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關連函數 (AssociativeFunction)

A BinaryFunction is associative if bracketing has no effect on the value returned by the Function. More precisely, a Function function is associative just in case (function inst1 (function inst2 inst3)) is equal to (function (function inst1 inst2) inst3), for all inst1, inst2, and inst3.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

[tree]
實體
is subclass of
  抽象的  
is subclass of
  關係  
is subclass of
  單值關係  
is subclass of
  函數  
is subclass of
[tree]
實體
is subclass of
  抽象的  
is subclass of
  關係  
is subclass of
  三元關係  
is subclass of
is subclass of
  二元函數  
is subclass of
  關連函數  

Instance(s)

乘法函數  加法函數  減法函數  除法函數  最大值函數  最小值函數 

Coordinate term(s)

可換函數 

Axioms (1)

(=>
      (instance ?FUNCTION AssociativeFunction)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (domain ?FUNCTION 1 ?CLASS)
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS)
                        (instance ?INST3 ?CLASS))
                  (equal
                        (AssignmentFn
                              ?FUNCTION
                              ?INST1
                              (AssignmentFn ?FUNCTION ?INST2 ?INST3))
                        (AssignmentFn
                              ?FUNCTION
                              (AssignmentFn ?FUNCTION ?INST1 ?INST2)
                              ?INST3)))))