In the physical sciences a rigorous theory is a hierarchy of descriptions in which causal relationships between many general types of entity at a phenomenological level can be derived from causal relationships between smaller numbers of simpler entities at more detailed levels. The hierarchy of descriptions resembles the modular hierarchy created in electronic systems in order to be able to modify a complex functionality without excessive side effects. Such a hierarchy would make it possible to establish a rigorous scientific theory (...) of consciousness. The causal relationships implicit in definitions of access consciousness and phe- nomenal consciousness are made explicit, and the corresponding causal relationships at the more detailed levels of perception, memory, and skill learning described. Extension of these causal relationships to physiological and neural levels is discussed. The general capability of a range of current consciousness models to support a modular hierarchy which could generate these causal relationships is reviewed, and the specific capabilities of two models with good general capabilities are compared in some detail. Ó 2003 Elsevier Inc. All rights reserved. (shrink)