Measuring Inconsistency in Knowledge via Quasi-Classical Models

Abstract

The language for describing inconsistency is underdeveloped. If a knowledgebase (a set of formulae) is inconsistent, we need illuminating ways to say how it is, or to say whether one knowledgebase is more inconsistent than another. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a 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 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 preference ordering, called the compromise relation, over knowledgebases. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge.