 In both McDermott-Doyle’s Nonmonotonic Logic I and Moore’s Autoepistemic logic (McDermott and Doyle, 1982; Moore, 1985; Konolige 1994), a modal operator \(M\) (representing a kind of epistemic possibility) is used. Default rules take the following form: \(((p \amp Mq) \rightarrow q)\), that is, if \(p\) is true and \(q\) is “possible” (in the relevant sense), then \(q\) is also true. In both cases, the extension of a theory is defined, as in Reiter’s default logic, by means of a fixed-point operation. \(Mp\) represents the fact that \(\neg p\) does not belong to the extension. For example, in Moore’s case, a set \(\Delta\) is a stable expansion of a theory \(\Gamma\) just in case \(\Delta\) is the set of classical consequences of the set \(\Gamma \cup \{\neg Mp: p \in \Delta \} \cup \{Mp: p \not\in \Delta \}\). As in the case of Reiter’s default logic, some theories will lack a stable expansion, or have more than one. In addition, these systems fail to incorporate Specificity.