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Entity > Abstract > Class > Relation > BinaryRelation > UnaryFunction

UnaryFunction
subject			fact

UnaryFunction	documentation The Class of Functions that require a single argument
	has axiom (<=> (and (holds ?REL ?INST1 ?INST2) (instance ?REL UnaryFunction)) (equal (AssignmentFn ?REL ?INST1) ?INST2))
	has axiom (=> (and (closedOn ?FUNCTION ?CLASS) (instance ?FUNCTION UnaryFunction)) (forall (?INST) (=> (instance ?INST ?CLASS) (instance (AssignmentFn ?FUNCTION ?INST) ?CLASS))))
	has axiom (=> (and (instance ?FUNCTION UnaryFunction) (equal (AssignmentFn ?FUNCTION ?ARG) ?VALUE1) (equal (AssignmentFn ?FUNCTION ?ARG) ?VALUE2)) (equal ?VALUE1 ?VALUE2))
	has axiom (=> (instance ?FUNCTION UnaryFunction) (valence ?FUNCTION 1))
	is a kind of BinaryRelation
	is a kind of Function
BinaryRelation	is first domain of DomainFn
	is first domain of equivalenceRelationOn
	is first domain of inverse
	is first domain of irreflexiveOn
	is first domain of partialOrderingOn
	is first domain of RangeFn
	is first domain of reflexiveOn
	is first domain of totalOrderingOn
	is first domain of trichotomizingOn
	is second domain of inverse
Function	is first domain of AssignmentFn
	is first domain of closedOn
	is first domain of range
	is first domain of rangeSubclass
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of UnaryFunction :

• AbsoluteValueFn (5 facts) - The value of (AbsoluteValueFn ?NUMBER) is the absolute value of the RealNumber ?NUMBER
• AbstractionFn (5 facts) - A UnaryFunction that maps a Class into the instance of Attribute that specifies the condition(s) for membership in the Class
• ArcCosineFn (5 facts) - (ArcCosineFn ?NUMBER) returns the arc cosine of the RealNumber ?NUMBER. It is the inverse of CosineFn
• ArcSineFn (5 facts) - (ArcSineFn ?NUMBER) returns the arc sine of the RealNumber ?NUMBER. It is the inverse of SineFn
• ArcTangentFn (5 facts) - (ArcTangentFn ?NUMBER) returns the arc tangent of the RealNumber ?NUMBER. It is the inverse of TangentFn
• BeginFn (19 facts) - A UnaryFunction that maps a TimeInterval to the TimePoint at which the interval begins
• CardinalityFn (7 facts) - (CardinalityFn ?CLASS) returns the number of instances in the Class or Collection ?CLASS
• CeilingFn (6 facts) - (CeilingFn ?NUMBER) returns the smallest Integer greater than or equal to the RealNumber ?NUMBER
• ComplementFn (7 facts) - The complement of a given Class C is the Class of all things that are not instances of C. In other words, an object is an instance of the complement of a Class C just in case it is not an instance of C
• CosineFn (5 facts) - (CosineFn ?DEGREE) returns the cosine of the PlaneAngleMeasure ?DEGREE. The cosine of ?DEGREE is the ratio of the side next to ?DEGREE to the hypotenuse in a right-angled triangle
• DenominatorFn (4 facts) - (DenominatorFn ?NUMBER) returns the denominator of the canonical reduced form of the RealNumber ?NUMBER
• DomainFn (10 facts) - The domain of a BinaryRelation ?REL is the Class of all things that bear ?REL to something
• EndFn (16 facts) - A UnaryFunction that maps a TimeInterval to the TimePoint at which the interval ends
• EngineeringComponentFn (5 facts) - A UnaryFunction that maps a Terminal to its corresponding EngineeringComponent
• ExtensionFn (5 facts) - A UnaryFunction that maps an Attribute into the Class whose condition for membership is the Attribute
• FloorFn (7 facts) - (FloorFn ?NUMBER) returns the largest Integer less than or equal to the RealNumber ?NUMBER
• FutureFn (9 facts) - A UnaryFunction that maps a TimePosition to the TimeInterval which it meets and which ends at PositiveInfinity
• GeneralizedIntersectionFn (6 facts) - A UnaryFunction that takes a Class of Classes as its single argument and returns a Class which is the intersection of all of the Classes in the original Class, i.e. the Class containing just those instances which are instances of all instances of the original Class
• GeneralizedUnionFn (5 facts) - A UnaryFunction that takes a Class of Classes as its single argument and returns a Class which is the merge of all of the Classes in the original Class, i.e. the Class containing just those instances which are instances of an instance of the original Class
• IdentityFn (5 facts) - The value of the identity function is just its argument
• ImaginaryPartFn (5 facts) - (ImaginaryPartFn ?NUMBER) returns the imaginary part of ?NUMBER
• ImmediateFutureFn (24 facts) - A UnaryFunction that maps a TimePosition to a short, indeterminate TimeInterval that immediately follows the TimePosition
• ImmediatePastFn (19 facts) - A UnaryFunction that maps a TimePosition to a short, indeterminate TimeInterval that immediately precedes the TimePosition
• IntegerSquareRootFn (4 facts) - (IntegerSquareRootFn ?NUMBER) returns the integer square root of ?NUMBER
• JunctionFn (4 facts) - A UnaryFunction that maps a Terminal to its corresponding Junction
• MagnitudeFn (5 facts) - The magnitude of a ConstantQuantity is the numeric value for the quantity. In other words, MagnitudeFn converts a ConstantQuantity with an associated UnitOfMeasure into an ordinary RealNumber. For example, the magnitude of the ConstantQuantity 2 Kilometers is the RealNumber 2. Note that the magnitude of a quantity in a given unit times that unit is equal to the original quantity
• NumeratorFn (4 facts) - (NumeratorFn ?NUMBER) returns the numerator of the canonical reduced form ?NUMBER
• OneToOneFunction (1 kind, 6 facts) - The Class of UnaryFunctions which are one to one. A function F is one to one just in case for all X, Y in the domain of F, if X is not identical to Y, then F(X) is not identical to F(Y)
• PastFn (9 facts) - A UnaryFunction that maps a TimePosition to the TimeInterval that meets it and that begins at NegativeInfinity
• PredecessorFn (9 facts) - A UnaryFunction that maps an Integer to its predecessor, e.g. the predecessor of 5 is 4
• PrincipalHostFn (7 facts) - A UnaryFunction that maps a Hole to the Object which is its principal host. The principle host of a Hole is its maximally connected host (a notion taken here to be defined only when the argument is a hole)
• PropertyFn (6 facts) - A UnaryFunction that maps an Agent to the Set of Property owned by the Agent
• RangeFn (6 facts) - The range of a BinaryRelation ?REL is the Class of all things such that something bears ?REL to them
• RationalNumberFn (4 facts) - (RationalNumberFn ?NUMBER) returns the rational representation of ?NUMBER
• RealNumberFn (5 facts) - (RealNumberFn ?NUMBER) returns the part of ?NUMBER that is a RealNumber
• ReciprocalFn (7 facts) - (ReciprocalFn ?NUMBER) is the reciprocal element of ?NUMBER with respect to the multiplication operator (MultiplicationFn), i.e. 1/?NUMBER. Not all numbers have a reciprocal element. For example the number 0 does not. If a number ?NUMBER has a reciprocal ?RECIP, then the product of ?NUMBER and ?RECIP will be 1, e.g. 3*1/3 = 1. The reciprocal of an element is equal to applying the ExponentiationFn function to the element to the power -1
• RoundFn (6 facts) - (RoundFn ?NUMBER) is the Integer closest to ?NUMBER on the number line. If ?NUMBER is halfway between two Integers (for example 3.5), it denotes the larger Integer
• SignumFn (8 facts) - (SignumFn ?NUMBER) denotes the sign of ?NUMBER. This is one of the following values: -1, 1, or 0
• SineFn (5 facts) - (SineFn ?DEGREE) is the sine of the PlaneAngleMeasure ?DEGREE. The sine of ?DEGREE is the ratio of the side opposite ?DEGREE to the hypotenuse in a right-angled triangle
• SkinFn (6 facts) - A UnaryFunction that maps a Hole to the skin of the Hole. The skin of a Hole is the fusion of those superficial parts (see superficialPart) of the Hole's principal host (see PrincipalHostFn) with which the Hole is externally connected
• SquareRootFn (5 facts) - (SquareRootFn ?NUMBER) is the principal square root of ?NUMBER
• SuccessorFn (9 facts) - A UnaryFunction that maps an Integer to its successor, e.g. the successor of 5 is 6
• TangentFn (5 facts) - (TangentFn ?DEGREE) is the tangent of the PlaneAngleMeasure ?DEGREE. The tangent of ?DEGREE is the ratio of the side opposite ?DEGREE to the side next to ?DEGREE in a right-angled triangle
• TerminalFn (4 facts) - A UnaryFunction that maps an EngineeringComponent to its corresponding Terminal
• TruthFn (4 facts) - The function mapping Sentences to TruthValues
• UnaryConstantFunctionQuantity (10 kinds, 37 facts) - The class of UnaryFunctions that map from the Class ConstantQuantity to the Class ConstantQuantity
• WealthFn (5 facts) - A UnaryFunction that maps an Agent to a CurrencyMeasure specifying the value of the property owned by the Agent. Note that this Function is generally used in conjunction with the Function PropertyFn, e.g. (WealthFn (PropertyFn BillGates)) would return the monetary value of the sum of Bill Gates' holdings
• WhenFn (42 facts) - A UnaryFunction that maps an Object or Process to the exact TimeInterval during which it exists. Note that, for every TimePoint ?TIME outside of the TimeInterval (WhenFn ?THING), ?THING is not existant at ?TIME
• YearFn (5 facts) - A UnaryFunction that maps a number to the corresponding calendar Year. For example, (YearFn 1912) denotes the Year 1912

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