When learning about when to use 了, we're typically given simple examples with clear-cut answers, such as the following:
I bought three books.
Expressing completion with "le"
We are taught that the reason we add the 了 is for completion: 买 is complete in the above example. Then we get thrown into the real world, where we might want to say something like:
He thinks I bought three books, but I didn't buy anything.
We have a grammar vs. context battle: the (local) grammar implies we should add the 了 (as above in 我买了三本书), while the context destroys the logic used above (买 is not complete), which gives a contradiction.
Question: When translating "he thinks I bought three books, but I didn't buy anything", do we add a completion 了 for "bought"?