weakening adj
1. causing debilitation [syn: debilitative, enervating, enfeebling]
2. moderating by making pain or sorrow weaker n
3. becoming weaker [ant: strengthening]
4. the act of reducing the strength of something [ant: strengthening]

Weaken \Weak"en\, v. t. [imp. & p. p. Weakened; p. pr. & vb. n. Weakening.]
1. To make weak; to lessen the strength of; to deprive of strength; to debilitate; to enfeeble; to enervate; as, to weaken the body or the mind; to weaken the hands of a magistrate; to weaken the force of an objection or an argument. Their hands shall be weakened from the work, that it be not done. --Neh. vi. 9.
2. To reduce in quality, strength, or spirit; as, to weaken tea; to weaken any solution or decoction.

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Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone just in case the rule is admissible. Logical systems with this property are occasionally called monotonic logics in order to differentiate them from non-monotonic logics.

To illustrate, starting from the natural deduction sequent:

weakening allows one to conclude:

In most logics, weakening is either an inference rule or a metatheorem if the logic doesn't have an explicit rule. Notable exceptions are:

• Forecasters: Alberto weakening - United Press International
  MIAMI, May 21 (UPI) -- Tropical Storm Alberto was becoming less organized and weakening off the coast of South Carolina, forecasters said late Sunday. At 11 p.m. EDT, the National Hurricane Center in Miami said the center of Alberto was 135 ... Read more on this news related to 'Weakening'
• Markets end flat amid weakening rupee - rediff.com
  Benchmark share indices erased most of the day gains and ended flat on Monday as the weakening Indian rupee weighed on market sentiment. The Indian rupee weakened to 54.85 against the US dollar. The Sensex ended at 16,183, up 30 points and the ... Read more on this news related to 'Weakening'
• Senate toughens Iran penalties over nuke program - msnbc.com
  By DONNA CASSATA Associated Press WASHINGTON (AP) - Intent on weakening Iran economically, the Senate on Monday approved tough new penalties on the Tehran regime to thwart its nuclear ambitions. By voice vote, the Senate backed the measure ahead of talks ... Read more on this news related to 'Weakening'