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Formalizing Oscillations


The buzzer oscillates, i.e. the situation repeats again and again. So does the stuffy room scenario with the two elaborations that cause Vent2 to become blocked and unblocked repeatedly. However, we don't need a complete repetition of the situation to have oscillation. Suppose, or example, we add a clock to the buzzer, a natural number valued fluent that each event increments by 1. Then although the whole situation would not repeat, we would still want to consider the system as oscillatory.

This suggests a relative notion of oscillatory, i.e. oscillatory with respect to certain fluents.

Moreover, we would like to consider the buzzer as oscillating even if we provide for it stopping its oscillation by being turned off.

As we have described the buzzer, it cannot be turned off. Likewise the stuffy room process cannot be changed once we have added the elaborations about people blocking and unblocking the vent. See (27) and (29).

Here's a way of putting interventions into the formalism.

Let a be an action, e.g. stopping that damn buzzer. The following two axioms describe an elaboration that interpolates an action after a normal internal action. In the buzzer case it would be opening an additional switch in the circuit. The additional switch isn't in Fig. 1 or described in section 3.




This is a limited kind of concurrency. Only certain kinds of interventions can be done this way.

John McCarthy
Fri Feb 8 17:29:20 PST 2002