A Mathematical Formalization of Self-Determining Agency

Defining agency is an extremely important challenge for cognitive science and artificial intelligence. Physics generally describes mechanical happenings, but there remains an unbridgeable gap between these and the acts of agents. To discuss the morality and responsibility of agents, it is necessary to model acts; whether such responsible acts can be fully explained by physical determinism remains an ongoing debate. Although we have already proposed a physical agent determinism model that appears to go beyond mere mechanical happenings, we have not yet established a strict mathematical formalism to eliminate ambiguity. Here, we explain why a physical system can follow coarse-graining agent-level determination without violating physical laws by formulating supervenient causation. Generally, supervenience including coarse graining does not change without a change in its lower base; therefore, a single supervenience alone cannot define supervenient causation. We define supervenient causation as the causal efficacy from the supervenience level to its lower base level. Although an algebraic expression composed of the multiple supervenient functions does supervenes on the base, an index sequence that determines the algebraic expression does not supervene on the base. Therefore, the sequence can possess unique dynamical laws that are independent of the lower base level. This independent dynamics creates the possibility for temporally preceding changes at the supervenience level to cause changes at the lower base level. Such a dual-laws system is considered useful for modeling self-determining agents such as humans.