“After her father?s assassinated, a sheltered princess must learn the forbidden arts from her exiled mother to extract revenge.”

What exactly are the ‘forbidden arts’? I’m pretty sure it’s magic, but what kind of magic? Why is forbidden? Is is necromancy? Scrying? Divination? Summoning otherworldly creatures? Rather than just say forbidden, in the logline state what it is. Fire magic? I have no clue, and neither would a producer, or whomever you pitch this to.
All she wants is revenge?

Here’s an example:?After her father is assassinated, a sheltered princess must learn dangerous blood magic from her exiled mother to extract revenge. (20)

I’ve commented on this premise before. Is the antagonist, the one who killed the king, a sorcerer or just a normal man(or woman)?
This version of the logline lacks the presence of a threatening antagonist. Who is the person who killed her father? A dangerous warrior tired of what he/she sees as tyranny? A magic user in search of some power that the king has? A survivor of a battle the king fought and won?

What I do with all of my stories is create a logline for more than just the protagonist(s). I create one for each of the major supporting characters, and especially the antagonist. I want to have a clear sense of who each of these characters are, what is driving them, and what they want. What is that drives this antagonist?

For example:?After his village is massacred by the royal army, a skilled swordsman must kill the king and end the tyranny his reign has brought.(24)

Even though we enter his(or her) story after the inciting incident, the antagonist has a clear goal, a driving force that should be felt even though there is distance from them.

I hope this helps.

I don’t see loglines as being tied to one thing. Meaning I don’t think you have to make one only to sell a story, but you can make one to help yourself write one. I’ve mentioned before that I write loglines for all main characters in my stories. But only one would be the one used to sell.
Besides, magazines that publish short stories often have a pitching process which might include a logline/elevator pitch. One thing that would help in evaluation is the length of the story. Is it a flash fiction story? Closer to a novella? Or 2000-20,000 words? ?I ask because the shorter it is, the more likely you won’t need a clear inciting incident.

“A bewildered woman pushed to her breaking point escapes into the woods when her overbearing husband tries to kill her.”

This is a bit vague. What pushed her to her breaking point? The inciting incident? You don’t state a clear goal. She escapes into the woods, yes, and that implies simply that she’s trying to survive. But what specifically is she trying to accomplish? Get to a hidden weapons cache in a shed? Get to the city? Is she a spy and she has to report to her superiors?