Is an automatic quiz generator possible?
It depends on what you call automatic, and what you consider a successful level of functionality. Something is definitely possible.
Is it that automatic, or do you have to enter your own questions and correct answers? Can it observe text syntax so that it can create questions based on a paragraph of information?
Yes, that’s possible, but again there’s a spectrum from only working for the simplest text and being easily confused (which is relatively easy to program – even a regular expression parser could do that), through to handling arbitrary real-world textual sources and getting say 80%+ of the facts out of the text and posing sensible questions for which it correctly identified the answer (which might take a team of 100 language and programming experts decades). Language analysis is difficult. If you want proof – try converting a paragraph of English text to another language using Babelfish or similar online translator, then convert it back… :-).
Can it work for other things rather than boolean answers (true and false)?
Of course, but again the more complex you make it, the less likely you’ll get anything that works…
can it observe text syntax so that it can accept answers that are close to the right answer, but is off by a few words?
It could, but the range of ways someone might phrase an answer is so varied that having to follow a simple template with a few words’ tolerance wouldn’t work well in general use.
General thoughts
Why don’t you search for existing educational quiz programs to get an idea of what other people have achieved…?
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solved The Possibility of a “True” Quiz Generator [closed]