logical deduction - Ask about "Delay Creates a Conclusion"

In a Messenger group full of logicians:

"Does anyone here understand the concept of sequential logic in digital circuit theory?" said someone.

There is a long pause, no one replied.

And when all members on the group have read the message, one of them answered, "No."

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Actually, I don't know whether there exists a logic concept/theory behind that story: a delay creates a conclusion. There is also a nice puzzle using the same concept which can be accessed here: https://tierneylab.blogs.nytimes.com/2009/03/16/the-puzzle-of-the-3-hats/

Does anyone in this community know about the theory? Is there any works related to it?

Update: How to interpret such concept on AIs? Let's say there are 3 AIs playing above puzzle of the 3 hats, or above Messenger group is full of IAs.

Answer

The term is called Argument from silence. It is when a person uses another person's silence (or absense of a statement) as an information in itself and not as just silence.

According to rationalwiki.org:

An argument from silence is an informal fallacy that occurs when someone interprets someone's or something's silence as anything other than silence, typically claiming that the silence was in fact communicating agreement or disagreement.

It is considered an informal fallacy because it is not a solid argument that support its conclusion with actual proofs. The silence could be due to various other reasons, thus the conclusion might as well be wrong as it might be correct. Take the three hats puzzle as an example, the prisoner's interpretation of the silent prisoner's silence could be wrong, the silence might be because:

• The prisoner is mute.


• The prisoner is blind, so he can't possibly deduce his hat color and give an answer even if he could.


• The prisoner might be slow-witted, so it should take him a longer time to deduce his hat color, thus the delay/silence is unreliable.


• ...

In all the above situations, the silence does not definitly indicate that the silent prisoner couldn't identify his hat color because of the arrangment of the hats alone.

But in the context of puzzles, one usually uses the best case scenario, where the argument from silence becomes a solid argument (the silence will only mean one thing, thus we use that thing in further deductions).

Note: The term, however, for @Bass comment is Arguments from ignorance. They're basically the same thing, except that AFS is interpreting silence, whereas AFI is interpreting ignorance of a matter/subject.