In general: Of course they are!
The communicative and reflective abilities of dragons in western mythology range from speech,
over being a lie detector to having an overly developed sense of pride ... they have to be sentient.
Don't really know about eastern dragons, but given their major importance it would be somewhat
weird if they weren't a sentient being either.
In Elements: No!
My dragons are but savage beasts that march where they are commanded ...
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The Evolution of dragons is cleary: Dinosaur -> early human imagination -> later human mythology -> modern phantasy
In some parts of the world, large Dinosaur-skeletons have been exposed over time without having to be excavated.
I picture early humans imagination go wild at the sight of those relics ...
There is actually a nice show on discovery channel, where a "scientist" is trying to reconstruct dragons from all kinds of dinosaur body-parts.