Measuring Inconsistency in Probabilistic Knowledge Bases
Resumo
In AI, inconsistency measures have been proposed as a way to manage inconsistent knowledge bases. This work investigates inconsistency measuring in probabilistic logic. We show that previously existing rationality postulates for inconsistency measures in probabilistic knowledge bases are themselves incompatible and introduce a new way of localising inconsistency to reconcile these postulates. We then show the equivalence between distance-based inconsistency measures, from the AI community, and incoherence measures, from philosophy, that are based on the disadvantageous gambling behaviour entailed by incoherent probabilistic beliefs (via Dutch books). This provides a meaningful interpretation to the former and efficient methods to compute the latter.
