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

In previous work, I have introduced nonmonotonic probabilistic logics under variablestrength 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. I also 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. 1Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, I-00198 Rome, Italy; e-mail: [email protected]. Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria; e-mail: [email protected]. Acknowledgements: This work was supported by a Heisenberg Professorship of the German Research Foundation (DFG). I am thankful to the reviewers of the ISIPTA-2005 abstract of this paper for their constructive comments, which helped to improve this work. Copyright c © 2006 by the authors INFSYS RR 1843-05-03 I