Looking for a cool toy "linguistic hypothesis" example to use with GM

I will be demoing the Grammar Matrix in my lecture tomorrow, and I am looking for a cool toy example of how to use it for linguistic hypothesis testing. For now I am thinking to just use English and ask them to pretend that we are approaching English as a language we do not really know about, although I could use some other language as well.

I suppose I could say: let’s hypothesize that English does not have a case system (plausible, if you haven’t really studied it much yet and start looking at it naively and not looking at pronouns). Then we will end up parsing things like The cat chases I. But what I don’t like about this example is it presupposes that we included The cat chases I in our test suite, which is this whole additional complication of having to explain how one would construct ungrammatical examples and why. I would rather use an example where something grammatical does not parse and I can elegantly fix it by making a different choice via the GM.

Ideas?

How about yes/no questions? You could start by suggesting that “do” is sentence-initial question particle, which covers a lot of cases, but won’t cover third person singular.

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