Published on *Computer Science Department at Princeton University* (http://www.cs.princeton.edu)

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.