Negation as failure

A common default assumption is that 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 F.

Related Topics:
Closed World Assumption - Default logic

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: rac{:{ eg}F}{{ eg}F}

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For example, the computer language Prolog uses a sort of default assumption when leading with negation: if a negative atom cannot be proved to be true, then it is assumed to be false.

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Note, however, that Prolog uses the so-called negation as failure: when the interpreter has to evaluate the atom eg F, it tries to prove that F is true, and conclude that eg F is true if it fails. In default logic, instead, a default having eg F as a justification can only be applied if eg F is consistent with the current knowledge.

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