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Relationships
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inheritable relation |
The class of Relations whose properties can be inherited downward in the class hierarchy via the subrelation Predicate.
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relation |
The Class of relations. There are two kinds of Relation: Predicate and Function. Predicates and Functions both denote sets of ordered n-tuples. The difference between these two Classes is that Predicates cover formula-forming operators, while Functions cover term-forming operators.
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partial ordering relation | A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation. |
| | unit of measure multiplier | Each instance of this Class is a UnaryFunction that, when evaluated on its single argument, a UnitOfMeasure, produces another UnitOfMeasure that is a numeric multiple of the argument. |
| Instances | absolute value | The value of (AbsoluteValueFn ?NUMBER) is the absolute value of the RealNumber ?NUMBER. |
| | Acceleration fn | Specifies the acceleration of an object, i.e. the change in speed for a given direction. |
| | addition | If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers. |
| | ancestor | The transitive closure of the parent predicate. (ancestor ?DESCENDANT ?ANCESTOR) means that ?ANCESTOR is either the parent of ?DESCENDANT or the parent of the parent of DESCENDANT or etc. |
| | angular measure | (angularMeasure ?ANGLE ?MEASURE) means that the two-dimensional geometric angle ?ANGLE has ?MEASURE. |
| | approximate diameter | The diameter of an object if it were a perfect sphere of the same volume |
| | arccosine | The inverse of CosineFn. |
| | arcsine | The inverse of SineFn. |
| | arctangent | The inverse of TangentFn. |
| | attribute | (attribute ?OBJECT ?PROPERTY) means that ?PROPERTY is a Attribute of ?OBJECT. For example, (attribute MyLittleRedWagon Red). |
| | begin | A UnaryFunction that maps a TimeInterval to the TimePoint at which the interval begins. |
| | begin node | A UnaryFunction that maps a GraphPath to the GraphNode that is the beginning of the GraphPath. Note that, unlike InitialNodeFn (which relates a GraphArc to a GraphNode), BeginNodeFn is a total function - every GraphPath has a beginning. |
| | ceiling | (CeilingFn ?NUMBER) returns the smallest Integer greater than or equal to the RealNumber ?NUMBER. |
| | center of circle | (CenterOfCircleFn ?CIRCLE) denotes the GeometricPoint that is the center of the Circle ?CIRCLE. |
| | changes location | (changesLocation ?EVENT ?OBJECT) means that during the Translocation event ?EVENT, ?OBJECT's location changes. ?OBJECT might also be the agent, patient, or experiencer of ?EVENT. |
| | complement | The complement of a given SetOrClass C is the SetOrClass of all things that are not instances of C. In other words, an object is an instance of the complement of a SetOrClass C just in case it is not an instance of C. |
| | conclusion | (conclusion ?ARGUMENT ?PROPOSITION) means that the Proposition ?PROPOSITION is the conclusion explicitly drawn from the Argument ?ARGUMENT. Note that it may or may not be the case that ?ARGUMENT entails ?PROPOSITION. |
| | contest participant | (contestParticipant ?CONTEST ?AGENT) means that ?AGENT is one of the sides in the Contest ?CONTEST. For example, if the ?CONTEST is a football game, then ?AGENT would be one of the opposing teams. For another example, if ?CONTEST is a Battle, then ?AGENT would be one of the sides fighting each other. |
| | cosine | (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. |
| | denominator | (DenominatorFn ?NUMBER) returns the denominator of the canonical reduced form of the RealNumber ?NUMBER. |
| | density | DensityFn maps an instance of MassMeasure and an instance of VolumeMeasure to the density represented by this proportion of mass and volume. For example, (DensityFn (MeasureFn 3 Gram) (MeasureFn 1 Liter)) represents the density of 3 grams per liter. |
| | diameter | (DiameterFn ?CIRCLE) denotes the length of the diameter of the Circle ?CIRCLE. |
| | diameter | (diameter ?CIRCLE ?LENGTH) means that the diameter of the Circle ?CIRCLE has a length of ?LENGTH. |
| | distance | (distance ?OBJ1 ?OBJ2 ?QUANT) means that the shortest distance between the two objects ?OBJ1 and ?OBJ2 is ?QUANT. Note that the difference between the predicates length and distance is that the length is used to state the LengthMeasure of one of the dimensions of a single object, while distance is used to state the LengthMeasure that separates two distinct objects. |
| | duration | (duration ?POS ?TIME) means that the duration of the TimeInterval ?POS is ?TIME. Note that this Predicate can be used in conjunction with the Function WhenFn to specify the duration of any instance of Physical. |
| | earlier | (earlier ?INTERVAL1 ?INTERVAL2) means that the TimeInterval ?INTERVAL1 ends before the TimeInterval ?INTERVAL2 begins. |
| | electron number | (electronNumber ?SUBSTANCE ?NUMBER) means that the PureSubstance ?SUBSTANCE has the number of Electrons ?NUMBER. |
| | end | A UnaryFunction that maps a TimeInterval to the TimePoint at which the interval ends. |
| | end node | A UnaryFunction that maps a GraphPath to the GraphNode that is the end of the GraphPath. Note that, unlike TerminalNodeFn (which relates a GraphArc to a GraphNode), EndNodeFn is a total function - every GraphPath has a end. |
| | event located | (eventLocated ?PROC ?OBJ) means that the entire Process ?PROC is located on Object ?OBJ, meaning that all subProcess of ?PROC is located on ?OBJ. |
| | exponentiation | (ExponentiationFn ?NUMBER ?INT) returns the RealNumber ?NUMBER raised to the power of the Integer ?INT. |
| | finishes | (finishes ?INTERVAL1 ?INTERVAL2) means that ?INTERVAL1 and ?INTERVAL2 are both TimeIntervals that have the same ending TimePoint and that ?INTERVAL2 begins before ?INTERVAL1. |
| | floor | (FloorFn ?NUMBER) returns the largest Integer less than or equal to the RealNumber ?NUMBER. |
| | future | A UnaryFunction that maps a TimePosition to the TimeInterval which it meets and which ends at PositiveInfinity. |
| | generalized intersection | A UnaryFunction that takes a SetOrClass of Classes as its single argument and returns a SetOrClass which is the intersection of all of the Classes in the original SetOrClass, i.e. the SetOrClass containing just those instances which are instances of all instances of the original SetOrClass. |
| | generalized union | A UnaryFunction that takes a SetOrClass of Classes as its single argument and returns a SetOrClass which is the merge of all of the Classes in the original SetOrClass, i.e. the SetOrClass containing just those instances which are instances of an instance of the original SetOrClass. |
| | geometric distance | (geometricDistance ?POINT1 ?POINT2 ?LENGTH) means that ?LENGTH is the distance between the two GeometricPoints ?POINT1 and ?POINT2. |
| | graph part | A basic relation for Graphs and their parts. (graphPart ?PART ?GRAPH) means that ?PART is a GraphArc or GraphNode of the Graph ?GRAPH. |
| | graph path | A BinaryFunction that maps two GraphNodes to the Class of GraphPaths between those two nodes. Note that the two GraphNodes must belong to the same Graph. |
| | greater than | (greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2. |
| | imaginary part | (ImaginaryPartFn ?NUMBER) returns the part of ?NUMBER that has the square root of -1 as its factor. |
| | immediate family | (ImmediateFamilyFn ?PERSON) denotes the immediate family of ?PERSON, i.e. the Group consisting of the parents of ?PERSON and anyone of whom ?PERSON is a parent. |
| | immediate future | A UnaryFunction that maps a TimePosition to a short, indeterminate TimeInterval that immediately follows the TimePosition. |
| | immediate past | A UnaryFunction that maps a TimePosition to a short, indeterminate TimeInterval that immediately precedes the TimePosition. |
| | intersection | A BinaryFunction that maps two SetOrClasses to the intersection of these SetOrClasses. An object is an instance of the intersection of two SetOrClasses just in case it is an instance of both of those SetOrClasses. |
| | interval | A BinaryFunction that maps two instances of ConstantQuantity to the subclass of ConstantQuantity that comprises the interval from the first ConstantQuantity to the second ConstantQuantity. For example, (IntervalFn (MeasureFn 8 Meter) (MeasureFn 14 Meter)) would return the subclass of ConstantQuantity comprising quantities between 8 and 14 meters in length. |
| | larger | (larger ?OBJ1 ?OBJ2) means that ?OBJ1 is larger, with respect to all LengthMeasures, than ?OBJ2. |
| | line measure | (lineMeasure ?LINE ?MEASURE) means that the straight line ?LINE has the LengthMeasure of ?MEASURE. |
| | list concatenate | A Function that returns the concatenation of the two Lists that are given as arguments. For example, the value of (ListConcatenateFn (ListFn Monday Tuesday) (ListFn Wednesday Thursday)) would be (ListFn Monday Tuesday Wednesday Thursday). |
| | list length | A Function that takes a List as its sole argument and returns the number of items in the List. For example, (ListLengthFn (ListFn Monday Tuesday Wednesday)) would return the value 3. |
| | located | (located ?OBJ1 ?OBJ2) means that ?OBJ1 is partlyLocated at ?OBJ2, and there is no part of ?OBJ1 that is not located at ?OBJ2. |
| | manner | (manner ?PROCESS ?MANNER) means that the Process ?PROCESS is qualified by the Attribute ?MANNER. The Attributes of Processes are usually denoted by adverbs and include things like the speed of the wind, the style of a dance, or the intensity of a sports competition. |
| | max | (MaxFn ?NUMBER1 ?NUMBER2) is the largest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MaxFn returns one of its arguments. |
| | maximal weighted path | This BinaryFunction assigns two GraphNodes to the GraphPath with the largest sum of weighted arcs between the two GraphNodes. |
| | maximum payload capacity | (maximumPayloadCapacity ?V ?MM) means that the Vehicle ?V has a maximum payload of ?MM. This means that the vehicle can transport Objects weighing less than ?MM, provided that their height and width are within the limits of maximumPayloadHeightWidth. |
| | maximum payload height width | (maximumHeightWidth ?V ?LMHEIGHT ?LMWIDTH) means that the Vehicle ?V can transport Objects with a height less then or equal to ?LMHEIGHT and width less than or equal to ?LMWIDTH, provided that the weight of these Objects is less than or equal to maximumPayloadCapacity. |
| | measure | This BinaryFunction maps a RealNumber and a UnitOfMeasure to that Number of units. It is used to express `measured' instances of PhysicalQuantity. Example: the concept of three meters is represented as (MeasureFn 3 Meter). |
| | meets temporally | (meetsTemporally ?INTERVAL1 ?INTERVAL2) means that the terminal point of the TimeInterval ?INTERVAL1 is the initial point of the TimeInterval ?INTERVAL2. |
| | mereological difference | (MereologicalDifferenceFn ?OBJ1 ?OBJ2) denotes the Object consisting of the parts which belong to ?OBJ1 and not to ?OBJ2. |
| | mereological product | (MereologicalProductFn ?OBJ1 ?OBJ2) denotes the Object consisting of the parts which belong to both ?OBJ1 and ?OBJ2. |
| | mereological sum | (MereologicalSumFn ?OBJ1 ?OBJ2) denotes the Object consisting of the parts which belong to either ?OBJ1 or ?OBJ2. |
| | min | (MinFn ?NUMBER1 ?NUMBER2) is the smallest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MinFn returns one of its arguments. |
| | minimal weighted path | This BinaryFunction assigns two GraphNodes to the GraphPath with the smallest sum of weighted arcs between the two GraphNodes. |
| | moves | (moves ?MOTION ?OBJECT) means that during the Motion event ?MOTION, ?OBJECT moves. This does not necessarily imply that the location of ?OBJECT changes during ?MOTION. See also changesLocation and Translocation. |
| | multiplication | If ?NUMBER1 and ?NUMBER2 are Numbers, then (MultiplicationFn ?NUMBER1 ?NUMBER2) is the arithmetical product of these numbers. |
| | numerator | (NumeratorFn ?NUMBER) returns the numerator of the canonical reduced form ?NUMBER. |
| | parent | The general relationship of parenthood. (parent ?CHILD ?PARENT) means that ?PARENT is a biological parent of ?CHILD. |
| | partly located | (partlyLocated ?OBJ1 ?OBJ2) means that the instance of Physical ?OBJ1 is at least partially located at ?OBJ2. For example, Istanbul is partly located in Asia and partly located in Europe. Note that partlyLocated is the most basic localization relation: located is an immediate subrelation of partlyLocated and exactlyLocated is an immediate subrelation of located. |
| | past | A UnaryFunction that maps a TimePosition to the TimeInterval that meets it and that begins at NegativeInfinity. |
| | path | (path ?MOTION ?PATH) means that ?PATH is a route along which ?MOTION occurs. For example, Highway 101 is the path in the following proposition: the car drove up Highway 101. |
| | per | PerFn maps two instances of PhysicalQuantity to the FunctionQuantity composed of these two instances. For example, (PerFn (MeasureFn 2 (MicroFn Gram)) (MeasureFn 1 (KiloFn Gram))) denotes the FunctionQuantity of 2 micrograms per kiogram. This function is useful, because it allows the knowledge engineer to dynamically generate instances of FunctionQuantity. |
| | person transport capability | (personTransportCapability ?PV ?I) means that the PassengerVehicle ?PV is able to carry ?I Humans. |
| | power set | (PowerSetFn ?CLASS) maps the SetOrClass ?CLASS to the SetOrClass of all subclasses of ?CLASS. |
| | predecessor | A UnaryFunction that maps an Integer to its predecessor, e.g. the predecessor of 5 is 4. |
| | premise | (premise ?ARGUMENT ?PROPOSITION) means that the Proposition ?PROPOSITION is an explicit assumption of the Argument ?ARGUMENT. |
| | premises | (PremisesFn ?ARGUMENT) returns the complete set of premises of the Argument ?ARGUMENT. |
| | probability | One of the basic ProbabilityRelations, ProbabilityFn is used to state the a priori probability of a state of affairs. (ProbabilityFn ?FORMULA) denotes the a priori probability of ?FORMULA. |
| | property | A UnaryFunction that maps an AutonomousAgent to the Set of Objects owned by the AutonomousAgent. |
| | proton number | (protonNumber ?SUBSTANCE ?NUMBER) means that the PureSubstance ?SUBSTANCE has the number of Protons ?NUMBER. |
| | radius | (radius ?CIRCLE ?LENGTH) means that the radius of the Circle ?CIRCLE has a length of ?LENGTH. |
| | radius | (RadiusFn ?CIRCLE) denotes the length of the radius of the Circle ?CIRCLE. |
| | relative angle | (relativeAngle ?O1 ?O2 ?MEASURE) means that the two-dimensional geometric angle formed by ?O1 and ?O2 has ?MEASURE. |
| | relative complement | A BinaryFunction that maps two SetOrClasses to the difference between these SetOrClasses. More precisely, (RelativeComplementFn ?CLASS1 ?CLASS2) denotes the instances of ?CLASS1 that are not also instances of ?CLASS2. |
| | relative time | A means of converting TimePositions between different TimeZones. (RelativeTimeFn ?TIME ?ZONE) denotes the TimePosition in CoordinatedUniversalTime that is contemporaneous with the TimePosition ?TIME in TimeZone ?ZONE. For example, (RelativeTimeFn (MeasureFn 14 HourDuration) EasternTimeZone) would return the value (MeasureFn 19 HourDuration). |
| | round | (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. |
| | signum | (SignumFn ?NUMBER) denotes the sign of ?NUMBER. This is one of the following values: -1, 1, or 0. |
| | sine | (SineFn ?DEGREE) is the sine of ?DEGREE. The sine of ?DEGREE is the ratio of the side opposite ?DEGREE to the hypotenuse in a right-angled triangle. |
| | smaller | (smaller ?OBJ1 ?OBJ2) means that ?OBJ1 is smaller, with respect to all LengthMeasures, than ?OBJ2. |
| | speed | Maps an instance of LengthMeasure and an instance of TimeDuration to the speed represented by this proportion of distance and time. For example, (SpeedFn (MeasureFn 55 Mile)(MeasureFn 1 HourDuration)) represents the velocity of 55 miles per hour. |
| | starts | (starts ?INTERVAL1 ?INTERVAL2) means that ?INTERVAL1 and ?INTERVAL2 are both TimeIntervals that have the same initial TimePoint and that ?INTERVAL1 ends before ?INTERVAL2. |
| | string concatenate fn | The result of applying this Function to two SymbolicString arguments is a third SymbolicString that is the concatenation of the two arguments. Example: (equal "Charles Darwin" (StringConcatenateFn "Charles " "Darwin")). |
| | string concatenation | (stringConcatenation ?SymbolicString-1 ?SymbolicString-2 ?SymbolicString-3) means that ?SymbolicString-3 can be formed by appending ?SymbolicString-1 and ?SymbolicString-2, in order. Example: (stringConcatenation "Charles " "Darwin" "Charles Darwin") is a True Sentence. |
| | string length | (stringLength ?NonnegativeInteger ?SymbolicString) means that the number of Characters in ?SymbolicString is ?NonnegativeInteger. Example: (stringLength 14 "Charles Darwin"), which is a True Sentence. |
| | string length fn | This UnaryFunction takes a SymbolicString as its sole argument. The result of evaluating a term formed with StringLengthFn is a NonnegativeInteger that denotes the number of Characters in the SymbolicString. Example: (equal 14 (StringLengthFn "Charles Darwin")). |
| | sub string | (subString ?SymbolicString-1 ?SymbolicString-2) means that ?SymbolicString-1 is part of ?SymbolicString-2. ?SymbolicString-2 includes all the same Characters as ?SymbolicString-1 and in the same order, but ?SymbolicString-2 may include more Characters than ?SymbolicString-1. See also inString. |
| | subtraction | If ?NUMBER1 and ?NUMBER2 are Numbers, then (SubtractionFn ?NUMBER1 ?NUMBER2) is the arithmetical difference between ?NUMBER1 and ?NUMBER2, i.e. ?NUMBER1 minus ?NUMBER2. An exception occurs when ?NUMBER1 is equal to 0, in which case (SubtractionFn ?NUMBER1 ?NUMBER2) is the negation of ?NUMBER2. |
| | successor | A UnaryFunction that maps an Integer to its successor, e.g. the successor of 5 is 6. |
| | tangent | (TangentFn ?DEGREE) is the tangent of ?DEGREE. The tangent of ?DEGREE is the ratio of the side opposite ?DEGREE to the side next to ?DEGREE in a right-angled triangle. |
| | temporal composition | The basic Function for expressing the composition of larger TimeIntervals out of smaller TimeIntervals. For example, if ThisSeptember is an instance of September, (TemporalCompositionFn ThisSeptember Day) denotes the Class of consecutive days that make up ThisSeptember. Note that one can obtain the number of instances of this Class by using the function CardinalityFn. |
| | time | This relation holds between an instance of Physical and an instance of TimePosition just in case the temporal lifespan of the former includes the latter. In other words, (time ?THING ?TIME) means that ?THING existed or occurred at ?TIME. Note that time does for instances of time what holdsDuring does for instances of Formula. The constants located and time are the basic spatial and temporal predicates, respectively. |
| | transaction amount | (transactionAmount ?TRANSACTION ?AMOUNT) means that ?AMOUNT is an instance of CurrencyMeasure being exhanged in the FinancialTransaction ?TRANSACTION. |
| | union | A BinaryFunction that maps two SetOrClasses to the union of these SetOrClasses. An object is an element of the union of two SetOrClasses just in case it is an instance of either SetOrClass. |
| | unit fn | UnitFn returns just the UnitOfMeasure of a PhysicalQuantity with an associated UnitOfMeasure and RealNumber magnitude. For example, the unit of the ConstantQuantity (MeasureFn 2 Kilometer) is the UnitOfMeasure Kilometer. |
| | velocity | Specifies the velocity of an object, i.e. the speed and the direction of the speed. For example (VelocityFn (MeasureFn 55 Mile) (MeasureFn 2 HourDuration) ?REFERENCE North) denotes the velocity of 55 miles per hour North of the given reference point ?REFERENCE. |
| | wealth | A UnaryFunction that maps an AutonomousAgent to a CurrencyMeasure specifying the value of the property owned by the AutonomousAgent. 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. |
| | weapon carrying capability | (weaponCarryingCapability ?MV ?WC ?I) means that the MilitaryVehicle ?MV is able to carry ?I Weapons of class ?WC. |
| | when | 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), (time ?THING ?TIME) does not hold. |
| | where | Maps an Object and a TimePoint at which the Object exists to the Region where the Object existed at that TimePoint. |
| | year | A UnaryFunction that maps a number to the corresponding calendar Year. For example, (YearFn 1912) returns the Class containing just one instance, the year of 1912. As might be expected, positive integers return years in the Common Era, while negative integers return years in B.C.E. Note that this function returns a Class as a value. The reason for this is that the related functions, viz. MonthFn, DayFn, HourFn, MinuteFn, and SecondFn, are used to generate both specific TimeIntervals and recurrent intervals, and the only way to do this is to make the domains and ranges of these functions classes rather than individuals. |
| | 互相 | (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. |