[asaph]

> Employing this interpretation, he found the Panini's "language machine" produced grammatically correct words with almost no exceptions.

If there are exceptions, I would think the problem isn’t solved. Perhaps the article is being loose with the wording. Close only counts in horseshoes and hand grenades.

[chmod775]

You're speaking a language that has some rules with almost no exceptions.

But almost means one can easily list the remaining special cases.

[asaph]

What’s the threshold of special cases allowed where the problem is considered solved?

[chmod775]

The second sentence in the comment you're replying to already answers your question.

If that is not good enough, I suspect that no possible answer would prove to be satisfactory.

[asaph]

“Almost” and “easily” are subjective and open to interpretation. My point is, that this is not a rigorous standard.

[chmod775]

Languages are generally not very amenable to these things.

If you want to construct the entire field of linguistics mathematically that would certainly be interesting to watch. Since a function that is described by a simple equation is mathematically equivalent to a function that is described by a table assigning the appropriate values to each element of the function domain, you could try to come up with a definition for what constitutes the "optimal" way to describe a function. Do the same for any kind of relation.

Until you've done so linguists will sadly be stuck applying nothing more than common sense.

[MockObject]

Just a few.

[bigbillheck]

Buddy, I'm speaking English, it's full of exceptions.

[082349872349872]

Close also counts in computation, where we routinely handle infinite (or at least combinatorially effectively so) numbers of possible inputs with a few general rules and a finite ("almost no", to use a technical term) number of exceptions.

[asaph]

Perhaps my impression that this grammatical problem should be treated with logical rigor, where even a single counter-example invalidates the solution, isn’t the way this is being treated. The way it was presented in the article was like it was a kind of logic puzzle, for which an elegant solution has finally been found. Sounds like it’s more like a better rule of thumb was discovered that reduced the error rate, not to zero.

[kuroguro]

It's also possible some of the writings have grammatical errors.

[asaph]

Well how would you know that if the rules of grammar are not fully resolved?

[cenazoic]

In English, think of all the plurals for which no ‘rule of grammar’ exists; you just have to memorize them.

Moose -> moose Goose -> geese House -> houses Mouse -> mice Etc.

[asaph]

In English, the exceptions to the rules are arbitrary and numerous. English is also a moving target. From a logic problem perspective, English grammar is more of a practical brute force endeavor than an interesting one. When I read the article, I was wasn’t comparing the problem to English grammar, but rather comparing it to a logic puzzle that has a perfect solution.

[somberi]

Could not resist Gad Elmaleh's frustrations about learning English (he did very well to do an hour's standup in English):

https://www.youtube.com/watch?v=qXR1PRbSfoA