Problem: Is "Jim signaled the barman and gestured toward Jim's empty glass." true if "Jim signaled the barman and gestured toward his empty glass."?
Answer: yes

Problem: Is "Lucy had studied so hard." true if "Anna did a lot worse than her good friend Lucy on the test because she had studied so hard."?
Answer: yes

Problem: Is "It was a fine selection of Shakespeare's writing." true if "This book introduced Shakespeare to Ovid; it was a fine selection of his writing."?
Answer: no

Problem: Is "Yakutsk was defeated within weeks." true if "In July, Kamtchatka declared war on Yakutsk. Since Yakutsk's army was much better equipped and ten times larger, they were defeated within weeks."?
Answer:
no