The dynamics of interaction of reflexive subjects operating with the two-valued versus many-valued logic

In this paper we aim to approach a model of interacting subjects with the opposite types of reflexion that belong to the Western (W) and Eastern (E) reflexive modes according to Vladimir Lefebvre (1992). The model represents an expansion of the previously developed model of the Double Homunculus (Sawa and Igamberdiev, 2016) that describes reflexive agents as holding “the image of the self in the image of the self”. A dialogue model between the two homunculus agents estimating their own reflexion in the opposite ways (generating the two-valued versus many-valued logic and loosely approximated as belonging to the W and E Lefebvre's types) is evolved. At the same time, the argument also unveils the relationship between a difference equation which is the key notion of the model and an emergence of logic. This can be a powerful tool for describing intercommunication of reflexive agents in the social environment as well as interactions between the entire social systems of different types.