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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

 實體

抽象的

關係

單值關係

函數
 實體

抽象的

關係

三元關係

二元函數

關連函數

## Axioms (1)

• if function關連函數實例,
• then for all inst1,inst2,inst3 holds: if function 的 論元 class實例 and inst1class實例 and inst2class實例 and inst3class實例, then "function(inst1,"function(inst2,inst3)")" 等於 "function("function(inst1,inst2)",inst3)"
• .
```(=>
(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)))))```