Tuesday, January 27, 2009

A simple example to illustrate contingent problem

Here is a simple example that illustrates the need for sensing (and contingent plans)

We have a patient who might or might not have a disease d.

If the patient has disease, then medicating her (M) will cure her.

If however, she *doesn't* have the disease, medicating her will kill her.

There is a simple injection I  that if given to a patient with the disease, makes their tongue
red; it has no effect on the patients without disease.

Your goal is to ensure that the patient doesn't have the disease (and is alive!).

The initial configuration is { D or ~D}

after injection

{(Disease, tongue-red) (disease, tongue-not-red)}

now we do a "look-see" and medicate only if the tongue is red.

So the full plan is:

If tongue-red
   then medicate
   {else do nothing}

Notice that this solution is not a "line" (or "sequence") plan. It corresponds to a
subgraph in the state-space.

This example also illustrates another  interesting point. The "disease" is not directly
observable, but it can be indirectly observed from the tongue-redness, after the
"injection" action. (So, while sensing can reduce uncertainty, it may not be as simple as
"just find out what state you are in"--you may have to do additional world-changing actions
before you can sense).


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