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

Abstract

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 lambda in [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 lambda and for computing tight consequences of strength lambda, 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.