This usage of ~ている only shows a state, so it cannot show action or motion. Note the time progression that results in the following sentences.
A raccoon dog (tanuki) wasdead on the street. It must have been hit by a car.
1. (これから）死ぬ = 今は生きている。 (The dog is still living)
2. 死にました。 (This is an instantaneous change in state from living to dead)
3. （ずっと／今も）死んでいる。 (The result of the change still exists, as the dog is still dead)
I already know the cause of the accident.
1. (これから）分かる = 今は分からない。 (You don't yet know the cause)
2. 分かりました。 (This is an instantaneous change in state from not knowing to knowing)
3. (今は）分かっている。 (You found out and are still in a state of knowing the cause.)
Usages notes (by users)
The ている construction is often shortened to てる colloquially. You can also shorten ています to てます, but if you're already being polite you'd probably want to say the full thing anyway.
Example: 父は太っている。→ 父は太ってる。 父は太っています。→ 父は太ってます。
All the conjugations are the same, just without the extra い.
雨が降っていた。 -> 雨が降ってた。 It had been raining. 雨が降っていない。 -> 雨が降ってない。It did not rain. 雨が降っていなかった。 -> 雨がふってなかった。It had not been raining.
The title on this page itself is fine, but on the main grammar library page, this pattern shows up as て居る. Again, I'm aware that いる uses the kanji 居る, but when combined with て-form, I'm pretty sure it's almost always written in kana.
I just came across another usage of ている-form as a description of constante state (not action, as in the examples above). I don't think this usage is covered by the explanations above so I'll put it down here.
ている-form in this case describes the constant state of things, the way they were from the very beginning. For example "彼女はクラウデぃア・シファーに似ています" She looks like Claudia Schiffer (she did't start looking like Schiffer two days ago, but she always looked like her). この道は曲がっています。 This street has a turn (?? not sure how to put this in English). Here again, this street has always been this way and didn't get this turn in the course of time.
So far though, I came across only two verbs that can be used in this way. Probably someone else here knows more of them?
If fits under the first definition, except that the first one is a bit too restrictive and doesn't allow these examples. The second one actually does fit in - whoever made the road originally curved it during construction (the action), leaving it in a curved state.
似ています....that one doesn't, though. Let me think on it.
2+ years ago.
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