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I am trying to create an AI that makes reasonable guesses at truths of statements. However...

Human: "Prove that no number exists which is one more than a billion."

AI: "Is it true for the number 1? No. I am 1% sure the statement is correct."

AI: "Is it true for the number 2? No. I am 2% sure the statement is correct."

...

AI: "Is it true for the number 999,999? No. I am 99.99% sure the statement is correct."

AI: "Having tested a large number of examples. I conclude that the statement is correct."

Human: "The statement is wrong: one billion and one."

What do you think has gone wrong?

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  • $\begingroup$ I believe that the whole reasoning is wrong. The fact that his certainty increases with the number is also weird: it is like the higher the number the more certain the AI is, which makes no sense. Furthermore, there's also the problem of not being able to generalise. $\endgroup$ – nbro Jul 23 at 20:16
  • $\begingroup$ The AI didn't try to disprove it... it hadn't "understood" the misleading question to a level where it could find the fastest route to a disproof (or proof). Disproof may be a missing strategy. $\endgroup$ – Paul Brown Jul 30 at 15:04
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I don't think that the "try all the numbers" approach is very representative, because I'm not sure whether or not the agent that uses that approach can be considered by any means AI.

There is no "intelligence" in just checking numbers to try to prove the statement. An agent that is considered to be intelligent should apply a more intelligent approach.

This becomes more evident because the question aims at exploiting the lack of scalability of the agent's strategy. If the question was "Prove that no number exists which is one more than 5", then the agent would have no trouble in finding the correct answer.

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  • $\begingroup$ Yes, perhaps the AI (or a human child) would have "noticed" some time ago that to get a bigger number all you have to do is add one to any number. And using this knowledge could solve the problem. $\endgroup$ – zooby Aug 24 at 1:11
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A human level AI would work out the task in the following way.

At first, the task is poured into the task container, which is the given statement, that no number exists above the threshold of one billion. Then the rules are poured into the rules container which are that a formal proof according to the mathematical laws is needed. Also the rule is given, that other mathematicians have to understand the proof the same way. And last but not least is x+1>x.

Now the planning container will execute rule-operators to the given task. The output of the planning container in natural language would be, that numbers can't be seen by itself, but they are referencing to things in reality. And in reality no thing has more entities then 1 billion. QED.

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  • $\begingroup$ Yes, I think that the strategy of "try all the numbers" is but one strategy and that evidence must be built up from multiple strategies. And perhaps different strategies for different questions. We might also have evidence that "try all the numbers" works best in certain situations and not others. $\endgroup$ – zooby Jul 23 at 21:19

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