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 give a precise picture of the complexity of deciding consistency of strength λ and of computing tight consequences of strength λ. Furthermore, I present algorithms for these tasks, which are based on reductions to the standard problems of deciding satisfiability and of computing tight logical consequences in model-theoretic probabilistic logic. Finally, I describe the system nmproblog, which includes a prototype implementation of these algorithms. © 2006 Elsevier Inc. All rights reserved.
Lukasiewicz, T. (2007). Nonmonotonic probabilistic logics under variable-strength inheritance with overriding: Complexity, algorithms, and implementation. International Journal of Approximate Reasoning, 44(3), 301–321. https://doi.org/10.1016/j.ijar.2006.07.015