Nonmonotonic Probabilistic Logics under Variable-Strength Inheritance with Overriding: Algorithms and Implementation in NMPROBLOG

In previous work, I have introduced nonmonotonic probabilistic logics under variable-strength inheritance with overriding. They are formalisms for probabilistic reasoning from sets of strict logical, default logical, and default probabilistic sentences, which are parameterized through a value λ ∈ [0, 1] that describes the strength of the inheritance of default probabilistic knowledge. In this paper, I continue this line of research. I present algorithms for deciding consistency of strength λ and for computing tight consequences of strength λ, which are based on reductions to the standard problems of deciding satisfiability and of computing tight logical consequences in model-theoretic probabilistic logic. Furthermore, I describe an implementation of these algorithms in the system NMPROBLOG. Keywords. Model-theoretic and nonmonotonic probabilistic logics, qualitative reasoning about uncertainty, probability rankings, algorithms for manipulating imprecise probabilities, convex sets of probability measures.