System Integrated Information

Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause-effect structure unfolded from a maximally irreducible substrate (a $\Phi$-structure). In this work we introduce a definition for the integrated information of a system ($\varphi_s$) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system integrated information. We then demonstrate how the proposed measure identifies complexes as systems whose $\varphi_s$ is greater than the $\varphi_s$ of any overlapping candidate systems.