How to refrain from answering Kripke's puzzle

In this paper, I investigate the prospects for using the distinction between rejection and denial to resolve Saul Kripke's puzzle about belief. One puzzle Kripke presents in "A Puzzle About Belief" poses what would have seemed a fairly straightforward question about the beliefs of the bilingual Pierre, who is disposed to sincerely and reflectively assent to the French sentence "Londres est jolie", but not to the English sentence "London is pretty", both of which he understands perfectly well. The question to be answered is whether Pierre believes that London is pretty, and Kripke argues, of each answer, that it is unacceptable. On my proposal, either answer to the question is to be rejected, but neither answer is to be denied, using the resource of partially-defined predicates. After demonstrating how this serves as a solution to the puzzle, I illustrate some philosophical motivations-independent of Kripke's puzzle-for adopting a view on which belief is a partially defined predicate. I conclude that there are decent prospects for the proposed response to Kripke's puzzle.