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,
In linear and affine logic, entailment is not idempotent.
See also
- No-deleting theorem
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Classical logic
- Quantifiers
- Predicate
- Connective
- Tautology
- Truth tables
- Truth function
- Truth value
- Well-formed formula
- Idempotency of entailment
- Logicism
- Problem of multiple generality
- Associativity
- Distribution
- Validity
- Soundness
- De Morgan's laws
- Material implication
- Transposition
- modus ponens
- modus tollens
- modus ponendo tollens
- Constructive dilemma
- Destructive dilemma
- Disjunctive syllogism
- Hypothetical syllogism
- Absorption
Introduction | |
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Elimination |
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