Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

Abstract

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.