Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone just in case the rule is admissible. Logical systems with this property are occasionally called monotonic logics in order to differentiate them from nonmonotonic logics.
To illustrate, starting from the natural deduction sequent:
weakening allows one to conclude:
In most logics, weakening is either an inference rule or a metatheorem if the logic doesn't have an explicit rule. Notable exceptions are:
