Formalisms such as the situation calculus of McCarthy and Hayes [MH69], and the event calculus of Kowalski [KS97] have been used to represent and reason about a changing world c.f [Sha97]. Neither of these formalisms is exactly what is needed to represent the kind of narratives we wish to consider.
The situation calculus in its most limited version does not allow us
to represent what events occur explicitly--rather every sequence of
events is assumed to occur. We can specify that a particular sequence
of events occurs by introducing a predicate, actual true of just
the sequence of situations that occur
. This is not ideal, as it forces
us to decide what events happened earlier, before we name the events
that happen later.
For this reason we use a modified situation calculus, adding a new
predicate 
, that states what events occur. Thus, rather
than the function 
serving two purposes, stating that
e occurred at s, and designating the resulting situation, we split
these two functions. We keep , but it now only denotes
the result of doing e in s when e 
at s. If e does
not occur, then the value of this function is an arbitrary
situation. This adds an event calculus style of presentation to
the underlying situation calculus formalism. In particular, it allows
us to specify a sequence of events, without making any claims as to
what other events may have happened in the meantime.