KSL-94-13
## A Probabilistic ATMS

**Reference: **
Srinivas, S. A Probabilistic ATMS. Knowledge Systems Laboratory, February, 1994.

**Abstract:** Truth maintenance systems (TMS) provide a method of improving the
efficiency of search during problem solving. The problem solver uses
the TMS to record the reasons that facts are derivable so that facts
need not be rederived during the course of the search. De Kleer's
Assumption Based Truth Maintenance system (ATMS) overcomes the
limitations of many earlier systems, such as not being able to switch
states swiftly and not being able to consider multiple solutions to a
problem at once. We describe a probabilistic extension to the ATMS --
An ATMS structure is augmented with a probability distribution over
the set of assumptions. A probabilistic model is then constructed in
the form of a Bayesian network from the ATMS structure. The
probabilistic ATMS provides significant new functionality such as the
derivation of the probability of a fact being derivable, the posterior
probability over the assumptions given that a fact is derivable and
the most probable context in which a fact is derivable. Our technique
does not require the probability distribution of an assumption to be
independent of the distributions of other assumptions. As an example
of the use of the probabilistic ATMS, we show that it can be applied
to construct probabilistic models to do multiple fault diagnosis. This
generalizes some aspects of de Kleer and Williams' work on model based
diagnosis. The probabilistic ATMS has been implemented in IDEAL, a
Bayesian network solver.

Full paper available as ps.

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