successor fn (SuccessorFn)

A UnaryFunction that maps an Integer to its successor, e.g. the successor of 5 is 6.

Ontology

SUMO / NUMERIC-FUNCTIONS

Class(es)

Classe

inheritable relation

FunzioneUnaria

successor fn

Coordinate term(s)

absolute value fn abstraction fn arc cosine fn arc sine fn arc tangent fn back fn begin fn begin node fn cardinality fn ceiling fn complement fn cosine fn cut set fn denominator fn end fn end node fn extension fn floor fn front fn future fn generalized intersection fn generalized union fn giga fn imaginary part fn immediate future fn immediate past fn initial node fn integer square root fn kilo fn list length fn magnitude fn mega fn micro fn milli fn minimal cut set fn nano fn numerator fn organization fn past fn path weight fn pico fn power set fn predecessor fn principal host fn probability fn property fn rational number fn real number fn reciprocal fn round fn signum fn sine fn skin fn square root fn tangent fn tera fn terminal node fn wealth fn when fn year fn

Type restrictions

NumeroIntero SuccessorFn(NumeroIntero)

Axioms (8)

"lunghezza di "(,item"" is uguale a "("lunghezza di "(""+1".

(equal
      (ListLengthFn
            (ListFn @ROW ?ITEM))
      (SuccessorFn
            (ListLengthFn
                  (ListFn @ROW))))

Se "lunghezza di list1" is uguale a number, allora esiste list2 tale che list1 inizias list2 e "(number+1" is uguale a "lunghezza di list2" e ""(number+1"th elemento di list2" is uguale a item.

(=>
      (equal
            (ListLengthFn ?LIST1)
            ?NUMBER)
      (exists
            (?LIST2)
            (and
                  (initialList ?LIST1 ?LIST2)
                  (equal
                        (SuccessorFn ?NUMBER)
                        (ListLengthFn ?LIST2))
                  (equal
                        (ListOrderFn
                              ?LIST2
                              (SuccessorFn ?NUMBER))
                        ?ITEM))))

"(number+1" is uguale a "(number+".

(equal
      (SuccessorFn ?NUMBER)
      (AdditionFn ?NUMBER 1))

Se "(int1+1" is uguale a "(int2+1", allora int1 is uguale a int2.

(=>
      (equal
            (SuccessorFn ?INT1)
            (SuccessorFn ?INT2))
      (equal ?INT1 ?INT2))

Se int é un' istanza di NumeroIntero, allora int é meno di"(int+1".

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

Se int1 é un' istanza di NumeroIntero e int2 é un' istanza di NumeroIntero, allora int1 é not meno diint2 o int2 é not meno di"(int1+1".

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

Se int é un' istanza di NumeroIntero, allora int is uguale a "("(int+2"+1".

(=>
      (instance ?INT Integer)
      (equal
            ?INT
            (SuccessorFn
                  (PredecessorFn ?INT))))

Se int é un' istanza di NumeroIntero, allora int is uguale a "("(int+1"+2".

(=>
      (instance ?INT Integer)
      (equal
            ?INT
            (PredecessorFn
                  (SuccessorFn ?INT))))