Closed World Assumption

The closed world assumption is the presumption that what can currently not be shown to be true is false.

This is a different kind of negation for which we use the symbol “not”. Remember that for $\neg A$ to be true, we need to explicitly prove $\neg A$; for this reason '$\neg$' is sometimes called strict negation.

For “not $A$” to be true, we need to show that $A$ is not known to be true; that is to say: every attempt to prove $A$ fails, there is no successful derivation tree for $A$.