A structural rule or structural principle of mathematical logic that states that the hypotheses of any derived fact may be freely extended with additional assumptions.

To illustrate, starting from the natural deduction sequent:

weakening allows one to conclude:

In the vast majority of logistic systems, weakening is either a rule of inference or a meta theorem if the logic doesn't have an explicit rule. Notable exceptions are:

• Strict logic or relevant logic, where every hypothesis must be necessary for the conclusion.
• Linear logic which disallows arbitrary contraction in addition to arbitrary weakening.
• Bunched implications where weakening is restricted to additive composition.

See also

• Contraction
• Exchange
• Substructural logic