The Double Homunculus model of self-reflective systems.

Vladimir Lefebvre introduced the principles of self-reflective systems and proposed the model to describe consciousness based on these principles (Lefebvre V.A., 1992, J. Math. Psychol. 36, 100-128). The main feature of the model is an assumption of "the image of the self in the image of the self", that is, "a Double Homunculus". In this study, we further formalize the Lefebvre's formulation by using difference equations for the description of self-reflection. In addition, we also implement a dialogue model between the two homunculus agents. The dialogue models show the necessity of both exchange of information and observation of object. We conclude that the Double Homunculus model represents the most adequate description of conscious systems and has a significant potential for describing interactions of reflective agents in the social environment and their ability to perceive the outside world.