Before revision:  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. The underlying definitions are a further development of the grounding of the scientific study of consciousness developed by David Chalmers and Thomas Nagel .
After revision:  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 that can be employed in the theory-building process .