What is the resolution to "Harry Potter and the Half-Blood Prince"?
In my opinion, this book does not really have a resolution. The climax of the story, to me, is when Snape kills Dumbledore right at the end. The conflict has been Harry and Dumbledore against the Horcruxes.
If you think about it, this conflict really does not get resolved. At the end of the story, Dumbledore is dead and we don't know what is going to happen next. In my opinion, the resolution of Book 6 is actually in Book 7. I think of the two of them as one long book.
The resolution of Half-Blood Prince is comprised of varous events, including Dumbledore's death, the recovery of a Horcrux which turns out to be fake, and the relevation that Severus Snape is the Half-Blood Prince. The book might be seen as a more of a set-up for the Deathly Hallows, but there are several important plot points introduced in the Half-Blood Prince that are also resolved in it.
The Horcrux storyline and the battle against Voldemort are certainly not resolved by the end of the sixth book, but the mystery surrounding Draco Malfoy's activities and the identity of the Half-Blood Prince certainly are. It is revealed that Draco was, in fact, a Death Eater who had been included in Voldemort's nefarious plots, and that the Half-Blood Prince, whom Harry had actually grown fond of, was actually Snape, the man who murdered Dumbledore.
Harry Potter and the Half-Blood Prince doesn't have a resoultion. The climax of the book is when Snape kills Dumblecore at the end of the book and then its an even bogger shock to Harry when Harry learns that Snape is the Half-Blood Prince.
This conflict doesn't get resolved because Dumbledore is dead and Snape is on the run. The resolution of the book is really in book 7 because Harry finds out that Dumbledore asked Snape to kill him.