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Markov Analysis of Qualitative Dynamics

Report ID:
January 1991
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Commonsense sometimes predicts events to be likely or unlikely rather
than merely possible. We extend methods of qualitative reasoning to
predict the relative likelihoods of possible qualitative behaviors by
viewing the dynamics of a system as a Markov chain over its transition
graph. This involves adding qualitative or quantitative estimates of
transition probabilities to each of the transitions and applying the
standard theory of Markov chains to distinguish persistent states from
transient states and to calculate recurrence times, settling times, and
probabilities for ending up in each state. Much of the analysis
depends solely on qualitative estimates of transition probabilities,
which follow directly from theoretical considerations and which lead to
qualitative predictions about entire classes of systems. Quantitative
estimates for specific systems are derived empirically and lead to
qualitative and quantitative conclusions, most of which are insensitive
to small perturbations in the estimated transition probabilities. The
algorithms are straightforward and efficient.

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