In previous papers some important properties of extensions of general default theories were given. In order to dedicate further research to default logic, a characterization of extensions is presented again and some new algorithms for reasoning tasks in default logic are presented in this paper. A class of default theories, auto-compatible default theory, is also developed. We show that the characterization and notions of compatibility and auto-compatibility, suitably applied to logic programs,

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... yield some sufficient conditions of existence of answer sets. All these essentially develop the theories of Reiter and his followers. ]