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\section*{Learning qualitative models}
Qualitative models are often better suited for several tasks
than traditional quantitative (numeric) methods. These tasks
include diagnosis, generating explanations of a system's
behaviour and designing novel devices from first principles.
A more fundamental problem in the theory of dynamic
systems is the identification of the system itself.
The basic problem is as follows. We are given examples of the behaviour of a dynamic
system. We want to find a model that explains these examples. Accomplishing
this, even at the qualitative level, is quite difficult. Consider the
simple system with two connected containers
\begin{figure*}[htb]
\centerline{\epsfbox{utube.eps}}
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Even this simple system can have almost almost 195,000 possible
qualitative states when using a QSIM formalism. Very few (only 32) of these are
actually ``legal''. The problem here is to learn rules that identify legal
states. These rules, along with built-in assumptions of continuity in QSIM,
are sufficient to identify the dynamics of the system. The data
here are as used in two different experiments. The first
concerns learning rules for legal states using the ILP
program {\em Golem\/} \cite{mugfeng:golem}. This requires determinate,
ground background knowledge, and results are reported in 
\cite{bratmugg:utube}. The information used for this task is:
\begin{itemize}
\item The target predicate is the relation {\bf state(La,Lb,Fab,Fba)},
	where {\bf La}, {\bf Lb}, {\bf Fa} and {\bf Fb} are as shown in
	the figure. 
\item The background knowledge is a tabulation of QSIM constraint
	primitives.
\item Consistency of infinite values in the {\bf add} constraint can be
	ignored for this problem. Further, since {\bf add} requires a very
	large number of ground facts, it is represented by three more
	efficient predicates. {\bf norm\_mag/4} normalises a qualitative
	value with respect to a landmark. {\bf lookup\_consist\_table/3} is a
	lookup table for adding signs. {\bf verify\_add\_deriv/3} os a lookup
	table for adding directions of derivatives.
\item Additional background predicates provide {\bf range} information.
	The QSIM constraints {\bf m\_plus/2} and {\bf m\_minus/2}
	were only tabulated for empty lists of corresponding values.
	All arguments of the background predicates are of the
	same type; they are compound terms of the form
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Func : QualValue/DirOfChange
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\end{itemize}

The more recent data uses the {\em Progol\/} program \cite{mugg:progol}.
This does not require the background to be determinate or ground. Consequently,
background knowledge consists of QSIM predicate definitions \cite{kuipers:qual}.

All data used in the {\em Progol\/} experiments are contained
in a single compressed file with a ``.pl.Z'' suffix.  

The data used in
the original {\em Golem\/} experiments are contained in a compressed
TAR file with a ``tar.Z'' suffix. Within this, the 
background knowledge files have a ``.b'' suffix,
positive example files have a ``.f'' suffix, and negative example files
have a ``.n'' suffix.


\begin{thebibliography}{}

\bibitem{bratmugg:utube}
Bratko I., Muggleton S. and Varsek A. (1992).
Learning Qualitative Models of Dynamic Systems.
In S. Muggleton editor.
{\sl Inductive Logic Programming}. Academic Press, London.

\bibitem{kuipers:qual}
Kuipers B. (1986).
Qualitative simulation.
{\sl Artificial Intelligence}, 29:289--338.

\bibitem{mugfeng:golem}
Muggleton S.H. and Feng C. (1990).
Efficient induction of logic programs.
{\sl Proceedings of the First Conference on Algorithmic Learning Theory},
Tokyo.

\bibitem{mugg:progol}
Muggleton S.H. (1995)
Inverse Entailment and Progol.
{\sl New Gen. Comput.} (to appear).

\end{thebibliography}

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