Good question, short answer first:
In a logline describe one goal and the one event that motivated the MC to achieve it, any other actions and or events are redundant. Therefore, you need to identify which single event first made the MC realise that he or she needs to take action, then identify what is the resulting objective they perceive for themselves (or through the help of a friend or mentor) and describe only these.
Long answer:
A logline's primary function is to describe a plot, subsequently, it can function as a marketing tool to sell the script and at the same time as a structuring tool to help the writer work on the story. A plot is a sequence of events that lead to a single goal within a finite amount of time as defined by a precipitating event (inciting incident) and a concluding event (achieving the goal or failing to achieve in some but fewer cases).
As you know from the poetics, a plot requires a unity of action. In other words, a set of actions where each one logically leads the character to take the next, all of which result inevitably in the MC achieving the goal. If you were to trace back all the way to the beginning of this sequence, you'll find the first event which motivated the MC. Go all the way at the end of the sequence, and you'll find the last one is the goal.
For the most part, any action or event that doesn't fit within this paradigm should not be included in the script or synopsis and certainly not in the logline. There are exceptions, of course, comedy tends to go off on tangents that fall well outside the plot requirements, but this is widely accepted by most audiences if it sets up a good joke or gag. There are other examples in other genres that work well, however, you'll find that for the most part they were done by incredibly skilled pros - it's highly recommended for an unproduced writer to stick to the conventions and master them first.
Ironically you chose a bad example to base your question on - the film Up. This is a great film, but an unconventionally structured one at that. It has a very long prolog at the beginning with nothing but back story and no A plot, it also has the death of the love interest before the end of act 1.
The plot in Up is about Carl needing to relocate his home, and the audience's empathy with his motivations for doing so was developed in the lengthy prolog. Again, all unusual writing choices, but they worked.
A brief rundown of the story's events:
Prolog - no plot related actions or events.
The inciting incident is the developers moving in and threatening his house, the nostalgic aspect of which was clearly established in the prolog.
Carl must find a solution to his problem, and he does, he has to move his house to a safe location and what better place than Paradise Falls (goal established), again the nostalgia associated with the location was clearly established in the prolog.
He then takes action to relocate, and literally goes up.
He then is forced to overcome his bitterness (character flaw) when bonding with the kid and dog while searching for the place and trying to land. They then have to fight (complication) the explorer (antagonist) in order to relocate the house to the falls (goal).
So in a logline this would look like:
After developers threaten his home, a bitter widower must fight a crazed explorer in order to fly his house with balloons to Paradise Falls, where his wife and he dreamed of visiting.
I suggest you look at more conventionally structured films to learn more about plots and loglines, but good question all up (pun intended).
