  A recent no-go theorem (Frauchiger and Renner, 2018) establishes a
contradiction from a specific application of quantum theory to a multi-agent
setting. The proof of this theorem relies heavily on notions such as 'knows' or
`is certain that'. This has stimulated an analysis of the theorem by Nurgalieva
and del Rio (2018), in which they claim that it shows the "[i]nadequacy of
modal logic in quantum settings" (ibid.). In this paper, we will offer a
significantly extended and refined reconstruction of the theorem in multi-agent
modal logic. We will then show that a thorough reconstruction of the proof as
given by Frauchiger and Renner requires the reflexivity of access relations
(system $\mathsf{\mathbf{T}}$). However, a stronger theorem is possible that
already follows in serial frames, and hence also holds in systems of
\emph{doxastic} logic (such as $\mathsf{\mathbf{KD45}}$). After proving this,
we will discuss the general implications for different interpretations of
quantum probabilities as well as several options for dealing with the result.
