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commutative Funktion (CommutativeFunction)

A BinaryFunction is commutative if the ordering of the arguments of the function has no effect on the value returned by the function. More precisely, a function function is commutative just in case (function inst1 inst2) is equal to (function inst2 inst1), for all inst1 and inst2.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

[tree]
Wesen
is subclass of
  abstrakter Gegenstand  
is subclass of
  Relation  
is subclass of
  einwertige Relation  
is subclass of
  Funktion  
is subclass of
[tree]
Wesen
is subclass of
  abstrakter Gegenstand  
is subclass of
  Relation  
is subclass of
  dreiwertige Relation  
is subclass of
is subclass of
  zweistellige Funktion  
is subclass of
  commutative Funktion  

Instance(s)

MultiplikationFn  AdditionFn  MaximumFn  MinumumFn 

Coordinate term(s)

associative Funktion 

Related WordNet synsets

commutative
(mathematics) of a binary operation; independent of order; as in e.g. "a x b = b x a"
commutative is similar to...  

Axioms (1)

(=>
      (instance ?FUNCTION CommutativeFunction)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (domain ?FUNCTION 1 ?CLASS)
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS))
                  (equal
                        (AssignmentFn ?FUNCTION ?INST1 ?INST2)
                        (AssignmentFn ?FUNCTION ?INST2 ?INST1)))))