Monday, February 21, 2011

The Meaning of Symbols in Problem Solving

The following is taken from here:

Another great problem in robotics is getting them to understand language. This is very important in problem-solving. For example, the four cards below have a letter on one side and a number on the other. If a card has a vowel (a, e, i, o, u) on one side then it has an even number on the other. Which cards do you have to turn over to see if this is true? Think about your answer, then point to a card to turn it over.
letter E with number 6 on reverse letter K with number 1 on back number 4 with letter U on reverse number 7 with letter A on reverse
Now consider the following cards where the rule is ‘every time I go to Paris I go by plane’. Which cards have to be turned over to test this? Again, think about your answer before turning the card over.
Paris card Madrid card Plane card Train card
The answer to the first question is that you have to turn over the E to see if it has an even number on the back and you have to turn over the 7 to check that it does not have a vowel on the back. In an experiment, only 12% of people got this second part right (did you?).
The answer to the second question is much easier. Of course you have to turn over the Paris card to check that it has the word plane on the back, but now it’s much more obvious that you have to turn over the train card to make sure it does not have Paris on the back. In the experiment mentioned above, 60% of people got the second part right.
These problems are logically the same, so the experimenters drew the conclusion that the meaning of the symbols is an important part of problem solving. Since robots have very poor language capabilities, their ability to use this kind of reasoning is very limited.