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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > PartialOrderingRelation
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PartialOrderingRelation comparison table
Subject have domain2 have domain1 be first domain of be second domain of documentation have inverse have axiom is a kind of is an instance of have relatedInternalConcept
beforeEqTimePointTimePointsingleValuedinverse(beforeEq ?POINT1 ?POINT2) means that ?POINT1 is identical with ?POINT2 or occurs before it on the universal timeline 
(=>
(instance ?REL BinaryPredicate)
(valence ?REL 2))
 PartialOrderingRelation 
greaterThanOrEqualToQuantityQuantityvalencesubrelation(greaterThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2lessThanOrEqualTo
(=>
(instance ?NUMBER NonnegativeRealNumber)
(greaterThanOrEqualTo ?NUMBER 0))
 RelationExtendedToQuantities 
lessThanOrEqualToQuantityQuantityvalencesubrelation(lessThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than or equal to the Quantity ?NUMBER2 
(=>
(instance (MonthFn ?NUMBER ?YEAR) Month)
(lessThanOrEqualTo ?NUMBER 12))
 RelationExtendedToQuantities 
locatedObjectPhysicaltrichotomizingOninverseA very general predicate. (located ?PHYS ?OBJ) means that ?PHYS is situated at ?OBJ, in some sense. The Predicates located and existant are spatial and temporal predicates, respectively 
(=>
(and
(instance ?VIRUS Virus)
(instance ?PROC Replication)
(effector ?PROC ?VIRUS))
(exists (?CELL)
(and
(located ?PROC ?CELL)
(instance ?CELL Cell))))
 PartialOrderingRelationexistant
overlapsTemporallyTimeIntervalTimeIntervalvalencesubrelation(overlapsTemporally ?INTERVAL1 ?INTERVAL2) means that the two TimeIntervals ?INTERVAL1 and ?INTERVAL2 have a TimeInterval in common. Note that this is consistent with ?INTERVAL1 and ?INTERVAL2 being the same TimeInterval 
(=>
(and
(time ?PHYS ?TIME1)
(time ?PHYS ?TIME2))
(or
(overlapsTemporally ?TIME1 ?TIME2)
(temporalPart ?TIME1 ?TIME2)
(temporalPart ?TIME2 ?TIME1)))
 TemporalRelation 
partSelfConnectedObjectSelfConnectedObjectvalencesubrelationThe basic mereological relation. All other mereological relations are defined in terms of this one. (part ?PART ?WHOLE) simply means that the Object ?PART is part of the Object ?WHOLE. Note that, since part is a ReflexiveRelation, every Object is a part of itself 
(=>
(overlapsPartially ?OBJ1 ?OBJ2)
(and
(not
(part ?OBJ1 ?OBJ2))
(not
(part ?OBJ2 ?OBJ1))))
 SpatialRelation 
subAttributeAttributeAttributesingleValuedinverseMeans that the second argument can be ascribed to everything which has the first argument ascribed to it 
(<=>
(subAttribute ?ATTR1 ?ATTR2)
(forall (?OBJ)
(=>
(attribute ?OBJ ?ATTR1)
(attribute ?OBJ ?ATTR2))))
 PartialOrderingRelation 
subclassClassClasssingleValuedinverseClass C is a subclass of Class P only if every instance of C is also an instance of P. A class may have multiple superclasses and subclasses 
(=>
(instance ?OBJ CorpuscularObject)
(exists (?SUBSTANCETYPE1 ?SUBSTANCETYPE2 ?SUBSTANCE1 ?SUBSTANCE2)
(and
(subclass ?SUBSTANCETYPE1 Substance)
(subclass ?SUBSTANCETYPE2 Substance)
(instance ?SUBSTANCE1 ?SUBSTANCETYPE1)
(instance ?SUBSTANCE2 ?SUBSTANCETYPE2)
(material ?SUBSTANCE1 ?OBJ)
(material ?SUBSTANCE2 ?OBJ)
(not (equal ?SUBSTANCE1 ?SUBSTANCE2)))))
 PartialOrderingRelation 
subProcessProcessProcesssingleValuedinverse(subProcess ?SUBPROC ?PROC) means that ?SUBPROC is a subprocess of ?PROC. A subprocess is here understood as a temporally distinguished part (proper or not) of a Process 
(=>
(subProcess ?SUBPROC ?PROC)
(forall (?REGION)
(=>
(located ?PROC ?REGION)
(located ?SUBPROC ?REGION))))
 PartialOrderingRelation 
subrelationRelationRelationsingleValuedinverseA Relation R is a subrelation Relation R' if R is a subclass R'. This implies that every tuple of R is also a tuple of R'. Again, if R holds for some arguments arg_1, arg_2, ... arg_n, then R' holds for the same arguments. Thus, a Relation and its subrelation must have the same valence. In CycL, subrelation is called #$genlPreds 
(=>
(subrelation ?PRED1 ?PRED2)
(exists (?NUMBER)
(and
(valence ?PRED1 ?NUMBER)
(valence ?PRED2 ?NUMBER))))
 PartialOrderingRelation 
subsumesContentClassContentBearingObjectContentBearingObjectsingleValuedinverseA BinaryPredicate that relates two subclasses of ContentBearingObject. (subsumesContentClass ?CLASS1 ?CLASS2) means that the content expressed by each instance of ?CLASS1 is also expressed by each instance of ?CLASS2. Examples include the relationship between a poem and one of its stanzas or between a book and one of its chapters. Note that this is a relation between subclasses of ContentBearingObject, rather than instances. If one wants to relate instances, the Predicate subsumesContentInstance can be used. Note that subsumesContentClass is needed in many cases. Consider, for example, the relation between the King James edition of the Bible and its Book of Genesis. This relation holds for every copy of this edition and not just for a single instance 
(<=>
(subsumesContentClass ?CLASS1 ?CLASS2)
(forall (?INFO ?OBJ1 ?OBJ2)
(=>
(and
(instance ?OBJ1 ?CLASS1)
(instance ?OBJ2 ?CLASS2)
(containsInformation ?OBJ1 ?INFO))
(containsInformation ?OBJ2 ?INFO))))
 PartialOrderingRelation 
subsumesContentInstanceContentBearingObjectContentBearingObjectsingleValuedinverseA BinaryPredicate relating two instances of ContentBearingObject. (subsumesContentInstance ?OBJ1 ?OBJ2) means that the content expressed by ?OBJ2 is part of the content expressed by ?OBJ1. An example is the relationship between a handwritten poem and one of its stanzas. Note that this is a relation between instances, rather than Classes. If one wants to assert a content relationship between Classes, e.g. between the version of an intellectual work and a part of that work, the relation subsumesContentClass should be used 
(=>
(subPlan ?PLAN1 ?PLAN2)
(forall (?OBJ1 ?OBJ2)
(=>
(and
(containsInformation ?OBJ1 ?PLAN1)
(containsInformation ?OBJ2 ?PLAN2))
(subsumesContentInstance ?OBJ2 ?OBJ1))))
 PartialOrderingRelationsubsumesContentClass
TotalOrderingRelation  trichotomizingOninverse"A BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation 
(=>
(instance ?REL TotalOrderingRelation)
(forall (?INST1 ?INST2)
(or
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST1))))
TrichotomizingRelation  

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