  We present a symbolic machinery that admits both probabilistic and causal
information about a given domain and produces probabilistic statements about
the effect of actions and the impact of observations. The calculus admits two
types of conditioning operators: ordinary Bayes conditioning, P(y|X = x), which
represents the observation X = x, and causal conditioning, P(y|do(X = x)), read
the probability of Y = y conditioned on holding X constant (at x) by deliberate
action. Given a mixture of such observational and causal sentences, together
with the topology of the causal graph, the calculus derives new conditional
probabilities of both types, thus enabling one to quantify the effects of
actions (and policies) from partially specified knowledge bases, such as
Bayesian networks in which some conditional probabilities may not be available.
