What exactly is "Half Lucid"?

I’m recording dreams on Lucidipedia’s “Dream Journal” section right now (awesome section, by the way) and one of their options on level of lucidity is “Half Lucid”.
I was wondering, what is it that usually counts as this?
Would I be “Half Lucid” if I start to think that certain events in a dream don’t make sense, for example if I start to question things and cannot find a logical answer to something?

For example, last night I dreamed that I was caring for one of my mother’s border-collies, and during the night in the dream I noticed that he kept running out of the house even when I had closed all the doors and windows.
I became suspicious and started wondering how he could leave the house like that, and even started looking for cracks or any kind of explanations.

Half lucid AkA - Semi Lucid is when;

You do know you’re dreaming but are not fully concious, you still follow the plot of the dream but do make choises for example:

You are in some kind of fight, and you realise this is a dream: The only thing you do then is use supernatural powers to overpower your enemy, or make the enemies dissapear, but you do not go off and do whatever you want.

When you are fully lucid you leave the plot (Mostly) and go do whatever you want.

I kind of understand it as when you know you are dreaming, but your awareness still didn’t kick in, so you’d still be pretty “dumb”