  Recent years witness a growing interest in nonstandard epistemic logics of
"knowing whether", "knowing what", "knowing how", and so on. These logics are
usually not normal, i.e., the standard axioms and reasoning rules for modal
logic may be invalid. In this paper, we show that the conditional "knowing
value" logic proposed by Wang and Fan \cite{WF13} can be viewed as a disguised
normal modal logic by treating the negation of the Kv operator as a special
diamond. Under this perspective, it turns out that the original first-order
Kripke semantics can be greatly simplified by introducing a ternary relation
$R_i^c$ in standard Kripke models, which associates one world with two
$i$-accessible worlds that do not agree on the value of constant $c$. Under
intuitive constraints, the modal logic based on such Kripke models is exactly
the one studied by Wang and Fan (2013,2014}. Moreover, there is a very natural
binary generalization of the "knowing value" diamond, which, surprisingly, does
not increase the expressive power of the logic. The resulting logic with the
binary diamond has a transparent normal modal system, which sharpens our
understanding of the "knowing value" logic and simplifies some previously hard
problems.
