小於 (lessThan)

(lessThan number1 number2) is true just in case the Quantity number1 is less than the Quantity number2.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

種類

可繼承關係

二元述詞

可遞關係

非反身關係

種類

可繼承關係

與量關係

小於

Coordinate term(s)

加法函數反面函數除法函數指數函數正面函數最大值函數最小值函數乘法函數倒數函數餘數函數整數函數減法函數弧線重量屬性作者先於先於或同時肇因次類肇因公民封閉於相連的已連結工程元件包含訊息共生複製相交日期降低可能性發展期形式無交集分配文字說明持續時間期間較早編者元素雇用相等等同關係於利用以...語言表達面對家族關係完成次數圖部分大於大於或等於有意圖有技巧在...期間為真須使...為真有權使...為真洞同一元素串列中在注意範圍中增加可能性獨立或然率居住抑制初始化序列實例內部倒序非反射於... 大於小於或等於方式/情狀物質測量空間上接觸時段相接情態屬性部分重疊時段重疊雙親偏序於... 部分位於路徑長擁有先決條件避免正部分特性出版範圍範圍次種類提及反射於... SUMO內部相關概念兄弟姊妹小於開始次屬性次聚集次圖次序列次組織次計畫次歷程次命題次種類次關係包含訊息種類包含訊息實例續接屬性封閉續接屬性外表部分時間部分時間全序於... 三分法使用（結合）價人造物版本

Type restrictions

lessThan(數量, 數量)

Related WordNet synsets

less: smaller in amount or degree: "the less I see of you the better"; "people have lost their heads for less"

See more related synsets on a separate page.

Axioms (21)

小於對實數是三分法.

(trichotomizingOn lessThan RealNumber)

大於是小於的倒序.

(inverse greaterThan lessThan)

number1 小於或等於 number2 if and only if number1 等於 number2 or number1 小於 number2.

(<=>
      (lessThanOrEqualTo ?NUMBER1 ?NUMBER2)
      (or
            (equal ?NUMBER1 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2)))

number 是負實數的實例 if and only if number 小於 and number 是實數的實例.

(<=>
      (instance ?NUMBER NegativeRealNumber)
      (and
            (lessThan ?NUMBER 0)
            (instance ?NUMBER RealNumber)))

rel 是全值關係的實例 if and only if there exists valence so that rel 是關係的實例 and rel %&有論元(s) valence and

if for all number,element,class holds: if number 小於 valence and rel 的論元 number 是 class 的實例 and element 等於 ""()" 的第二元素", then element 是 class 的實例,
then there exists item so that rel(,item) (不) 成立s

(<=>
      (instance ?REL TotalValuedRelation)
      (exists
            (?VALENCE)
            (and
                  (instance ?REL Relation)
                  (valence ?REL ?VALENCE)
                  (=>
                        (forall
                              (?NUMBER ?ELEMENT ?CLASS)
                              (=>
                                    (and
                                          (lessThan ?NUMBER ?VALENCE)
                                          (domain ?REL ?NUMBER ?CLASS)
                                          (equal
                                                ?ELEMENT
                                                (ListOrderFn
                                                      (ListFn @ROW)
                                                      ?NUMBER)))
                                    (instance ?ELEMENT ?CLASS)))
                        (exists
                              (?ITEM)
                              (holds ?REL @ROW ?ITEM))))))

If formula1 (不）降低s) %2 的可能性 and "formula2 的或然率" 等於 number1 and formula1 的機率是 formula2 在 formula2 為真的情況下 , then number2 小於 number1.

(=>
      (and
            (decreasesLikelihood ?FORMULA1 ?FORMULA2)
            (equal
                  (ProbabilityFn ?FORMULA2)
                  ?NUMBER1)
            (conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
      (lessThan ?NUMBER2 ?NUMBER1))

if list 是序列的實例,
then there exists number1 so that there exists item1 so that "list 的第二元素" 等於 item1 and for all number2 holds: if number2 是正整數的實例 and number2 小於 number1, then there exists item2 so that "list 的第二元素" 等於 item2

(=>
      (instance ?LIST List)
      (exists
            (?NUMBER1)
            (exists
                  (?ITEM1)
                  (and
                        (not
                              (equal
                                    (ListOrderFn ?LIST ?NUMBER1)
                                    ?ITEM1))
                        (forall
                              (?NUMBER2)
                              (=>
                                    (and
                                          (instance ?NUMBER2 PositiveInteger)
                                          (lessThan ?NUMBER2 ?NUMBER1))
                                    (exists
                                          (?ITEM2)
                                          (equal
                                                (ListOrderFn ?LIST ?NUMBER2)
                                                ?ITEM2))))))))

If "number 的上限" 等於 int, then there doesn't exist 整數 otherint so that otherint 大於或等於 number and otherint 小於 int.

(=>
      (equal
            (CeilingFn ?NUMBER)
            ?INT)
      (not
            (exists
                  (?OTHERINT)
                  (and
                        (instance ?OTHERINT Integer)
                        (greaterThanOrEqualTo ?OTHERINT ?NUMBER)
                        (lessThan ?OTHERINT ?INT)))))

if " 的最小公倍數" 等於 number,
then there doesn't exist less so that less 小於 number and for all element holds: if element 是 "()" 的一成員, then "less 取餘數 element" 等於

(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?LESS)
                  (and
                        (lessThan ?LESS ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?LESS ?ELEMENT)
                                          0)))))))

If "number1 和 number2 的最小值 " 等於 number, then

number 等於 number1 and number1 小於 number2
number 等於 number2 and number2 小於 number1
number 等於 number1 and number 等於 number2

(=>
      (equal
            (MinFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (or
            (and
                  (equal ?NUMBER ?NUMBER1)
                  (lessThan ?NUMBER1 ?NUMBER2))
            (and
                  (equal ?NUMBER ?NUMBER2)
                  (lessThan ?NUMBER2 ?NUMBER1))
            (and
                  (equal ?NUMBER ?NUMBER1)
                  (equal ?NUMBER ?NUMBER2))))

if "整數 1" 等於 number2,
then
- if "(number1-"最大整數小於或等於 number1")" 小於 , then number2 等於 "最大整數小於或等於 number1"
- if "(number1-"最大整數小於或等於 number1")" 大於或等於 , then number2 等於 "number1 的上限"

(=>
      (equal
            (RoundFn ?NUMBER1)
            ?NUMBER2)
      (or
            (=>
                  (lessThan
                        (SubtractionFn
                              ?NUMBER1
                              (FloorFn ?NUMBER1))
                        0.5)
                  (equal
                        ?NUMBER2
                        (FloorFn ?NUMBER1)))
            (=>
                  (greaterThanOrEqualTo
                        (SubtractionFn
                              ?NUMBER1
                              (FloorFn ?NUMBER1))
                        0.5)
                  (equal
                        ?NUMBER2
                        (CeilingFn ?NUMBER1)))))

If int 是整數的實例, then int 小於 "(int+1)".

(=>
      (instance ?INT Integer)
      (lessThan
            ?INT
            (SuccessorFn ?INT)))

If int1 是整數的實例 and int2 是整數的實例, then int1 小於 int2 or int2 小於 "(int1+1)".

(=>
      (and
            (instance ?INT1 Integer)
            (instance ?INT2 Integer))
      (not
            (and
                  (lessThan ?INT1 ?INT2)
                  (lessThan
                        ?INT2
                        (SuccessorFn ?INT1)))))

If int1 是整數的實例 and int2 是整數的實例, then int2 小於 int1 or "(int1+2)" 小於 int2.

(=>
      (and
            (instance ?INT1 Integer)
            (instance ?INT2 Integer))
      (not
            (and
                  (lessThan ?INT2 ?INT1)
                  (lessThan
                        (PredecessorFn ?INT1)
                        ?INT2))))

There don't exist 劃分 graph 為兩獨立圖表的相交路�| path1,劃分 graph 為兩獨立圖表的最小相交路�| path2 so that path1 的路�|長是 number1 and path2 的路�|長是 number2 and number1 小於 number2.

(not
      (exists
            (?PATH1 ?PATH2)
            (and
                  (instance
                        ?PATH1
                        (CutSetFn ?GRAPH))
                  (instance
                        ?PATH2
                        (MinimalCutSetFn ?GRAPH))
                  (pathLength ?PATH1 ?NUMBER1)
                  (pathLength ?PATH2 ?NUMBER2)
                  (lessThan ?NUMBER1 ?NUMBER2))))

If hour 是 "小時 number" 的實例, then number 小於 .

(=>
      (instance
            ?HOUR
            (HourFn ?NUMBER ?DAY))
      (lessThan ?NUMBER 24))

If minute 是 "分鐘 number" 的實例, then number 小於 .

(=>
      (instance
            ?MINUTE
            (MinuteFn ?NUMBER ?HOUR))
      (lessThan ?NUMBER 60))

If second 是 "秒鐘函數(number,minute)" 的實例, then number 小於 .

(=>
      (instance
            ?SECOND
            (SecondFn ?NUMBER ?MINUTE))
      (lessThan ?NUMBER 60))

If decrease 是減少的實例 and obj 是 decrease 的受事者, then there exist unit,quant1,quant2 so that "obj unit(s)" 等於 quant1 ""decrease 存在的時間" 不久之前"a(之中) "decrease 存在的時間" 不久之前 and "obj unit(s)" 等於 quant2 ""decrease 存在的時間" 不久之後"a(之中) "decrease 存在的時間" 不久之後 and quant2 小於 quant1.

(=>
      (and
            (instance ?DECREASE Decreasing)
            (patient ?DECREASE ?OBJ))
      (exists
            (?UNIT ?QUANT1 ?QUANT2)
            (and
                  (holdsDuring
                        (ImmediatePastFn
                              (WhenFn ?DECREASE))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT1))
                  (holdsDuring
                        (ImmediateFutureFn
                              (WhenFn ?DECREASE))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT2))
                  (lessThan ?QUANT2 ?QUANT1))))

If cool 是降溫的實例 and obj 是 cool 的受事者, then there exist 溫度單位 unit,quant1,quant2 so that "obj unit(s)" 等於 quant1 ""cool 存在的時間" 不久之前"a(之中) "cool 存在的時間" 不久之前 and "obj unit(s)" 等於 quant2 ""cool 存在的時間" 不久之後"a(之中) "cool 存在的時間" 不久之後 and quant2 小於 quant1.

(=>
      (and
            (instance ?COOL Cooling)
            (patient ?COOL ?OBJ))
      (exists
            (?UNIT ?QUANT1 ?QUANT2)
            (and
                  (instance ?UNIT TemperatureMeasure)
                  (holdsDuring
                        (ImmediatePastFn
                              (WhenFn ?COOL))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT1))
                  (holdsDuring
                        (ImmediateFutureFn
                              (WhenFn ?COOL))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT2))
                  (lessThan ?QUANT2 ?QUANT1))))

if
- path1 伴隨 process 發生的 process路徑
- process (不) �_源s 於 source
- process (不) 終結not(s) dest
- path1 的長度是 measure1
- there don't exist path2,measure2 so that path2 伴隨 process 發生的 process路徑 and process (不) �_源s 於 origin and process (不) 終結not(s) dest and path2 的長度是 measure2 and measure2 小於 measure1
,
then for all obj holds: if obj 是 path1 的部分), then obj 介於 source 和 dest 中間

(=>
      (and
            (path ?PROCESS ?PATH1)
            (origin ?PROCESS ?SOURCE)
            (destination ?PROCESS ?DEST)
            (length ?PATH1 ?MEASURE1)
            (not
                  (exists
                        (?PATH2 ?MEASURE2)
                        (and
                              (path ?PROCESS ?PATH2)
                              (origin ?PROCESS ?ORIGIN)
                              (destination ?PROCESS ?DEST)
                              (length ?PATH2 ?MEASURE2)
                              (lessThan ?MEASURE2 ?MEASURE1)))))
      (forall
            (?OBJ)
            (=>
                  (part ?OBJ ?PATH1)
                  (between ?SOURCE ?OBJ ?DEST))))