WordNet

made weak or weaker
become weaker; "The prisoners resistance weakened after seven days"
lessen the strength of; "The fever weakened his body"

PrepTutorEJDIC

;‘を'『弱くする』 / ;‘を'薄くする / 弱くなる / 〈人・人の態度が〉軟化する,ぐらつく

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/10/19 16:59:35」(JST)

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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 if and only if 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 C

weakening allows one to conclude:

Γ, A 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:

Strict logic or relevant logic, where every hypothesis must be necessary for the conclusion.
Linear logic which disallows arbitrary contraction in addition to arbitrary weakening.
Bunched implications where weakening is restricted to additive composition.
Various types of default reasoning.
Abductive reasoning, the process of deriving the most likely explanations of the known facts.
Reasoning about knowledge, where statements specifying that something is not known need to be retracted when that thing is learned.

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English Journal

Daily physical complaints and hippocampal function: An fMRI study of pain modulation by anxiety.

Gondo M, Moriguchi Y, Kodama N, Sato N, Sudo N, Kubo C, Komaki G.SourceDepartment of Psychosomatic Research, National Institute of Mental Health, National center of neurology and psychiatry, Tokyo 187-8553, Japan; Department of Psychosomatic Medicine, Graduate School of Medical Sciences, Kyushu University, Fukuoka 812-8582, Japan.
NeuroImage.Neuroimage.2012 Nov 15;63(3):1011-9. doi: 10.1016/j.neuroimage.2012.07.025. Epub 2012 Jul 22.
Pain is a popular physical complaint in human. It is known that experimental anxiety modulates pain processing through hippocampal amplification, whereas it is not known whether a similar experimental reaction is related to daily physical complaints known as 'somatization'. The purpose of this study
PMID 22831862

Physical origin of hydrophobicity studied in terms of cold denaturation of proteins: comparison between water and simple fluids.

Yoshidome T, Kinoshita M.SourceInstitute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan. kinoshit@iae.kyoto-u.ac.jp.
Physical chemistry chemical physics : PCCP.Phys Chem Chem Phys.2012 Nov 14;14(42):14554-66. doi: 10.1039/c2cp41738c. Epub 2012 Sep 26.
A clue to the physical origin of the hydrophobicity is in the experimental observations, which show that it is weakened at low temperatures. By considering a solvophobic model protein immersed in water and three species of simple solvents, we analyze the temperature dependence of the changes in free
PMID 23014986

Japanese Journal

女子大学生の体格・体力の現状及び経年変化

Science reports of Tokyo Woman's Christian University 65(3), 2001-2012, 20150315-00-00
NAID 120005673166

東風時に弱化され易い宗谷暖流

北海道大学水産科学研究彙報 65(2), 47-59, 2015-08-20
NAID 120005649143

Exaggerated perception of facial expressions is increased in individuals with schizotypal traits.

Scientific reports 5, 2015-07-02
NAID 120005670898

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