  In recent years, promising mathematical models have been suggested which aim
to describe conscious experience and its relation to the physical domain.
Whereas the axioms and metaphysical ideas of these theories have been carefully
motivated, their mathematical formalism has not. In this article we aim to
remedy this situation. We give an account of what warrants mathematical
representation of phenomenal experience, derive a general mathematical
framework which takes into account consciousness' epistemic context and study
which mathematical structures some of the key characteristics of conscious
experience imply, showing precisely where mathematical approaches allow to go
beyond what the standard methodology can do. The result is a general
mathematical framework for models of consciousness that can be employed in the
theory-building process.
