Reasoning by symmetry in non-monotonic inference

Symmetry had been well studied in classical logics and constraint programming since a decade. Early, Krishna-murthy showed that some tricky formulas admit short proofs when augmenting the propositional logic resolution proof system by the symmetry rule. However, in Artificial Intelligence, we usually manipulate incomplete information and need to include uncertainty to reason on knowledge with exceptions and non-monotonicity. Several non classic logics are introduced for that purpose, but as far as we know, symmetry for these frameworks had not been studied yet. Here, we are interested to extend the notion of symmetry to that non classical logics such as preferential logics, X-logics and default logics, then give a new symmetry inference rule for the X-logics and the default logics. Finally, we show how symmetry reasoning is profitable for these logics and how they handle some symmetries that do not exist in classical logics.