Idempotency of entailment

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,

\frac{\Gamma,C,C\vdash B}{\Gamma,C\vdash B}

Classical logic

Law of excluded middle Double negative elimination Law of noncontradiction Principle of explosion Monotonicity of entailment Idempotency of entailment Commutativity of conjunction De Morgan's laws Principle of bivalence Propositional logic Predicate logic

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