On the SAT problem I was mentioning after the class..

[Subbarao Kambhampati <rao@asu.edu>]

Hi Michael

 I believe it was to you that I was mentioning a simple SAT problem to give an idea of how things get "interesting" with incomplete information. I don't know if I wrote the problem right.  Here it is

Suppose we have a linear function f(x), which is specified this way

if x is 3, y is 5

if x is 2, y is a

if x is 4, y is b

What is the value of a+b? 

Note that kids typically know how to figure out the equation y=mx+c of a line given two points on it. And once they do, they can predict x values given y values etc. So, having two points is complete information for this problem.

If they are given just one point, and are asked to predict value of y given x, they know that this can't be done, as there are infinite such values.

In this case, they have an "in between" situation. The temptation is to say that it is not possible to tell what a+b is. But if you take a moment, you realize you can indeed tell that a+b will have to be 10 (even though you can't tell what a and b have to be). 

[And to stretch the analogy, given incomplete information, the decision maker has to resist the urge to declare "not enough information", and actually has to go through the sometimes complex reasoning to figure out whether it is actually possible to solve the problem at hand despite the incomplete information]

Rao

ps: I am bcc'ing this to the class