This investigation develops a perspective toward a mathematical foundation of a
theory of responsibility linked to the actions of seemingly complex autonomous
machines — those not continuously controlled or supervised by humans while
operating. Such devices, many falling within the domains of mechatronics, robotics,
and artificial intelligence, are expected to have a significant social impact in the near
future. The foundational structure of this theory begins with a qualitative analysis
that proposes arguments to identify and formalize the notion of responsibility. The
first part of the paper examines how responsibility is anchored in the decision-making
processes characteristic of autonomous devices. The second part investigates the
possibility of a rigorous mathematical translation of this probability-based notion of
responsibility within the framework of variational control of stochastic dynamical
systems.
