I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-valued logic).
Take the sentence, "The King of the United States treats his subjects well."
Obviously, there is no King of the United States, so calling this sentence true would be absurd. However, calling this statement false seems absurd to me as well because that may imply that there exists a King of the United States, but he doesn't treat his subjects well. My textbook states that Russell's view on syncategorematic definite descriptions stems down to his view of a definite description -- "there exists an X, there is no more than one such X, and X has quality Y." Using this definition, we can symbolize the above statement.
(Ǝx)(Kx ^ (y)(Ky → x=y) ^ Tx)
Where Kx ↔ x is a king
Tx ↔ x treats x's subjects well
x=y (identity -- x is y)
This symbolization seems odd to me. Would this be the proper way to symbolize the above sentence using Russell's view? If this is the correct way, are there other competing views that would give an alternate symbolization? If there are any popular alternate views, I would like them to remain within the realm of two-valued logic.