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less than or equal to (lessThanOrEqualTo)

(lessThanOrEqualTo number1 number2) is true just in case the Quantity number1 is less than or equal to the Quantity number2.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

Classe
is instance of
  inheritable relation  
is instance of
  PredicatoBinario  
is instance of
RelazioneDiOrdineParziale
is instance of
Classe
is instance of
  inheritable relation  
is instance of
  RelazioneEstesaAQuantitá  
is instance of
is instance of
  less than or equal to  

Coordinate term(s)

addition fn  division fn  exponentiation fn  max fn  min fn  multiplication fn  reciprocal fn  remainder fn  round fn  subtraction fn  arc weight  authors  before or equal  causes  causes subclass  citizen  closed on  connected  contains information  cooccur  copy  date  decreases likelihood  developmental form  disjoint  distributes  documentation  duration  earlier  editor  element  employs  equal  equivalence relation on  exploits  expressed in language  faces  family relation  finishes  frequency  graph part  greater than  greater than or equal to  has purpose  has skill  holds during  holds obligation  holds right  hole  identity element  in list  in scope of interest  increases likelihood  independent probability  inhabits  inhibits  initial list  instance  inverse  irreflexive on  larger  less than  located  material  measure  meets temporally  modal attribute  overlaps temporally  parent  part  partial ordering on  partly located  path length  possesses  precondition  prevents  property  publishes  range  range subclass  refers  reflexive on  related internal concept  sibling  smaller  starts  sub attribute  sub collection  sub graph  sub list  sub process  sub proposition  subclass  subrelation  subsumes content class  subsumes content instance  successor attribute  successor attribute closure  temporal part  time  total ordering on  trichotomizing on  uses  valence  version 

Type restrictions

lessThanOrEqualTo(Quantitá, Quantitá)

Related WordNet synsets

lower bound
(mathematics) a number equal to or less than any other number in a given set
lower bound is kind of (all)...   lower bound is kind of...  
at most, at the most
not more than; "spend at most $20 on the lunch"
at most is opposite to...  

Axioms (10)

less than or equal to é tricotomizzante su NumeroReale. 
(trichotomizingOn lessThanOrEqualTo RealNumber)
number1 é minore o uguale a number2 se e solo se number1 is uguale a number2 o number1 é meno dinumber2. 
(<=>
      (lessThanOrEqualTo ?NUMBER1 ?NUMBER2)
      (or
            (equal ?NUMBER1 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2)))
greater than or equal to é un inverso di less than or equal to. 
(inverse greaterThanOrEqualTo lessThanOrEqualTo)
Se "lunghezza di list" is uguale a number1, allora per ogni number2 vale: esiste item tale che "number2th elemento di list" is uguale a item se e solo se number2 é minore o uguale a number1. 
(=>
      (equal
            (ListLengthFn ?LIST)
            ?NUMBER1)
      (forall
            (?NUMBER2)
            (<=>
                  (exists
                        (?ITEM)
                        (equal
                              (ListOrderFn ?LIST ?NUMBER2)
                              ?ITEM))
                  (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))))
list3 is uguale a "la lista composta di list1 e list2" se e solo se per ogni number1,number2 vale: se number1 é minore o uguale a "lunghezza di list1" e number2 é minore o uguale a "lunghezza di list2" e number1 é un' istanza di NumeroInteroPositivo e number2 é un' istanza di NumeroInteroPositivo, allora "number1th elemento di list3" is uguale a "number1th elemento di list1" e ""("lunghezza di list1"+number2"th elemento di list3" is uguale a "number2th elemento di list2". 
(<=>
      (equal
            ?LIST3
            (ListConcatenateFn ?LIST1 ?LIST2))
      (forall
            (?NUMBER1 ?NUMBER2)
            (=>
                  (and
                        (lessThanOrEqualTo
                              ?NUMBER1
                              (ListLengthFn ?LIST1))
                        (lessThanOrEqualTo
                              ?NUMBER2
                              (ListLengthFn ?LIST2))
                        (instance ?NUMBER1 PositiveInteger)
                        (instance ?NUMBER2 PositiveInteger))
                  (and
                        (equal
                              (ListOrderFn ?LIST3 ?NUMBER1)
                              (ListOrderFn ?LIST1 ?NUMBER1))
                        (equal
                              (ListOrderFn
                                    ?LIST3
                                    (AdditionFn
                                          (ListLengthFn ?LIST1)
                                          ?NUMBER2))
                              (ListOrderFn ?LIST2 ?NUMBER2))))))
(=>
      (initialList ?LIST1 ?LIST2)
      (forall
            (?NUMBER1 ?NUMBER2)
            (=>
                  (and
                        (equal
                              (ListLengthFn ?LIST1)
                              ?NUMBER1)
                        (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))
                  (equal
                        (ListOrderFn ?LIST1 ?NUMBER2)
                        (ListOrderFn ?LIST2 ?NUMBER2)))))
Se "the il maggior numero intero minore o uguale a number" is uguale a int, allora non esiste NumeroIntero otherint tale che otherint é minore o uguale a number e otherint é più grande di int. 
(=>
      (equal
            (FloorFn ?NUMBER)
            ?INT)
      (not
            (exists
                  (?OTHERINT)
                  (and
                        (instance ?OTHERINT Integer)
                        (lessThanOrEqualTo ?OTHERINT ?NUMBER)
                        (greaterThan ?OTHERINT ?INT)))))
(=>
      (and
            (equal
                  (MaximalWeightedPathFn ?NODE1 ?NODE2)
                  ?PATH)
            (equal
                  (PathWeightFn ?PATH)
                  ?NUMBER))
      (forall
            (?PATH2)
            (=>
                  (and
                        (instance
                              ?PATH2
                              (GraphPathFn ?NODE1 ?NODE2))
                        (equal
                              (PathWeightFn ?PATH2)
                              ?NUMBER2))
                  (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))))
quantity é un' istanza di "l' intervallo da from a to" se e solo se quantity é più grande di o uguale a from e quantity é minore o uguale a to. 
(<=>
      (instance
            ?QUANTITY
            (IntervalFn ?FROM ?TO))
      (and
            (greaterThanOrEqualTo ?QUANTITY ?FROM)
            (lessThanOrEqualTo ?QUANTITY ?TO)))
Se day é un' istanza di "il giorno number", allora number é minore o uguale a . 
(=>
      (instance
            ?DAY
            (DayFn ?NUMBER ?MONTH))
      (lessThanOrEqualTo ?NUMBER 31))