A mathematical framework using the graphical calculus of process theories (symmetric monoidal categories with Frobenius algebras) provides an ontologically neutral language to model aspects of consciousness. A toy example demonstrates how this axiomatic approach recovers features of conscious experience, including the distinction between external and internal subjective perspectives, the privacy or unreadability of personal subjective experience, and phenomenal unity—a key challenge for scientific studies of consciousness. These features emerge naturally from the compositional structure of the calculus.
Consciousness is treated as fundamental and characterized by other-dependence, meaning conscious processes are defined by their relations to one another. A mathematical framework using compact closed categories is introduced, where morphisms represent conscious processes composed of generators specified by their interrelations. This compositional model may help avoid the hard problem of consciousness and address the combination problem of conscious experiences.