Idempotency of entailment
- 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. In sequent calculi this property can be captured by a structural rule called contraction and in such systems one may say that entailment is idempotent just in case contraction is an admissible rule.
Rule of Contraction: from
A,C,C -> B
is derived A,C -> B.
Or in sequent calculus notation,:
Wikimedia Foundation.
2010.
Look at other dictionaries:
Classical logic — identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well.[1][2] They are characterised by a number of properties:[3] Law of the excluded middle and… … Wikipedia
Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… … Wikipedia
Non-classical logic — Non classical logics (and sometimes alternative logics) is the name given to formal systems which differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done,… … Wikipedia
Contraction — may refer to: In physiology: Muscle contraction, one that occurs when a muscle fiber lengthens or shortens Uterine contraction, contraction of the uterus, such as during childbirth Contraction, a stage in wound healing In linguistics: Synalepha,… … Wikipedia
Material conditional — The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q (typically read if p then q or p implies q ) is logically equivalent to the negative compound: not (p and not q). A… … Wikipedia
