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)

class

inheritable relation

unary function

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

integer SuccessorFn(integer)

Axioms (8)

"length of "(,item)"" is equal to "("length of "()""+1)".

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

If "length of list1" is equal to number, then there exists list2 so that list1 starts list2 and "(number+1)" is equal to "length of list2" and ""(number+1)"th element of list2" is equal to 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 equal to "(number+)".

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

If "(int1+1)" is equal to "(int2+1)", then int1 is equal to int2.

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

If int is an instance of integer, then int is less than "(int+1)".

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

If int1 is an instance of integer and int2 is an instance of integer, then int1 is not less than int2 or int2 is not less than "(int1+1)".

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

If int is an instance of integer, then int is equal to "("(int+2)"+1)".

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

If int is an instance of integer, then int is equal to "("(int+1)"+2)".

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