In proof theory, a structural rule is an inference rule that does not refer to any logical connective, but instead operates on the judgment or sequents directly. Structural rules often mimic intended meta-theoretic properties of the logic. Logics that deny one or more of the structural rules are classified as substructural logics.
Common structural rules
Three common structural rules are:
Weakening, where the hypotheses or conclusion of a sequent may be extended with additional members. In symbolic form weakening rules can be written as on the left of the turnstile, and on the right.
Contraction, where two equal (or unifiable) members on the same side of a sequent may be replaced by a single member (or common instance). Symbolically: and . Also known as factoring in automated theorem proving systems using resolution.
Exchange, where two members on the same side of a sequent may be swapped. Symbolically: and . (This is also known as the permutation rule.)
A logic without any of the above structural rules would interpret the sides of a sequent as pure sequences; with exchange, they are multisets; and with both contraction and exchange they are sets.
Article by WN.com Correspondent DallasDarling. In nations of great political and cultural diversity, favorable and useful infrastructures are always crucial to unify and subsequently allow economic growth - if not yet widespread and equitable development ... What’s more, which presidential candidate has the best plan for improving the nation’s infrastructures?. Underdeveloped or Well-Developed Infrastructures Determines Destiny ... Like Mr ... 9....
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Nothing inspires like success. But then, for a country our size and potential, a few bursts of enthusiasm are not enough ...Playing is fun, but it comes packaged with a set of rules implemented by the supervisory authority ... Becoming a sporting nation or one that has long-term investors both require a commitment to rule-based, fair and ethical play that can be fun ... Sports offer a simple reward structure the brain understands easily ....
In a press statement, the Security Council 'urged national actors to abide by the Constitution and the rule of law, while striving to find a political solution to the crisis through good-faith dialogue' and also 'urged the security forces of Guinea-Bissau to maintain their non-interference in the political situation, to continue the restraint shown in this regard, and maintain respect for civilian control.'....