Very interesting. I haven't thought about this before.
Your question is basically in relation to the intention, and almost to the notion of contract. It is not asking "can I not fast" but "if I decided to fast, is it okay to change my mind". In other words, "does the decision to fast constitute some sort of contract that presents an extra moral obligation to pursue".
So my answer is based on the assumption that you just decided to fast, i.e. you started your day, thought you could complete the day, and realized you couldn't (nothing more, e.g. you did not swear "I promise to Allah that I will finish this fast" or anything like that).
I would say that, since you are allowed to not fast, then fasting is in the same category as "mustahab": something that is not an obligation but that you would be rewarded for if you do, and, most importantly, would not be punished if you cannot do. If you decide to plant a hundred trees, and then get tired, and only plant 50, you still tried to complete a task and it's fine if you stop.
So you follow the normal procedure as if you haven't started fasting.
That being said, if you break your fast because of legitimate reasons (heat, thurst, fatigue, etc), then I would argue it would have been wrong of you not to break your fast, anyway. Because God gave you a benefit, a mercy, and I would consider it an insult to His generosity if you refuse to take it. Remember that, next to the verses about fasting, it is specifically said " يُرِيدُ اللَّهُ بِكُمُ الْيُسْرَ وَلَا يُرِيدُ بِكُمُ الْعُسْرَ". So putting too much hardship on the body that God gave you, and risking harm to it, by imposing on yourself something that was very clearly not an obligation, is, in my opinion, very wrong.
But I am not sure. I couldn't find any thing about this.