  In epistemic logic, a way to deal with knowledge-wh is to interpret them as a
kind of mention-some knowledge (MS-knowledge). But philosophers and linguists
have challenged both the sufficiency and necessity of such an account: some
argue that knowledge-wh has, in addition to MS-knowledge, also a sensitivity to
false belief (FS); others argue that knowledge-wh might only imply mention-some
true belief (MS-true belief). In this paper, we offer a logical study for all
these different accounts. We apply the technique of bundled operators, and
introduce four different bundled operators: $[\mathsf{tB}^\mathtt{MS}]^x \phi
:= \exists x (\mathsf{[B]} \phi \wedge \phi)$,
$[\mathsf{tB}^\mathtt{MS}_\mathtt{FS}]^x \phi := \exists x (\mathsf{[B]} \phi
\wedge \phi) \wedge \forall x (\mathsf{[B]} \phi \to \phi)$,
$[\mathsf{K}^\mathtt{MS}]^x \phi := \exists x \mathsf{[K]} \phi$ and
$[\mathsf{K}^\mathtt{MS}_\mathtt{FS}]^x \phi := \exists x \mathsf{[K]} \phi
\wedge \forall x (\mathsf{[B]} \phi \to \phi)$, which characterize the notions
of MS-true belief, MS-true belief with FS, MS-knowledge and MS-knowledge with
FS respectively. We axiomatize the four logics which take the above operators
(as well as $\mathsf{[K]}$) as primitive modalities on the class of
$S4.2$-constant-domain models, and compare the patterns of reasoning in the
obtained logics, in order to show how the four accounts of knowledge-wh differ
from each other, as well as what they have in common.
