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# 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)

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))))```