verbs - How do you differentiate between "I have" and "There is"?

My confusion surfaced when I came across a song named 「君がいるから」which I could either interpret as "Because you are mine." or "Because you are here." Is there a different way to say "You are mine" in Japanese, so this sentence isn't ambiguous to speakers?

I could use a different sentence:

「犬がいます。」

My understanding is that this can mean both "I have a dog." and "There is a dog." Is the only way to tell through context?

Answer

You've asked two different questions here, but I'm going to try and answer both of them.

First of all, in regard to how to say "because you are mine", the very literal translation would be something like:

君は僕のだから

Second of all, let's talk about the difference between "I have" and "there is".

I encourage yourself to picture a Venn diagram for the meanings of "I have" and "there is", and really ask yourself how much they overlap. It may be more than you think.

For example, take this sentence

I have three siblings.

In Japanese this would be

私は兄弟が３人います。

Which translated very literally is

As for me, there are three sisters.

They look very different, but that's because English really likes to stretch out the verb have. Do you own your sisters? Are they really yours? Or is this just English's way of saying that in your case there happen to be three other people with the same parents as you?

A lot of the cases where we would use have in English that are not really possessive in Japanese end up being 何々がある・いる, but I think this can be fairly intuitive if you give it a chance.

Lastly, there are a couple other verbs that are used for specific cases.

If you want to talk about owning a pet, you (as user27280 mentioned) use 飼う. Think of this as keeping an animal.

However, for objects that are explicitly yours, the verb 持つ is also used. It's usually taught as "have/hold", but as you can see here it can also mean "have" in the sense of possession/ownership. You wouldn't use it for your sister(s) or a dog, but you could certainly say

私は車を３台持っています。

Edit: I also want to draw attention to user27280's answer, and specifically the usage of 私には何々がいる, which implies more possession/relationship than just 私は何々がいる.