Consolidation of probabilistic knowledge bases by inconsistency minimization

Abstract

Consolidation describes the operation of restoring consistency in an inconsistent knowledge base. Here we consider this problem in the context of probabilistic conditional logic, a language that focuses on probabilistic conditionals (if-then rules). If a knowledge base, i. e., a set of probabilistic conditionals, is inconsistent traditional model-based inference techniques are not applicable. In this paper, we develop an approach to repair such knowledge bases that relies on a generalized notion of a model of a knowledge base that extends to classically inconsistent knowledge bases. We define a generalized approach to reasoning under maximum entropy on these generalized models and use it to repair the knowledge base. This approach is founded on previous work on inconsistency measures and we show that it is well-defined, provides a unique solution, and satisfies other desirable properties.