We test the principles of classical modal logic in fully quantum settings.
Modal logic models our reasoning in multi-agent problems, and allows us to
solve puzzles like the muddy children paradox. The Frauchiger-Renner thought
experiment highlighted fundamental problems in applying classical reasoning
when quantum agents are involved; we take it as a guiding example to test the
axioms of classical modal logic. In doing so, we find a problem in the original
formulation of the Frauchiger-Renner theorem: a missing assumption about
unitarity of evolution is necessary to derive a contradiction and prove the
theorem. Adding this assumption clarifies how different interpretations of
quantum theory fit in, i.e., which properties they violate. Finally, we show
how most of the axioms of classical modal logic break down in quantum settings,
and attempt to generalize them. Namely, we introduce constructions of trust and
context, which highlight the importance of an exact structure of trust
relations between agents. We propose a challenge to the community: to find
conditions for the validity of trust relations, strong enough to exorcise the
paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947
