  Which theories lead to a contradiction between simple reasoning principles
and modelling observers' memories as physical systems? Frauchiger and Renner
have shown that this is the case for quantum theory, with a thought experiment
that leads to a multi-agent paradox. Here we generalize the conditions of the
Frauchiger-Renner result so that they can be applied to arbitrary physical
theories, and in particular to those expressed as generalized probabilistic
theories (GPTs). We then apply them to a particular GPT, box world, and find a
deterministic contradiction in the case where agents may share a PR box, which
is stronger than the quantum paradox, in that it does not rely on
post-selection. Obtaining an inconsistency for the framework of GPTs broadens
the landscape of theories which are affected by the application of classical
rules of reasoning to physical agents. In addition, we model how observers'
memories may evolve in box world, in a way consistent with Barrett's criteria
for allowed operations.
