Branching Continuous Time and the Semantics of Continuous Action

Ernest Davis

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 acceleration. We show how such models can be described using a continuous branching time structure. We discuss mathematical foundations of continuous branch-ing 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.

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