RI: a logic for reasoning with inconsistency

The authors present a logic, called RI (reasoning with inconsistency), that treats any set of clauses, either consistent or not, in a uniform way. In this logic, consequences of a contradiction are not nearly as damaging as in the standard predicate calculus, and meaningful information can still be extracted from an inconsistent set of formulas. RI has a resolution-based sound and complete proof procedure. It is a much richer logic than the predicate calculus, and the latter can be imitated within RI in several different ways (depending on the intended meaning of the predicate calculus formulas). The authors also introduce a novel notion of epistemic entailment and show its importance for investigating inconsistency in the predicate calculus