Methods for restoring consistency in probabilistic knowledge bases

This chapter presents a model to change an inconsistent probabilistic knowledge base (PKB) into a consistent one. It discusses several techniques for restoring consistency in PKBs. The chapter also presents several consistency-restoring algorithms and analyzes their complexity. It proposes the solutions of two problems, namely, the norm-based consistency-restoring problem and the unnormalized consistency-restoring problem. The solution of the first problem consists of two approaches which employ the violation vector or the satisfying restored probability vector to compute new probability for each probabilistic constraint. For the second problem, three approaches are proposed which employ a balanced consistency-restoring operator or equitable consistency-restoring operator or an amerced restoring operator compute new probability for each probabilistic constraint. Finally, a set of axioms which represent the relationship between the logical properties and operators have been investigated and discussed.