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.