Before revision:  Its aim is to develop a scientific account, formulated in terms of formal mathematical laws or regularities, of how conscious experience relates to  the physical domain (e. g. to brain processes). Even though several models of consciousness have been proposed in the literature, details of the underlying conceptual terminology and formal framework remain poorly understood. This paper aims to improve this situationby proposing a grounding of the scientific study of consciousness which is based on a concise definition of the object of investigation and gives rise to a clear-cut mathematical framework for models of consciousness . Several examples are studied and an application of this framework is given.
After revision:  Its aim is to develop a scientific account, formulated in terms of formal mathematical laws or regularities, of how conscious experience relates 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 . Several examples are studied and an application of this framework is given.