 Furthermore, there is no guarantee that if \(E\) and \(E'\) are both extensions of theory \(T\), then the intersection of \(E\) and \(E'\) is also an extension (the intersection of two fixed points need not be itself a fixed point). Default logic is usually interpreted as a credulous system: as a system of logic that allows the reasoner to select any extension of the theory and believe all of the members of that theory, even though many of the resulting beliefs will involve propositions that are missing from other extensions (and may even be contradicted in some of those extensions).