Inconsistency measures for probabilistic logics

Inconsistencies in knowledge bases are of major concern in knowledge representation and reasoning. In formalisms that employ model-based reasoning mechanisms inconsistencies render a knowledge base useless due to the non-existence of a model. In order to restore consistency an analysis and understanding of inconsistencies are mandatory. Recently, the field of inconsistency measurement has gained some attention for knowledge representation formalisms based on classical logic. An inconsistency measure is a tool that helps the knowledge engineer in obtaining insights into inconsistencies by assessing their severity. In this paper, we investigate inconsistency measurement in probabilistic conditional logic, a logic that incorporates uncertainty and focuses on the role of conditionals, i.e. if-then rules. We do so by extending inconsistency measures for classical logic to the probabilistic setting. Further, we propose novel inconsistency measures that are specifically tailored for the probabilistic case. These novel measures use distance measures to assess the distance of a knowledge base to a consistent one and therefore takes the crucial role of probabilities into account. We analyze the properties of the discussed measures and compare them using a series of rationality postulates.