Evaluating Significance of Inconsistencies

Inconsistencies frequently occur in knowledge about the real-world. Some of these inconsistencies may be more significant than others, and some knowledgebases (sets of formulae) may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap’s four-valued logic, and unlike other paraconsistent logics, allows the connectives to appear to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasi-classical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a measure of significance of inconsistencies in each knowledgebase. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge.