AskDefine | Define weakening

The Collaborative Dictionary

moderating \moderating\ adj. lessening in intensity or strength. Opposite of intensifying. [Narrower terms: tempering; weakening] [WordNet 1.5]
Weaken \Weak"en\, v. t. [imp. & p. p. Weakened; p. pr. & vb. n. Weakening.] [1913 Webster]
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. [1913 Webster] Their hands shall be weakened from the work, that it be not done. --Neh. vi.
[1913 Webster]
To reduce in quality, strength, or spirit; as, to weaken tea; to weaken any solution or decoction. [1913 Webster]

Word Net

weakening adj
1 causing debilitation [syn: debilitative, enervating, enfeebling]
2 moderating by making pain or sorrow weaker

Noun

1 becoming weaker [ant: strengthening]
2 the act of reducing the strength of something [ant: strengthening]

English

Verb

weakening
  1. present participle of weaken

Noun

  1. An instance or process of loss of strength
  2. A structural principle of mathematical logic that states that the hypotheses of any derived fact may be freely extended with additional assumptions
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.

Weakening rule

To illustrate, starting from the natural deduction sequent:
Γ \vdash C
weakening allows one to conclude:
Γ, A \vdash C

Non-monotonic logics

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

See also

weakening in German: Monotonie (Logik)
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