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positive integer (PositiveInteger)

An Integer that is greater than zero.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

[tree]
entity
is subclass of
  abstract  
is subclass of
  quantity  
is subclass of
  number  
is subclass of
  real number  
is subclass of
  rational number  
is subclass of
  integer  
is subclass of
[tree]
entity
is subclass of
  abstract  
is subclass of
  quantity  
is subclass of
  number  
is subclass of
  real number  
is subclass of
  nonnegative real number  
is subclass of
is subclass of
  nonnegative integer  
is subclass of
[tree]
entity
is subclass of
  abstract  
is subclass of
  quantity  
is subclass of
  number  
is subclass of
  real number  
is subclass of
  nonnegative real number  
is subclass of
  positive real number  
is subclass of
is subclass of
  positive integer  

Constrains relations

edition fn  list order fn  log fn  periodical issue fn  series volume fn  domain  domain subclass  path length  valence 

Related WordNet synsets

natural number
the number 1 and any other number obtained by adding 1 to it repeatedly
natural number is kind of (all)...   natural number is kind of...  
See more related synsets on a separate page.

Axioms (2)

(=>
      (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))))))))
list3 is equal to "the list composed of list1 and list2" if and only if for all number1,number2 holds: if number1 is less than or equal to "length of list1" and number2 is less than or equal to "length of list2" and number1 is an instance of positive integer and number2 is an instance of positive integer, then "number1th element of list3" is equal to "number1th element of list1" and ""("length of list1"+number2)"th element of list3" is equal to "number2th element of 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))))))