Realization for causal nondeterministic input-output systems

Studia Logica 67 (3):419-437 (2001)
Abstract
There are two well-developed formalizations of discrete time dynamic systems that evidently share many concerns but suffer from a lack of mutual awareness. One formalization is classical systems and automata theory. The other is the logic of actions in which the situation and event calculi are the strongest representatives. Researchers in artificial intelligence are likely to be familiar with the latter but not the former. This is unfortunate, for systems and automata theory have much to offer by way of insight into problems raised in the logics of action. This paper is an outline of how the input-output view of systems and its associated solution of state realization may be applied to the formalization of dynamics that uses a situation calculus approach. In particular, because the latter usually admits incompletely specified dynamics, which induces a non-deterministic input-output system behavior, we first show that classical state realization can still be achieved if the behavior is causal. This is a novel systems-theoretic result. Then we proceed to indicate how situation calculi dynamic specifications can be understood in systems-theoretic terms, and how automata can be viewed as models of such specifications. As techniques for reasoning about automata are abundant, this will provide yet more tools for reasoning about actions.
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