Function Comparison Table

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Function comparison table

Subject have domain1 partition into be first domain of have range be second domain of documentation have axiom is a kind of is an instance of

AssignmentFn Function rangeSubclass Entity subrelation If F is a function with a value for the objects denoted by N1,..., NK, then the term (AssignmentFn F N1 ... NK) denotes the value of applying F to the objects denoted by N1,..., NK. Otherwise, the value is undefined
(=>
(instance ?FUNCTION CommutativeFunction)
(forall (?INST1 ?INST2)
(=>
(and
(instance ?INST1 (DomainFn ?FUNCTION))
(instance ?INST2 (DomainFn ?FUNCTION)))
(equal (AssignmentFn ?FUNCTION ?INST1 ?INST2)
(AssignmentFn ?FUNCTION ?INST2 ?INST1)))))
VariableArityRelation

BinaryFunction identityElement distributes The Class of Functions that require two arguments
(=>
(instance ?FUNCTION BinaryFunction)
(valence ?FUNCTION 2))
TernaryRelation

ContinuousFunction rangeSubclass subrelation Functions which are continuous. This concept is taken as primitive until representations for limits are devised
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
Function

FunctionQuantity ConstantQuantity, FunctionQuantity rangeSubclass SubtractionFn A FunctionQuantity is a Function that maps from one or more instances of ConstantQuantity to another instance of ConstantQuantity. For example, the velocity of a particle would be represented by a FunctionQuantity mapping values of time (which are ConstantQuantities) to values of distance (also ConstantQuantities). Note that all instances of FunctionQuantity are Functions with a fixed arity. Note too that all elements of the range of a FunctionQuantity have the same physical dimension as the FunctionQuantity itself
(<=>
(instance ?ABS Abstract)
(not
(exists (?POINT)
(or
(located ?ABS ?POINT)
(existant ?ABS ?POINT)))))
PhysicalQuantity

GreatestCommonDivisorFn rangeSubclass Integer subrelation (GreatestCommonDivisorFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the greatest common divisor of ?NUMBER1 through ?NUMBER
(=>
(instance ?REL VariableArityRelation)
(not
(exists (?INT)
(valence ?REL ?INT))))
VariableArityRelation

LeastCommonMultipleFn rangeSubclass Integer subrelation (LeastCommonMultipleFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the least common multiple of ?NUMBER1 through ?NUMBER
(=>
(instance ?REL VariableArityRelation)
(not
(exists (?INT)
(valence ?REL ?INT))))
VariableArityRelation

TernaryFunction rangeSubclass subrelation The Class of Functions that require exactly three arguments
(=>
(instance ?FUNCTION TernaryFunction)
(valence ?FUNCTION 3))
QuaternaryRelation

UnaryFunction rangeSubclass inverse The Class of Functions that require a single argument
(=>
(instance ?FUNCTION UnaryFunction)
(valence ?FUNCTION 1))
Function

Subject	have domain1	partition into	be first domain of	have range	be second domain of	documentation	have axiom	is a kind of	is an instance of
AssignmentFn	Function		rangeSubclass	Entity	subrelation	If F is a function with a value for the objects denoted by N1,..., NK, then the term (AssignmentFn F N1 ... NK) denotes the value of applying F to the objects denoted by N1,..., NK. Otherwise, the value is undefined	(=> (instance ?FUNCTION CommutativeFunction) (forall (?INST1 ?INST2) (=> (and (instance ?INST1 (DomainFn ?FUNCTION)) (instance ?INST2 (DomainFn ?FUNCTION))) (equal (AssignmentFn ?FUNCTION ?INST1 ?INST2) (AssignmentFn ?FUNCTION ?INST2 ?INST1)))))		VariableArityRelation
BinaryFunction			identityElement		distributes	The Class of Functions that require two arguments	(=> (instance ?FUNCTION BinaryFunction) (valence ?FUNCTION 2))	TernaryRelation
ContinuousFunction			rangeSubclass		subrelation	Functions which are continuous. This concept is taken as primitive until representations for limits are devised	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))	Function
FunctionQuantity		ConstantQuantity, FunctionQuantity	rangeSubclass		SubtractionFn	A FunctionQuantity is a Function that maps from one or more instances of ConstantQuantity to another instance of ConstantQuantity. For example, the velocity of a particle would be represented by a FunctionQuantity mapping values of time (which are ConstantQuantities) to values of distance (also ConstantQuantities). Note that all instances of FunctionQuantity are Functions with a fixed arity. Note too that all elements of the range of a FunctionQuantity have the same physical dimension as the FunctionQuantity itself	(<=> (instance ?ABS Abstract) (not (exists (?POINT) (or (located ?ABS ?POINT) (existant ?ABS ?POINT)))))	PhysicalQuantity
GreatestCommonDivisorFn			rangeSubclass	Integer	subrelation	(GreatestCommonDivisorFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the greatest common divisor of ?NUMBER1 through ?NUMBER	(=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))		VariableArityRelation
LeastCommonMultipleFn			rangeSubclass	Integer	subrelation	(LeastCommonMultipleFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the least common multiple of ?NUMBER1 through ?NUMBER	(=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))		VariableArityRelation
TernaryFunction			rangeSubclass		subrelation	The Class of Functions that require exactly three arguments	(=> (instance ?FUNCTION TernaryFunction) (valence ?FUNCTION 3))	QuaternaryRelation
UnaryFunction			rangeSubclass		inverse	The Class of Functions that require a single argument	(=> (instance ?FUNCTION UnaryFunction) (valence ?FUNCTION 1))	Function

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