  The main aim of the present paper is to use a proof system for hybrid modal
logic to formalize what are called falsebelief tasks in cognitive psychology,
thereby investigating the interplay between cognition and logical reasoning
about belief. We consider two different versions of the Smarties task,
involving respectively a shift of perspective to another person and to another
time. Our formalizations disclose that despite this difference, the two
versions of the Smarties task have exactly the same underlying logical
structure. We also consider the Sally-Anne task, having a somewhat more
complicated logical structure, presupposing a "principle of inertia" saying
that a belief is preserved over time, unless there is belief to the contrary.
