  We analyse the philosopher Davidson's semantics of actions, using a strongly
typed logic with contexts given by sets of partial equations between the
outcomes of actions. This provides a perspicuous and elegant treatment of
reasoning about action, analogous to Reiter's work on artificial intelligence.
We define a sequent calculus for this logic, prove cut elimination, and give a
semantics based on fibrations over partial cartesian categories: we give a
structure theory for such fibrations. The existence of lax comma objects is
necessary for the proof of cut elimination, and we give conditions on the
domain fibration of a partial cartesian category for such comma objects to
exist.
