Branching continuous time and the semantics of continuous action

Abstract

It is often useful to model the behavior of an autonomous intelligent creature in terms of continuous control and choice. For example, a robot who moves through space can be idealized as able to execute any continuous motion, subject to constraints on velocity and accelleration; in such a model, the robot can "choose" at any instant to change his accelleration. We show how such models can be described using a continuous branching time structure. We discuss mathematical foundations of continuous branching structures, theories of continuous action in physical worlds, embedding of discrete theories of action in a continuous structure, and physical and epistemic feasibility of plans with continuous action. 1 Continuous Plans It is often useful to model the behavior of an autonomous intelligent creature in terms of continuous control and choice. Imagine a creature that can move in the plane up to 1 meter per second but no faster, and that wants to catch unintelligent prey that mov...