 In  Antonelli (1999)  a notion of general extension for default logic is introduced, showing that this notion yields a well-behaved relation of defeasible consequence \(\nc\) that satisfies Supraclassicality (if \(\Gamma \vDash \phi\) then \(\Gamma \nc \phi\)) and the three central requirements for NMLs Reflexivity, Cut, and Cautious Monotony from  Gabbay (1985).  The idea behind general extensions can be explained in a particularly simple way in the case of pre-requisite free default theories (called “categorical” in Antonelli (1999)). A general extension for such a default theory is a pair \((\Gamma^+, \Gamma^-)\) of sets of defaults (or conclusions thereof) that simultaneously satisfies two fixpoint equations. The set \(\Gamma^+\) comprises (conclusions of) defaults that are explicitly triggered, and the set \(\Gamma^-\) comprises (conclusions of) defaults that are explicitly ruled out. The intuition is that defaults that are not ruled out can still prevent other defaults from being triggered (although they might not be triggered themselves). We thus obtain a “3-valued” approach (not unlike that of Kripke’s theory of truth  (Kripke 1975)),  in virtue of which general extensions are now endowed with a non-trivial (i.e., not “flat”) algebraic structure. It is then possible to pick out, in a principled way, a particular general extension (for instance, the unique least one, which is always guaranteed to exist) on which to base a notion of defeasible consequence. 