible cause-effect repertoires. This work reformulates IIT in the language of probabilistic models, where a system's dynamics are described by a first-order time-invariant Markov process. The authors provide a constructive rule for decomposing a system into subsystems based on marginalization and factorization of the joint probability distribution over two adjacent time points.
Integrated information theory (IIT) identifies consciousness with maximally integrated conceptual information, quantified by Φ^max, and holds that phenomenal experience corresponds to the maximally irreducible cause-effect repertoires of a physical system in a given state. This work provides a general formulation of Φ^max using probabilistic models, treating the system as a first-order time-invariant Markov process and specifying all operations via the system's joint probability distribution over two adjacent time points.