Chapter 1 concerns issues in the construction of formal models of intensional notions. Intensional notions may be treated as modal operators or as predicates. Halbach and Welch (2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that the two methods are ultimately compatible. I show that the monotonicity constraint in the Halbach-Welch technique fails for almost all possible-worlds theories of knowledge. Since the monotonicity constraint is an important element of the proof of the Halbach-Welch rapprochement strategy in the case of necessity, the present results show that the most obvious way of emulating this strategy in the epistemic setting fail.In Chapter 2, I reconstruct and recon...