Compressed Constraints in Probabilistic Logic and Their Revision

In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three­ valued logic (true, false, and "don't care"). The three-valued approach allows the construction of "compressed" constraint systems which have the same solution sets as their two-valued counterparts, but which may involve dramatically fewer variables. Techniques to calculate point estimates for the posterior probabilities of entailed sentences are discussed. 1. PROLIFERATION OF WORLDS An entailment problem in Nilsson's (1986) probabilistic logic derives an estimate for the prior probability of one sentence (hereafter, the "target") from the priors for a set of other ("source") sentences. The prior beliefs about the source sentences establish constraints of the form P=VW L wi = l Wi <': 0 sum over all "worlds"