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pian1 xu4 yu1... (partialOrderingOn)

A BinaryRelation is a partial ordering on a SetOrClass only if the relation is reflexiveOn the SetOrClass, and it is both an AntisymmetricRelation, and a TransitiveRelation.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

zhong3 lei4
is instance of
  ke3 ji4 cheng2 guan1 xi4  
is instance of
  er4 yuan2 shu4 ci2  
is instance of
bu2 dui4 chen4 guan1 xi4
is instance of
is instance of
  pian1 xu4 yu1...  

Coordinate term(s)

fan3 mian4 han2 shu4  ji4 shu4 han2 shu4  zheng4 mian4 han2 shu4  zhu3 ti1 han2 shu4  huo4 ran2 lv4 han2 shu4  biao3 pi2 han2 shu4  hu2 xian4 zhong4 liang4  shu3 xing4  zuo4 zhe3  xian1 yu1 huo4 tong5 shi2  zhao4 yin1  ci4 lei4 zhao4 yin1  gong1 min2  feng1 bi4 yu1  tian2 man3  xiang1 lian2 de5  bao1 han2 xun4 xi1  gong4 sheng1  fu4 zhi4  xiang1 jiao1  ri4 qi1  jiang4 di1 ke3 neng2 xing4  fa1 zhan3 qi1 xing2 shi4  wu2 jiao1 ji2  fen1 pei4  wen2 zi4 shuo1 ming2  chi2 xu4 shi2 jian1  jiao4 zao3  bian1 zhe3  yuan2 su4  gu4 yong4  xiang1 deng3  deng3 tong2 guan1 xi4 yu1  li4 yong4  yi3...yu3 yan2 biao3 da2  mian4 dui4  jia1 zu2 guan1 xi4  tian2 chong1  wan2 cheng2  ci4 shu4  tu2 bu4 fen5  da4 yu1  da4 yu1 huo4 deng3 yu1  you3 yi4 tu2  you3 ji4 qiao3  zai4...qi1 jian1 wei2 zhen1  xu1 shi3...wei2 zhen1  you3 quan2 shi3...wei2 zhen1  dong4  tong2 yi1 yuan2 su4  zhi2 jie1 shi2 li4  zhi2 jie1 ci4 zhong3 lei4  chuan4 lie4 zhong1  zai4 zhu4 yi4 fan4 wei2 zhong1  zeng1 jia1 ke3 neng2 xing4  du2 li4 huo4 ran2 lv4  ju1 zhu4  yi4 zhi4  chu1 shi3 hua4 xu4 lie4  shi2 li4  dao4 xu4  fei1 fan3 she4 yu1...  da4 yu1  xiao3 yu1  xiao3 yu1 huo4 deng3 yu1  fang1 shi4/qing2 zhuang4  wu4 zhi4  ce4 liang4  shi2 duan4 xiang1 jie1  cheng2 yuan2  qing2 tai4 shu3 xing4  shi2 duan4 zhong4 die2  Âù¿Ë  bu4 fen5 tian2 chong1  bu4 fen5 wei4 yu1  lu4 jing4 chang2  chuan1 ru4  yong1 you3  xian1 jue2 tiao2 jian4  bi4 mian3  zheng4 bu4 fen5  shi4 dang4 tian2 chong1  te4 xing4  chu1 ban3  fan4 wei2  fan4 wei2 ci4 zhong3 lei4  shi2 xian4  ti2 ji2  fan3 she4 yu1...  SUMOna4 bu4 xiang1 guan1 gai4 nian4  xiong1 di4 zi3 mei4  xiao3 yu1  kai1 shi3  ci4 shu3 xing4  ci4 ju4 ji2  ci4 tu2  ci4 xu4 lie4  ci4 li4 cheng2  ci4 ming4 ti2  ci4 zhong3 lei4  ci4 guan1 xi4  bao1 han2 xun4 xi1 zhong3 lei4  bao1 han2 xun4 xi1 shi2 li4  xu4 jie1 shu3 xing4  feng1 bi4 xu4 jie1 shu3 xing4  biao3 mian4  shi2 jian1 bu4 fen5  shi2 jian1  quan2 xu4 yu1...  san1 fen1 fa3  shi3 yong4  jie2 he2 jia4  ren2 zao4 wu4 ban3 ben3 

Type restrictions

partialOrderingOn(er4 yuan2 guan1 xi4, ji2 he2 huo4 zhong3 lei4)

Axioms (2)

If relation pian1 xu4 yu1 class, then relation fan3 ying4 yu1 class and relation shi4 ke3 di4 guan1 xi4 de5 shi2 li4 and relation shi4 fan3 dui4 chen4 guan1 xi4 de5 shi2 li4. 
(=>
      (partialOrderingOn ?RELATION ?CLASS)
      (and
            (reflexiveOn ?RELATION ?CLASS)
            (instance ?RELATION TransitiveRelation)
            (instance ?RELATION AntisymmetricRelation)))
relation quan2 xu4 yu1 class if and only if relation pian1 xu4 yu1 class and relation dui4 class shi4 san1 fen1 fa3. 
(<=>
      (totalOrderingOn ?RELATION ?CLASS)
      (and
            (partialOrderingOn ?RELATION ?CLASS)
            (trichotomizingOn ?RELATION ?CLASS)))