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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,C → B
is derived
- A,C → B.
Or in sequent calculus notation,
In linear and affine logic, entailment is not idempotent.
