Continuous Processes in the Fluent Calculus

Among the known predicate calculus formalisms for axiomatizing commonsense reasoning about actions, the Fluent Calculus stands out in offering a solution not only to the representational but also the inferential aspect of the fundamental Frame Problem. In this paper we extend this formalism to modeling hybrid systems, which involve both discrete and continuous change. We borrow basic notions from an existing extension of the Situation Calculus to this end, but depart from it in a crucial aspect: Exogenous events are uncoupled from the action sequence performed by the agent. In this way we solve the problem of non-existence of simple plans caused by incomplete knowledge of the ongoing processes, and we enable solutions to Zeno’s paradox.