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Default logic is an important and influential formalization of commonsense reasoning. Determining whether a given default theory has an extension is the main computational problem pertinent to default logic, the analog of testing for validity and finding deductions in more classical logics. Substantially generalizing a result by Etherington  we show that all default theories that have no odd cycles (in some precise sense) have an extension, which can be found efficiently. We also give adoi:10.1016/0004-3702(94)90087-6 fatcat:4vs3cuo7lffbrbj3sjqkzsnn3e