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Sigma KEE - KappaFn
KappaFn

appearance as argument number 1
-------------------------


(documentation KappaFn EnglishLanguage "A class-forming operator that takes two arguments: a variable and a formula containing at least one unbound occurrence of the variable. The result of applying kappa to a variable and a formula is the set or class of things that satisfy the formula. For example, we can denote the set or class of prime numbers that are less than 100 with the following expression: (KappaFn ?NUMBER (and (instance ?NUMBER PrimeNumber) (lessThan ?NUMBER 100))). Note that the use of this function is discouraged, since there is currently no axiomatic support for it.") Merge.kif 4387-4395
(domain KappaFn 1 SymbolicString) Merge.kif 4384-4384 The number 1 argument of kappa is an instance of symbolic string
(domain KappaFn 2 Formula) Merge.kif 4385-4385 The number 2 argument of kappa is an instance of formula
(instance KappaFn BinaryFunction) Merge.kif 4383-4383 Kappa is an instance of binary function
(range KappaFn Class) Merge.kif 4386-4386 The range of kappa is an instance of class

appearance as argument number 2
-------------------------


(format EnglishLanguage KappaFn "the class described by %1") english_format.kif 297-297
(termFormat EnglishLanguage KappaFn "kappa") domainEnglishFormat.kif 5149-5149 term format english language, kappa and "kappa"

antecedent
-------------------------


(<=>
    (and
        (instance ?Account PersonalAccount)
        (greaterThan
            (CardinalityFn
                (KappaFn ?Agent
                    (accountHolder ?Account ?Agent))) 1))
    (instance ?Account JointAccount))		 FinancialOntology.kif 913-917 A financial account is an instance of personal account and the number of instances in the class described by ?Agent is greater than 1 if and only if financial account is an instance of joint account
(=>
    (and
        (instance ?VEHICLE CargoVehicle)
        (instance ?OB
            (KappaFn ?O
                (not
                    (instance ?O Human)))))
    (capability Transportation patient ?OB))		 Transportation.kif 1903-1910

consequent
-------------------------


(<=>
    (equal
        (BirthsPerThousandFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (and
        (equal
            (DivisionFn
                (PopulationFn ?AREA) 1000) ?THOUSANDS)
        (equal ?BIRTHCOUNT
            (CardinalityFn
                (KappaFn ?BIRTH
                    (and
                        (instance ?BIRTH Birth)
                        (experiencer ?BIRTH ?INFANT)
                        (instance ?INFANT Human)
                        (during
                            (WhenFn ?BIRTH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?BIRTH
                                (WhenFn ?BIRTH)) ?AREA)))))
        (equal
            (DivisionFn ?BIRTHCOUNT ?THOUSANDS) ?REALNUMBER)))		 People.kif 104-117 The births per thousand of a geopolitical area and the year an integer is equal to a real number if and only if the population of geopolitical area and 1000 is equal to a quantity and a number is equal to the number of instances in the class described by ?BIRTH and number and quantity is equal to real number
(<=>
    (equal
        (DeathsPerThousandFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (and
        (equal
            (DivisionFn
                (PopulationFn ?AREA) 1000) ?THOUSANDS)
        (equal ?DEATHCOUNT
            (CardinalityFn
                (KappaFn ?DEATH
                    (and
                        (instance ?DEATH Death)
                        (experiencer ?DEATH ?PERSON)
                        (instance ?PERSON Human)
                        (during
                            (WhenFn ?DEATH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?DEATH
                                (WhenFn ?DEATH)) ?AREA)))))
        (equal
            (DivisionFn ?DEATHCOUNT ?THOUSANDS) ?REALNUMBER)))		 People.kif 138-151 The deaths per thousand of a geopolitical area and the year an integer is equal to a real number if and only if the population of geopolitical area and 1000 is equal to a quantity and a number is equal to the number of instances in the class described by ?DEATH and number and quantity is equal to real number
(<=>
    (equal
        (DeathsPerThousandLiveBirthsFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (and
        (equal ?BIRTHCOUNT
            (CardinalityFn
                (KappaFn ?BIRTH
                    (and
                        (instance ?BIRTH Birth)
                        (experiencer ?BIRTH ?INFANT)
                        (instance ?INFANT Human)
                        (during
                            (WhenFn ?BIRTH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?BIRTH
                                (WhenFn ?BIRTH)) ?AREA)))))
        (equal
            (DivisionFn ?BIRTHCOUNT 1000) ?THOUSANDSOFBIRTHS)
        (equal ?INFANTDEATHCOUNT
            (CardinalityFn
                (KappaFn ?DEATH
                    (and
                        (instance ?DEATH Death)
                        (experiencer ?DEATH ?INFANT)
                        (experiencer ?BIRTH ?INFANT)
                        (instance ?INFANT Human)
                        (age ?INFANT
                            (MeasureFn ?AGE YearDuration))
                        (lessThan ?AGE 1)
                        (during
                            (WhenFn ?DEATH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?DEATH
                                (WhenFn ?DEATH)) ?AREA)))))
        (equal
            (DivisionFn ?INFANTDEATHCOUNT ?THOUSANDSOFBIRTHS) ?REALNUMBER)))		 People.kif 253-278 The deaths per thousand live births of a geopolitical area and the year an integer is equal to a real number if and only if a number is equal to the number of instances in the class described by ?BIRTH and number and 1000 is equal to a quantity and number is equal to the number of instances in the class described by ?DEATH and number and quantity is equal to real number
(<=>
    (equal
        (FemaleLifeExpectancyAtBirthFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (exists (?LIST)
        (and
            (instance ?LIST List)
            (instance
                (ListLengthFn ?LIST) ?COUNT)
            (forall (?LISTITEM)
                (=>
                    (inList ?LISTITEM ?LIST)
                    (and
                        (instance ?LISTITEM ?LIFEEXPECTANCYAGE)
                        (not
                            (exists (?NUMBER)
                                (and
                                    (instance ?NUMBER ?LIFEEXPECTANCYAGE)
                                    (not
                                        (inList ?NUMBER ?LIST)))))
                        (equal ?COUNT
                            (CardinalityFn
                                (KappaFn ?LIFEEXPECTANCYAGE
                                    (and
                                        (instance ?BIRTH Birth)
                                        (experiencer ?BIRTH ?INDIVIDUAL)
                                        (instance ?INDIVIDUAL Human)
                                        (attribute ?INDIVIDUAL Female)
                                        (during
                                            (WhenFn ?BIRTH)
                                            (YearFn ?YEAR))
                                        (equal
                                            (WhereFn ?BIRTH
                                                (WhenFn ?BIRTH)) ?AREA)
                                        (instance ?DEATH Death)
                                        (experiencer ?DEATH ?INDIVIDUAL)
                                        (holdsDuring
                                            (WhenFn ?DEATH)
                                            (age ?INDIVIDUAL
                                                (MeasureFn ?LIFEEXPECTANCYAGE YearDuration))))))))))
            (average ?LIST ?REALNUMBER))))		 People.kif 412-443 The female life expectancy at birth of a geopolitical area and the year an integer is equal to a real number if and only if there exists a list so that list is an instance of list and length of list is an instance of a set or class and for all listITEM and real number is an average of list
(<=>
    (equal
        (LifeExpectancyAtBirthFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (exists (?LIST)
        (and
            (instance ?LIST List)
            (instance
                (ListLengthFn ?LIST) ?COUNT)
            (forall (?LISTITEM)
                (=>
                    (inList ?LISTITEM ?LIST)
                    (and
                        (instance ?LISTITEM ?LIFEEXPECTANCYAGE)
                        (not
                            (exists (?NUMBER)
                                (and
                                    (instance ?NUMBER ?LIFEEXPECTANCYAGE)
                                    (not
                                        (inList ?NUMBER ?LIST)))))
                        (equal ?COUNT
                            (CardinalityFn
                                (KappaFn ?LIFEEXPECTANCYAGE
                                    (and
                                        (instance ?BIRTH Birth)
                                        (experiencer ?BIRTH ?INDIVIDUAL)
                                        (instance ?INDIVIDUAL Human)
                                        (during
                                            (WhenFn ?BIRTH)
                                            (YearFn ?YEAR))
                                        (equal
                                            (WhereFn ?BIRTH
                                                (WhenFn ?BIRTH)) ?AREA)
                                        (instance ?DEATH Death)
                                        (experiencer ?DEATH ?INDIVIDUAL)
                                        (holdsDuring
                                            (WhenFn ?DEATH)
                                            (age ?INDIVIDUAL
                                                (MeasureFn ?LIFEEXPECTANCYAGE YearDuration))))))))))
            (average ?LIST ?REALNUMBER))))		 People.kif 324-354 The life expectancy at birth of a geopolitical area and the year an integer is equal to a real number if and only if there exists a list so that list is an instance of list and length of list is an instance of a set or class and for all listITEM and real number is an average of list
(<=>
    (equal
        (MaleLifeExpectancyAtBirthFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (exists (?LIST)
        (and
            (instance ?LIST List)
            (instance
                (ListLengthFn ?LIST) ?COUNT)
            (forall (?LISTITEM)
                (=>
                    (inList ?LISTITEM ?LIST)
                    (and
                        (instance ?LISTITEM ?LIFEEXPECTANCYAGE)
                        (not
                            (exists (?NUMBER)
                                (and
                                    (instance ?NUMBER ?LIFEEXPECTANCYAGE)
                                    (not
                                        (inList ?NUMBER ?LIST)))))
                        (equal ?COUNT
                            (CardinalityFn
                                (KappaFn ?LIFEEXPECTANCYAGE
                                    (and
                                        (instance ?BIRTH Birth)
                                        (experiencer ?BIRTH ?INDIVIDUAL)
                                        (instance ?INDIVIDUAL Human)
                                        (attribute ?INDIVIDUAL Male)
                                        (during
                                            (WhenFn ?BIRTH)
                                            (YearFn ?YEAR))
                                        (equal
                                            (WhereFn ?BIRTH
                                                (WhenFn ?BIRTH)) ?AREA)
                                        (instance ?DEATH Death)
                                        (experiencer ?DEATH ?INDIVIDUAL)
                                        (holdsDuring
                                            (WhenFn ?DEATH)
                                            (age ?INDIVIDUAL
                                                (MeasureFn ?LIFEEXPECTANCYAGE YearDuration))))))))))
            (average ?LIST ?REALNUMBER))))		 People.kif 368-399 The male life expectancy at birth of a geopolitical area and the year an integer is equal to a real number if and only if there exists a list so that list is an instance of list and length of list is an instance of a set or class and for all listITEM and real number is an average of list
(<=>
    (equal
        (MaleToFemaleRatioFn ?AREA) ?REALNUMBER)
    (and
        (equal ?MALECOUNT
            (CardinalityFn
                (KappaFn ?MALE
                    (and
                        (instance ?MALE Human)
                        (attribute ?MALE Male)
                        (inhabits ?MALE ?AREA)))))
        (equal ?FEMALECOUNT
            (CardinalityFn
                (KappaFn ?FEMALE
                    (and
                        (instance ?FEMALE Human)
                        (attribute ?FEMALE Female)
                        (inhabits ?FEMALE ?AREA)))))
        (equal
            (DivisionFn ?MALECOUNT ?FEMALECOUNT) ?REALNUMBER)))		 People.kif 221-238 The male to female ratio of a geopolitical area is equal to a real number if and only if a number is equal to the number of instances in the class described by ?MALE and number is equal to the number of instances in the class described by ?FEMALE and number and number is equal to real number
(<=>
    (equal
        (MigrantsPerThousandFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (and
        (equal
            (SubtractionFn ?YEAR ?PREVIOUSYEAR) 1)
        (holdsDuring
            (YearFn ?YEAR)
            (equal
                (PopulationFn ?AREA) ?POPULATION))
        (equal
            (DivisionFn ?POPULATION 1000) ?THOUSANDS)
        (equal ?IMMIGRATION
            (CardinalityFn
                (KappaFn ?PERSON
                    (and
                        (instance ?PERSON Human)
                        (holdsDuring
                            (YearFn ?PREVIOUSYEAR)
                            (not
                                (inhabits ?PERSON ?AREA)))
                        (holdsDuring
                            (YearFn ?YEAR)
                            (inhabits ?PERSON ?AREA))))))
        (equal ?EMMIGRATION
            (CardinalityFn
                (KappaFn ?PERSON
                    (and
                        (instance ?PERSON Human)
                        (holdsDuring
                            (YearFn ?PREVIOUSYEAR)
                            (inhabits ?PERSON ?AREA))
                        (holdsDuring
                            (YearFn ?YEAR)
                            (not
                                (inhabits ?PERSON ?AREA)))))))
        (equal
            (SubtractionFn ?IMMIGRATION ?EMMIGRATION) ?MIGRATIONCOUNT)
        (equal
            (DivisionFn ?MIGRATIONCOUNT ?THOUSANDS) ?REALNUMBER)))		 People.kif 174-202 The migrants per thousand of a geopolitical area and the year an integer is equal to a real number if and only if ( integer and integer) is equal to 1 and the population of geopolitical area is equal to a integer holds during the year integer and integer and 1000 is equal to a quantity and a number is equal to the number of instances in the class described by ?PERSON and number is equal to the number of instances in the class described by ?PERSON and ( number and number) is equal to quantity and quantity and quantity is equal to real number
(<=>
    (lengthOfBroadGaugeRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS BroadGaugeRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 177-184 A length measure is a length of broad gauge railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfCrudeOilPipeline ?AREA ?LENGTH)
    (length
        (KappaFn ?PIPELINE
            (and
                (instance ?PIPELINE CrudeOilPipeline)
                (located ?PIPELINE ?AREA))) ?LENGTH))		 Transportation.kif 674-681 A length measure is a length of crude oil pipeline of a geographic area if and only if the length of the class described by ?PIPELINE is length measure
(<=>
    (lengthOfDualGaugeRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS DualGaugeRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 205-212 A length measure is a length of dual gauge railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfElectrifiedRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS ElectrifiedRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 123-130 A length measure is a length of electrified railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfExpresswaySystem ?AREA ?LENGTH)
    (length
        (KappaFn ?HIGHWAYS
            (and
                (instance ?HIGHWAYS Expressway)
                (located ?HIGHWAYS ?AREA))) ?LENGTH))		 Transportation.kif 524-530 A length measure is a length of expressway system of a geographic area if and only if the length of the class described by ?HIGHWAYS is length measure
(<=>
    (lengthOfMultipleTrackRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS MultipleTrackRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 150-157 A length measure is a length of multiple track railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfNarrowGaugeRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS NarrowGaugeRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 233-240 A length measure is a length of narrow gauge railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfNaturalGasPipeline ?AREA ?LENGTH)
    (length
        (KappaFn ?PIPELINE
            (and
                (instance ?PIPELINE NaturalGasPipeline)
                (located ?PIPELINE ?AREA))) ?LENGTH))		 Transportation.kif 698-705 A length measure is a length of natural gas pipeline of a geographic area if and only if the length of the class described by ?PIPELINE is length measure
(<=>
    (lengthOfPavedHighway ?AREA ?LENGTH)
    (length
        (KappaFn ?HIGHWAYS
            (and
                (instance ?HIGHWAYS SurfacedRoadway)
                (located ?HIGHWAYS ?AREA))) ?LENGTH))		 Transportation.kif 498-504 A length measure is a length of paved highway of a geographic area if and only if the length of the class described by ?HIGHWAYS is length measure
(<=>
    (lengthOfPetroleumProductPipeline ?AREA ?LENGTH)
    (length
        (KappaFn ?PIPELINE
            (and
                (instance ?PIPELINE PetroleumProductPipeline)
                (located ?PIPELINE ?AREA))) ?LENGTH))		 Transportation.kif 722-729 A length measure is a length of petroleum product pipeline of a geographic area if and only if the length of the class described by ?PIPELINE is length measure
(<=>
    (lengthOfStandardGaugeRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS StandardGaugeRailway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 261-268 A length measure is a length of standard gauge railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfUnclassifiedGaugeRailway ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (located ?RAILWAYS ?AREA)
                (not
                    (instance ?RAILWAYS
                        (UnionFn StandardGaugeRailway
                            (UnionFn BroadGaugeRailway
                                (UnionFn DualGaugeRailway NarrowGaugeRailway))))))) ?LENGTH))		 Transportation.kif 290-302 A length measure is a length of unclassified gauge railway of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure
(<=>
    (lengthOfUnpavedHighway ?AREA ?LENGTH)
    (length
        (KappaFn ?HIGHWAYS
            (and
                (instance ?HIGHWAYS UnsurfacedRoadway)
                (located ?HIGHWAYS ?AREA))) ?LENGTH))		 Transportation.kif 556-562 A length measure is a length of unpaved highway of a geographic area if and only if the length of the class described by ?HIGHWAYS is length measure
(<=>
    (totalFacilityTypeInArea ?AREA
        (ExtensionFn AirportWithPavedRunway) ?COUNT)
    (cardinality
        (KappaFn ?AIRPORT
            (exists (?RUNWAY)
                (and
                    (instance ?AIRPORT Airport)
                    (instance ?RUNWAY PavedRunway)
                    (part ?RUNWAY ?AIRPORT)
                    (located ?AIRPORT ?AREA)))) ?COUNT))		 Transportation.kif 1416-1427 A geographic area total facility type in area the class corresponding to airport with paved runway for a nonnegative integer if and only if nonnegative integer is a cardinality of the class described by ?AIRPORT
(<=>
    (totalFacilityTypeInArea ?AREA ?TYPE ?COUNT)
    (cardinality
        (KappaFn ?ITEM
            (and
                (instance ?ITEM ?TYPE)
                (located ?ITEM ?AREA))) ?COUNT))		 Transportation.kif 1358-1365 A geographic area total facility type in area a class for a nonnegative integer if and only if nonnegative integer is a cardinality of the class described by ?ITEM
(<=>
    (totalLengthOfHighwaySystem ?AREA ?LENGTH)
    (length
        (KappaFn ?HIGHWAYS
            (and
                (instance ?HIGHWAYS Roadway)
                (located ?HIGHWAYS ?AREA))) ?LENGTH))		 Transportation.kif 444-450 A length measure is a total length of highway system of a geographic area if and only if the length of the class described by ?HIGHWAYS is length measure
(<=>
    (totalLengthOfRailwaySystem ?AREA ?LENGTH)
    (length
        (KappaFn ?RAILWAYS
            (and
                (instance ?RAILWAYS Railway)
                (located ?RAILWAYS ?AREA))) ?LENGTH))		 Transportation.kif 96-103 A length measure is a total length of railway system of a geographic area if and only if the length of the class described by ?RAILWAYS is length measure

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statement
-------------------------


(equal
    (AvailableForMilitaryServiceMaleFn ?AREA)
    (CardinalityFn
        (KappaFn ?PERSON
            (and
                (instance ?PERSON Human)
                (attribute ?PERSON Male)
                (militaryAge ?AREA ?MILITARYAGE)
                (age ?PERSON ?AGE)
                (greaterThanOrEqualTo ?AGE ?MILITARYAGE)
                (inhabits ?PERSON ?AREA)))))		 Military.kif 820-829 The available for military service male of a geopolitical area is equal to the number of instances in the class described by ?PERSON
(equal
    (ChildrenBornPerWomanFn ?AREA
        (YearFn ?YEAR))
    (CardinalityFn
        (KappaFn ?INFANT
            (and
                (instance ?BIRTH Birth)
                (experiencer ?BIRTH ?INFANT)
                (agent ?BIRTH ?WOMAN)
                (instance ?WOMAN Human)
                (attribute ?WOMAN Female)
                (holdsDuring
                    (YearFn ?YEAR)
                    (inhabits ?WOMAN ?AREA))))))		 People.kif 463-473 The children born per woman of a geopolitical area and the year an integer is equal to the number of instances in the class described by ?INFANT
(equal
    (FitForMilitaryServiceMaleFn ?AREA)
    (CardinalityFn
        (KappaFn ?PERSON
            (and
                (instance ?PERSON Human)
                (attribute ?PERSON Male)
                (instance ?PROCESS MilitaryProcess)
                (fitForMilitaryService ?PERSON ?PROCESS)
                (militaryAge ?AREA ?MILITARYAGE)
                (age ?PERSON ?AGE)
                (greaterThanOrEqualTo ?AGE ?MILITARYAGE)
                (inhabits ?PERSON ?AREA)))))		 Military.kif 843-854 The fit for military service male of a geopolitical area is equal to the number of instances in the class described by ?PERSON
(equal
    (PopulationFn ?AREA)
    (CardinalityFn
        (KappaFn ?PERSON
            (and
                (instance ?PERSON Human)
                (inhabits ?PERSON ?AREA)))))		 People.kif 49-54 The population of a geopolitical area is equal to the number of instances in the class described by ?PERSON
(equal
    (ReachingMilitaryAgeAnnuallyMaleFn ?AREA ?YEAR)
    (CardinalityFn
        (KappaFn ?PERSON
            (and
                (instance ?PERSON Human)
                (attribute ?PERSON Male)
                (militaryAge ?AREA ?MILITARYAGE)
                (equal ?AGEMINUSONE
                    (SubtractionFn ?AGE 1))
                (holdsDuring ?YEAR
                    (or
                        (age ?PERSON ?AGEMINUSONE)
                        (age ?PERSON ?AGE)))
                (equal ?AGE ?MILITARYAGE)
                (inhabits ?PERSON ?AREA)))))		 Military.kif 881-894 The reaching military age annually male of a geopolitical area and a year is equal to the number of instances in the class described by ?PERSON


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