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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,doi:10.1006/inco.1996.0075 fatcat:ywcuxj5nejc6jjlk5j2d4mfgrq