I had thought that I would ask ChatGTP a difficult question: 

“Yes and no are both logical values. Is the proposition I don't know also a logical value?”

But it turned out, to my pleasant surprise, that ChatGTP could answer the question correctly:

“In classical two-valued logic, which assigns either true or false to propositions, "I don't know" is not considered to be a logical value. However, there are other systems of logic, such as three-valued logic and multi-valued logic, which do include the value "I don't know" as a separate logical value.”

Das war kurz und knapp und richtig. Jetzt will ich es etwas genauer wissen:

“Can you explain to me how the proposition "I don't know" is represented in those systems of logic?”

OK, something like that can happen. I'll try again:

“In three-valued logic, in addition to true and false, there is a third value, "unknown", which is used to represent the proposition "I don't know." The "unknown" value is typically represented by a symbol such as "?". In this system, logical operations such as negation, conjunction, and disjunction are redefined to work with the three values, and a set of truth tables are used to define their behavior.

For example, in negation operation the value "Unknown" when negated results in "Unknown" as well, as the truth of the proposition can't be determined. In multi-valued logics, the representation could be different and would have to be defined according to the specific system.

In multi-valued logic, there can be any number of values greater than two. Here, the "I don't know" proposition can be represented by any value or set of values that are not true or false. However the way these operations and tables are defined will vary based on the specific system and context.

It's worth noting that usage of "I don't know" values are not limited to these system but also used in others such as fuzzy logic and probabilistic logic where indeterminacy is represented by a degree of certainty.“

Here, too, everything is right. Of course, everything remains somewhat vague, but it answered the questions correctly. For me the answer is satisfying.