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Relationships
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AntisymmetricRelation |
BinaryRelation ?REL is an AntisymmetricRelation if for distinct ?INST1 and ?INST2, (?REL ?INST1 ?INST2) implies not (?REL ?INST2 ?INST1). In other words, for all ?INST1 and ?INST2, (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST1) imply that ?INST1 and ?INST2 are identical. Note that it is possible for an AntisymmetricRelation to be a ReflexiveRelation.
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ReflexiveRelation |
Relation ?REL is reflexive iff (?REL ?INST ?INST) for all ?INST.
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TotalValuedRelation |
A Relation is a TotalValuedRelation just in case there exists an assignment for the last argument position of the Relation given any assignment of values to every argument position except the last one. Note that declaring a Relation to be both a TotalValuedRelation and a SingleValuedRelation means that it is a total function.
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TransitiveRelation |
A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
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TotalOrderingRelation | A BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation. |
| Instances | beforeOrEqual | (beforeOrEqual ?POINT1 ?POINT2) means that ?POINT1 is identical with ?POINT2 or occurs before it on the universal timeline. |
| | coordinates | (coordinates ?PROCESS1 ?PROCESS2) means that ?PROCESS1 coordinates ?PROCESS2 |
| | geometricPart | (geometricPart ?PART ?WHOLE) means that the GeometricFigure ?PART is part of the GeometricFigure ?WHOLE. |
| | greaterThanOrEqualTo | (greaterThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than or equal to the Quantity ?NUMBER2. |
| | initialList | (initialList ?LIST1 ?LIST2) means that ?LIST1 is a subList of ?LIST2 and (ListOrderFn ?LIST1 ?NUMBER) returns the same value as (ListOrderFn ?LIST2 ?NUMBER) for all of the values of ?NUMBER over which (ListOrderFn ?LIST1 ?NUMBER) is defined. |
| | lessThanOrEqualTo | (lessThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than or equal to the Quantity ?NUMBER2. |
| | abstractPart | A meronymy relation similar to part, but for abstract rather than physical things. |
| | part | The 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. |
| | subAttribute | Means that the second argument can be ascribed to everything which has the first argument ascribed to it. |
| | subCollection | (subCollection ?COLL1 ?COLL2) means that the Collection ?COLL1 is a proper part of the Collection ?COLL2. |
| | subLanguage | (subLanguage ?Language-1 ?Language-2) means that ?Language-1 is included in, or subsumed by, ?Language-2. Since subLanguage is a ReflexiveRelation, every Language is a subLanguage of itself. |
| | subList | (subList ?LIST1 ?LIST2) means that ?LIST1 is a sublist of ?LIST2, i.e. every element of ?LIST1 is an element of ?LIST2 and the elements that are common to both Lists have the same order in both Lists. Elements that are common to both Lists and are consecutive in one list must also be consecutive in the other list. (Therefore - the list of prime numbers smaller than 10 [1 2 3 5 7] is not a subList of the natural numbers smaller than 10 [1 2 3 4 5 6 7 8 9]). |
| | subOrganization | (subOrganization ?ORG1 ?ORG2) means that ?ORG1 is an Organization which is a part of the Organization ?ORG2. Note that subOrganization is a ReflexiveRelation, so every Organization is a subOrganization of itself. |
| | subProcess | (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. |
| | subclass | (subclass ?CLASS1 ?CLASS2) means that ?CLASS1 is a subclass of ?CLASS2, i.e. every instance of ?CLASS1 is also an instance of ?CLASS2. A Class may have multiple superclasses and subclasses. |
| | subrelation | (subrelation ?REL1 ?REL2) means that every tuple of ?REL1 is also a tuple of ?REL2. In other words, if the Relation ?REL1 holds for some arguments arg_1, arg_2, ... arg_n, then the Relation ?REL2 holds for the same arguments. A consequence of this is that a Relation and its subrelations must have the same valence. |
| | subsumesContentClass | A BinaryPredicate that relates two subclasses of ContentBearingPhysical. (subsumesContentClass ?CLASS1 ?CLASS2) means that the content expressed by each instance of ?CLASS2 is also expressed by each instance of ?CLASS1. 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. |
| | subsumesContentInstance | A BinaryPredicate relating two instances of ContentBearingPhysical. (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. |
| | temporalPart | The temporal analogue of the spatial part predicate. (temporalPart ?POS1 ?POS2) means that TimePosition ?POS1 is part of TimePosition ?POS2. Note that since temporalPart is a ReflexiveRelation every TimePostion is a temporalPart of itself. |