Inconsistency Management and Prioritized Syntax-Based Entailment

The idea of ordering plays a basic role in commonsense reasoning for addressing three interrelated tasks: inconsistency handling, belief revision and plausible inference. We study the behavior of non-monotonic inferences induced by various methods for priority-based handling of inconsistent sets of classical formulas. One of them is based on a lexicographic ordering of maximal consistent subsets, and refines Brewka's preferred sub-theories. This new approach leads to a non-monotonic inference which satisfies the "rationality" property while solving the problem of blocking of property inheritance. It differs from and improves previous equivalent approaches such as Gardenfors and Makinson's expectation-based inference, Pearl's System Z and possibilistic logic.