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A dynamical model for individual and social cognitive infocommunications over truth values

In this paper, I give a method to capture the dynamical cognitive process of a statement from logical systems to belief systems for a subject and a society. For a subject part, a reinforcement function is utilized to model the dynamical enhancement of belief over the span of his life. There are two situations to be considered here: a closed system and an open system. In a closed system, the subject inherits no belief from his environment regarding one statement and the truth value of the statement is decided by the subject only after the interaction with other subjects; while, in an open one, he inherits some belief from it. I use a hereditary function to capture such inheritance. In this case, the truth value of the statement for a subject is decided by the community, though the weights might differ from subject to subject. For the society part, a dynamical social belief is represented by the average belief of all the subjects in it.