Deontic Reasoning Based on Inconsistency Measures

Conflicts are inherent to normative systems. In this paper, we explore a novel approach to normative reasoning by quantifying the amount of conflicts within normative systems. We refine the idea from classical logic, according to which a formula is a consequence of a knowledge base in case its negation renders the knowledge base inconsistent. In our approach, whether a formula is a logical consequence depends, for instance, on its negation's marginal contribution to the inconsistency of the given knowledge base. Accordingly, various inconsistency measures and corresponding (nonmonotonic and paraconsistent) normative entailment relations are analyzed relative to a number of logical properties. To illustrate our approach, we adopt Input/Output logic, a renowned formalism in deontic logic, specifically designed for defeasible normative reasoning. As an application, the resulting entailment relations provide recommendations to agents for minimizing norm conflicts, and may be incorporated in a number of implementations (like the Tweety libraries and the LogiKey framework) by involving inconsistency measurements in normative reasoning.