Idempotency of entailment explained

Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. This property can be captured by a structural rule called contraction, and in such systems one may say that entailment is idempotent if and only if contraction is an admissible rule.

Rule of contraction: from

A,C,CB

is derived

A,CB.

Or in sequent calculus notation,

\Gamma,C,C\vdashB
\Gamma,C\vdashB

In linear and affine logic, entailment is not idempotent.

See also