Subject-verb agreement in English for nouns without determiners

When a plural noun preceded by a determiner is followed by a singular verb, the result is correctly marked as an error, e.g.

All cars is useful. The books is important.

However, when there is no determiner, the sentences above pass with the message “No errors were found”, e.g.

Cars is useful. Books is important.

Thank you for your error report.
I have added a rule which catches the error in “Cars is useful.”. It is, however, difficult to write a general rule that does not generate false positives (“Windows is a very popular operating system” / “Measles is a terrible illness.”) Therefore, the error “Books is important” is currently not detected.

Surely, it makes more sense to add a rule that may catch tens of thousands of errors and then add exceptions for false positives than not to have a rule at all?

In general, it would be quite useful to have separate rules for “possible errors” shown as bright yellow (or another less intrusive colour) that would essentially mean “make sure that this is correct because what you have written is usually an error, but not always”.

False positives are a much smaller problem in proofreading than false negatives (it is much easier to judge whether something marked as an error actually is an error than to see an unmarked error in a text).

however, false positives can distract from false negatives.

You can always proofread your text yourself without any error detection and other distractions. The point is to catch errors that you have missed and are unlikely to catch otherwise.

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I see your point, but LanguageTool is not only for proofeading purposes. So, by convention, the default rule set that is active in the online version of LT seeks to keep the number of false positives low.
There are many rules that you can activate in the offline version if your focus is on proofreading and false positives are no big problem.

LanguageTool names itself “LanguageTool proofreading service” in the main website.
Maybe I am being obtuse, but what other purposes is LanguageTool supposed to fulfill?

Yes, you are right, of course!
What I actually wanted to say: There are different audiences LT has to serve.
A well-educated native speaker on the one hand is probably willing to accept stricter rules, which generate more false positives, as the number of errors in his/her texts is low anyway.
Consider now a non-native speaker: If there are many error warnings from LT, and it turns out that every second or third is a false positive, the error checking could become really annoying.

Each user can configure his/her preferred rule configuration in the standalone version.
For the online version it has been common practice - at least as far as I understood it - that we activate only rules with a low ration of false positives.

Now I understand. I started to think that I was out of the loop on this.

I understand, and I know that here that is the common practice.
Looking at online user increase in the last year in the Portuguese and Galician language, I would argue that it maybe the general user base prefers a slightly more lax enforcement of the rules, and probably accepts a little bit more false positives, as long as it provides significantly more useful advice.
This also allows rules to be perfected more easily over time, and it intimidates less new contributors.

However, calibrating the effectiveness takes time, and if low quality rules accumulate or have to be maintained by other people, they become a big burden that can easily tarnish the proofreading of the language as a whole.