Subdynamics in Knowledge-Based Systems

Using a set of six equations, I propose to model “interactions,” the “organization of meaning,” and “self-organization” as three coordination mechanisms among expectations; three further equations can be derived to operationalize “double contingency,” “identity,” and “reflection.” One can expect that the subdynamics update one another in co-evolutions as feedbacks and feed-forwards. Interfaces among two (sub)dynamics can be expected to operate with time differences (At). Interactions among horizontal and vertical time differences can generate hyper-incursivity in interhuman communications. Hyper-incursion enables us to reconstruct expectations. The social system is probably the only system which can be expected to carry “strong” anticipation while being reproduced as expectations. A system of expectations is not alive, is not constrained by a life-cycle, and does not need to “exist” otherwise than as expectations. The dynamics against the arrow of time are “cultural”: they rest on codes as the pillars of discursive knowledge driven upward into horizons of meaning.

Multivaluedness in Cellular Automata with Strong Anticipation and Some Prospects for Computation Theory

It is considered the general formulations and properties of cellular automata with cells which have the strong anticipatory property (introduced by D. Dubois). Multivalued behavior (hyperincursion) of solutions of such CA is described. It was posed new research problems of computation theory related to presumable multivaluedness of cellular automata with strong anticipation property. Extending of classical automata, Turing machine and algorithms had been proposed. Also some relation of such cellular automata and quantum mechanics are discussed.