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I am reading The Book of Why: The New Science of Cause and Effect by Judea Pearl, and in page 12 I see the following diagram.

Diagram from The Book of Why by Pearl, page 12

The box on the right side of box 5 "Can the query be answered?" is located before box 6 and box 9 which are the processes to actually answer the question. I thought that means that telling if we can answer a question would be easier than actually answering it.

Questions

  1. Do we need less information to tell if we can answer a problem (epistemic uncertainty) than actually answer it?
  2. Do we need to try to answer the problem and then realize that we cannot answer it?
  3. Do we answer the problem and at the same time provide an uncertainty estimation?
DukeZhou
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Lerner Zhang
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1 Answers1

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No in general.

Example: What values can x assume?

1. a * x^2 + b * x + c = 0, a,b,c are integer numbers.
2. a = 44^2 + 347829 ^ 21 
3. b = 39289238
4. c = 999!

To know if you can answer this question you only need information 1. It is a quadratic equation, so yes you can find values for x. But to actually answer the question you need also 2,3,4.

Yet there are questions in which knowing if we can answer a question requires answering the question. For instance consider a webpage with a lone password input field which only allows inputs with less than 10 characters. Can you login? Since the password field may be dummy (no input will allow you to login) and there is no indication of what the password may be you are forced to brute force all possible passwords until you either login or conclude that no login is possible.

Rexcirus
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