OK, let's see how complicated I can get this to be
For the sake of argument, I'm going to assume that we are talking about a glass in normal Earth atmosphere conditions in room temperature, and that "half full" means half full with some simple drinkable liquid like water. If we counted air to also trigger the condition of "filling" the glass, then the glass would be full at all times, which would make the question kind of silly. And also, I'm skipping the whole idea that this question is some sort of abstract metaphor for life - it's strictly the glass and the liquid.
I'd say that there's a more fundamental question to be asked first. Which is the default position of existence for this glass in question: filled with something or empty? The meaning why drinking glasses exist is because people want to have some better way of containing liquids and an easier way to drink then cupping their hands, trying to hold the liquid there and awkwardly pouring the liquid into their mouths. This notion of meaning of a drinking glass might make it intuitive that since glasses are made for drinking liquids, the default position is that the glass is full and can be emptied from that state.
But I disagree with this notion. When basic raw materials are formed into glassware meant for drinking, they don't form containing some liquid. Drinking glasses (and all glass containers) begin as a combination of extremely hot materials of some indeterminate shape. Later they are made into some shape by various means, slowly cooled down and only then can they be used to contain some liquid (and at least I store my glasses empty and fill them with something later ). Since all glasses begin their existence from this state, I'd argue that the default position for the glass is to be empty.
Every drinking glass begins it's existence by being empty, waiting to be filled. The glass can be both filled half way, and it can also be filled to the brim and then emptied half way. But the default position for the glass remains to be empty in all situations. Even in the latter case of first filling the glass to the brim and then emptying it half way, the default position is to be empty. The glass began by being empty, at some point in time it was filled completely, and it was then drained to be only half full. I'd say considering the default position and it's implications has given us the answer.
To answer the question: the glass is unarguably, undeniably and unchangeably half full, period.
Have a nice day