Agree is one of the few core syntactic operations posited in minimalist syntax (Chomsky, 2000, 2001) and as such its nature has been subject to debate from various perspectives. While the standard assumption is that the result of Agree does not affect interpretation, this dissertation shows that Agree can not only affect PF but can also affect LF by providing arguments to some semantic predicates. In particular, I claim that some functional heads are semantic predicates that select their arguments via Agree over index features.I first establish the claim by examining Object Honorifics in Japanese. Previous syntactic literature has considered object agreement over an honorific feature borne by the object (Toribio, 1990; Hasegawa, 2017, a.o.)...