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\section{Topic and approach}


\subsection{The ramification problem}

The \emp{ramification problem} for reasoning about actions and change
has been described as follows by Ginsberg and Smith, \cite{Gin:87t}:
\begin{quotation}
   The difficulty is that it is unreasonable to explicitly record
   all of the consequences of an action, even the immediate ones.
   For example [...]  For any given action there are essentially
   an infinite number of possible consequences that depend upon the
   details of the situation in which the action occurs.
\end{quotation}
More concretely, the difference between ramification and the
simpler case of strict inertia is that strict inertia assumes action
laws to specify \emp{all} the effects of the action explicitly,
whereas in ramification the action law only needs to specify
\emp{some of} the effects; the others are to be deduced. On the
other hand, the logic cannot do magic; those other effects must also
be declared somehow. One can think of two specific reasons why
ramification is useful:
\begin{enumerate}
\item  In order to avoid duplication of the same information on the
  consequent side of several action laws. Suppose, for a trivial example,
  that both \emp{alive}$(x)$ and \emp{dead}$(x)$ occur as state variables.
  Under strict inertia, every action that causes a change in \emp{alive}$(x)$
  must also specify the corresponding change in \emp{dead}$(x)$.
\item  In order to avoid configuration-dependent action laws. Suppose
  the scenario world consists of a number of interconnected objects,
  where a change in one of them may cause changes in neighboring objects,
  and different scenarios in the same world contain different
  configurations. If the same action law is going to be used in all
  scenarios, it must apply regardless of the choice of configuration,
  and then it is not possible to represent the secondary changes
  explicitly in the action law.
\end{enumerate}
We shall refer to these as the \emp{redundancy} reason and the
\emp{propagation} reason for ramification, respectively.