In Italian, both the indefinite and the definite article change in spelling and pronunciation depending on the following sound, in the masculine gender.
Before vowels, the masculine indefinite article is un and the definite article is l' (elision of lo):
un albero (a tree), l'albero (the tree)
Before single consonants or consonants followed by semivowels ...
A famous example is the Arabic language where the the definite article al assimilates to one half of the potential following consonants called Sun letters in Arabic grammar. So it is an-Nil "the Nile" or ash-shams "the sun", but al-qamar "the moon".
Quite similarly to Italian (see @LjL very complete answer) and a few other Romance languages, French does this for indefinite and definite articles, but not really the same way English does, in the sense that what we call "Liaison" is very common, though it rarely changes the writing of the articles.
Un verre /œ̃ vɛʁ/ (a glass)
Catalan masculine singular definite articles.
/l/ before a vowel sound.
/el/ before anything else.
What triggers this allomorphy is clearly the sound, not the letter, as we see l'interval /linteɾval/ but el iode /eljod/, because of the glide /j/. Also l'hivern /liveɾn/ but el hiat /eljat/.
I think it is pretty common to "change the indefinite or definite ...
Well, I explained the why it's useful in your other question so if you're asking about the process as curiousdannii said, that is you are asking about the grammaticalisation cycle, I could explain a little about the process.
Latin has a rich case system allowing free word order which is used as as a discourse marker; words encoding new or salient ...
Most of the famous examples in Europe and the Mediterranean have been mentioned, but we should add the languages where the definite article is simply a suffix, for example the core languages of the Balkan Sprachbund, like Albanian and Romanian, and Armenian, which works very much like they do in this regard.
Turkish does not really have an article but ...
Ancient Greek arguably has a dual indefinite article tiné. Literally it means "some [two things]", and is unrelated to the numeral "two".
To elaborate a bit more: Ancient Greek didn't have mandatory indefinite articles during the Classical period, but the indefinite correlative tis was in the process of grammaticalizing into that niche. The dual wasn't ...
Once "a" is removed from the above sentence, it becomes ungrammatical as follows:
*I made mistake.
Now, is this sentence ungrammatical because now mistake isn't indefinite anymore without "a"?
No, your example sentence is ungrammatical in English because the rules of English require that all singular countable nouns have some sort of ...
The "indefinite article" is called that because it is an article* and it is used with indefinite noun phrases. It certainly isn't a necessary part of all indefinite noun phrases: the English indefinite article is specifially a singular article, unlike the definite article, so it isn't used with plural or non-count nouns.
As you've noted, not all ...
In Spanish, before a feminine noun with stressed initial /a/, the usual feminine singular definite article la has an alomorph el (which is identical to the masculine singular definite article).
la vaca (f)
el agua (f)
el libro (m)
Why is “agua” masculine in singular form and feminine in plural? “El agua” / “Las aguas” (Spanish SE)
The Leipzig Wortschatz Portal is a good place to get answers for this kind of questions. The definite article is more than twice as frequent as the indefinite one (158M vs 67M + 10M).
Unfortunately, no further breakdown is in there, they just count wordforms, but on very large corpora.
The indefinite article surely is a quantifier -- as you say, it quantifies an NP to indicate existence and, more arguably, uniqueness.
The reason you haven't found it explicitly listed as such might be because in traditional formal semantics, "a" is often treated as synonymous to "some".
I think it solves most of the natural language problem to realize that a definite description conveys the uniqueness of its referent (rather than assuming it). And the rest is solved when you realize that there is a variety of circumstances that make utterances difficult for hearers to interpret. The possibility that the speaker apparently conveys ...
Replacing "He" in the antecedent by "one of two boys" would be ambiguous, because mere repitition could mean the other boy. "the/this/that one of the two boys" makes a difference, to begin with. Therefore the question seems meaningful.
Representing anaphora with dependent types might not be the reference you want, but the one ...
I strongly recommend looking at systemic functional linguistics. SFL can offer a few different perspectives. At the syntax level, which SFL calls lexicogrammar, it would be useful to look at the use of the nominal group structure. At another level, which SFL calls discourse semantics, it would be useful to look at the system of reference e.g. https://books....
Czech seems to be developing some sort of definite/indefinite articles with definite ones being evolved from demonstrative pronoun "ten" (this), while indefinite ones from the undetermined pronominal adjective "nějaký" (some), which has no connection to the numeral "one".
Mind you this is far from fully grammaticalised form but even now the uses are very ...