what is not known to be true is believed to be false. This is known as the Closed-World Assumption, and is formalized in default logic using a default like the following one for every fact . For example, the computer language Prolog uses a sort of default assumption when dealing with negation: if a negative atom cannot be proved to be true, then it is assumed to be false. Note, however, that Prolog uses the so-called negation as failure: when the interpreter has to evaluate the atom , it tries to prove that is true, and conclude that is true if it fails. In default logic, instead, a default having as a justification can only be applied if is consistent with the current knowledge. Restrictions A default is categorical or prerequisite-free if it has no prerequisite (or, equivalently, its prerequisite is tautological). A default is normal if it has a single justification that is equivalent to its conclusion. A default is supernormal if it is both categorical and normal. A default is seminormal if all its justifications entail its conclusion. A default theory is called categorical, normal, supernormal, or seminormal if all defaults it contains are categorical, normal, supernormal, or seminormal, respectively. Semantics of default logic A default rule can be applied to a theory if its precondition is entailed by the theory and its justifications are all consistent with the theory. The application of a default rule leads to the addition of its consequence to the theory. Other default rules may then be applied to the resulting theory. When the theory is such that no other default can be applied, the theory is called an extension of the default theory. The default rules may be applied in different order, and this may lead to different extensions. The Nixon diamond example is a default theory with two extensions: Since Nixon is both a Republican and a Quaker, both defaults can be applied. However, applying the first default leads to the conclusion that Nixon is not a pacifist, which makes the second default not applicable. In the same way, applying the second default we obtain that Nixon is a pacifist, thus making the first default not applicable. This particular default theory has therefore two extensions, one in which is true, and one in which is false. The original semantics of default logic was based on the fixed point of a function.