In English, we care about whether something is general or specific. That's why we use articles like "a" and "the":

I saw a dog.

I saw the dog.

The first sentence is general. It's about a dog which the listener doesn't know about. The second sentence is specific. It's about a certain dog that the listener has seen or heard about.

But sometimes "the" isn't strong enough by itself. One way to make it stronger is with the word "specific":

I've seen a dog that looks like the one you described. I don't know if it was the specific dog you were referring to, though.