Groups
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Update: 4/5/02
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#$Group groups
A collection of temporal objects. Each instance of
#$Group is a
composite object made up of one or more individual objects
or events. A group is related to each of its members by the
predicate #$groupMembers
(q.v.). Note that instances of #$Group are _not_
collections. A group has temporal extent and might have
spatial location, while a collection is timeless and
nonspatial. It is of course possible to define a collection
parallel to any given group, so that the instances of the
collection are exactly the group-members of that group; e.g.
each toe on my left foot (and nothing else) is both an
instance of the collection of my left toes and a member of
the group of toes on my left foot. But that group (of my
left toes) is a spatiotemporal thing while the correlated
collection (of my left toes) is not. Similarly, if a certain
flock of pigeons is considered as having a location, a
spatial extent, and a time of existence, then the flock is
being considered a _group_ and not a collection. Finally,
unlike a collection, a group cannot be empty, but must have
_at_least_one_ group-member. As a default, a group whose
group-members all are instances of #$SomethingExisting
is itself an instance of #$SomethingExisting,
and a group whose group-members all are #$Events is itself an #$Event. Instances of #$Group include
#$QueensGuard, #$ThreeWiseMen, #$SantasReindeer, and #$InternationalCommunity.
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direct instance of:
#$ObjectType
direct specialization of:
#$TemporalThing
direct generalization of:
#$PhysicalSeries
#$Mob #$Holdings
#$GroupFn group fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
An instance of #$CollectionDenotingFunction
used for representing specializations of #$Group. (#$GroupFn OBJTYPE)
denotes the collection of all groups whose members (see #$groupMembers)
are instances of OBJTYPE. Note that an application of #$GroupFn denotes a
_collection_ that has groups as instances, rather than an
individual group. For example, (#$GroupFn
#$BallisticMissile) denotes the collection of all groups of
ballistic missiles, which includes Russia's ballistic
missiles, China's ballistic missiles, the US's ballistic
missiles, etc. Also, a particular group of 101 Dalmatians is
an instance of (#$GroupFn #$Dog).
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direct instance of:
#$ReifiableFunction
#$UnaryFunction #$CollectionDenotingFunction
#$Individual
#$subGroups subgroup
(reflexive binary predicate)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
This predicate relates a group to its subgroups. (#$subGroups GROUP
SUBGROUP) means that (1) all #$groupMembers of
SUBGROUP are members of GROUP (2) if SUBGROUP is different
from GROUP, then the members of SUBGROUP constitute a #$Group in their own
right that is some sort of specialization within GROUP, and
(3) if a new member were to join SUBGROUP, by doing so it
would also become a member of GROUP. Examples: the stars in
#$BigDipper-Asterism constitute one of the #$subGroups of
#$MilkyWay-Galaxy; the Democrats in the House of
Representatives in a given year constitute a subgroup of the
group of #$USRepresentatives for that year. CounterExample:
the groupe of Democrats in the House of Representatives and
the group of people currently located in the territory of
the #$DistrictOfColumbia -- even if every member of the
first group is a member of the second, and it isn't totally
happenstance, a member of SUBGROUP could cease membership in
GROUP without ceasing membership in SUBGROUP.
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direct instance of:
#$CotemporalObjectsSlot
#$ReflexiveBinaryPredicate #$TransitiveBinaryPredicate
#$groupMembers group members
This predicate relates a group (see #$Group) to its
individual members. (#$groupMembers
GROUP MEMBER) means that MEMBER is a member of GROUP. For
example, #$PyramidOfCheops is a group-member of the
#$SevenWondersOfTheAncientWorld, and #$BillClinton is a
group-member of the #$DemocraticParty.
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direct instance of:
#$CotemporalObjectsSlot
direct specialization of:
#$temporallyIntersects
#$cardinality cardinality
(intensional representation predicate)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$cardinality
SETORCOL N) means that the #$SetOrCollection
SETORCOL has N members. For instance, #$TheEmptySet has a
#$cardinality 0.
Note that cardinality is most clear for finite sets, and
only in special branches of mathematics does one speak of
cardinality of infinite sets. See also, #$entityCardinality,
#$Note-cardinality-vs-entityCardinality, #$groupCardinality.
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direct instance of:
#$IntervalBasedQuantitySlot
#$CollectionPredicate
#$groupCardinality group cardinality
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The predicate #$groupCardinality
is used to indicate the total number of members there are in
a particular group. (#$groupCardinality
GROUP INTEGER) means that the number of members in the #$Group GROUP is
INTEGER. For example, the #$groupCardinality
of the #$SevenWondersOfTheAncientWorld is 7. Cyc infers that
the #$groupCardinality
of any group that is a pair is 2, and that of a dozen is 12.
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direct instance of:
#$IntervalBasedQuantitySlot
#$Mob mobs (groups)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
A specialization of #$Group. Each instance
of #$Mob is a group
that contains a large number of objects or events of the
same type. Mobs typically have more members than would be
feasible to enumerate or reify. One rarely refers to
particular members of a given mob; and when one does, it is
usually only to relatively few of them. Examples: the
#$Andes-Mountains is a mob of mountains; each instance of
#$Galaxy is a mob of stars; a cupful of sand is a mob of
grains of sand; and making popcorn involves a mob of corn
kernel bursting events.
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direct instance of:
#$ExistingStuffType
direct specialization of:
#$Group
#$MobFn mob (relationship)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
A #$CollectionDenotingFunction
used for referring to specializations of #$Mob. Thus, applications
of #$MobFn return
_collections_ (of mobs) rather than individual mobs. #$MobFn takes any
instance of #$ObjectType as its
argument and returns a subcollection of #$Mob, namely the
collection of those mobs whose #$groupMembers
are instances of that #$ObjectType. That
is, (#$MobFn
OBJ-TYPE) denotes the collection of all mobs whose members
all are instances of OBJ-TYPE. For example, a clump of hair
on my head is an instance of (#$MobFn #$Hair-Strand);
the collection #$Galaxy is a specialization of (#$MobFn #$Star); and
the collection #$Applauding-Clapping (i.e. all applause
events) could be referred to as (#$MobFn
HandClappingEvent ).
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direct instance of:
#$ReifiableFunction
#$UnaryFunction #$CollectionDenotingFunction
#$Individual
#$groupMembers group members
This predicate relates a group (see #$Group) to its
individual members. (#$groupMembers
GROUP MEMBER) means that MEMBER is a member of GROUP. For
example, #$PyramidOfCheops is a group-member of the
#$SevenWondersOfTheAncientWorld, and #$BillClinton is a
group-member of the #$DemocraticParty.
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direct instance of:
#$CotemporalObjectsSlot
direct specialization of:
#$temporallyIntersects
#$groupMemberType group
member type
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The predicate #$groupMemberType
is used in characterizing the members of a particular group.
(#$groupMemberType
GROUP TYPE) means that all of GROUP's members are elements
of the collection TYPE. For example, to state that the #$groupMembers of
the Austin City Council are humans, one would write (#$groupMemberType
AustinCityCouncil #$Person). The
members of a particular group might be characterized in more
than one way; e.g., a Hispanic Business Council may have
both the #$groupMemberType
#$EthnicGroupOfHispanics and the #$groupMemberType
#$BusinessPerson
(provided that all of its members are Hispanic business
people). For 'typical' or 'expected' characteristics of
members, see also #$memberTypes and #$typeHasTypicalMemberTypes.
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direct instance of: #$BinaryPredicate
#$groupPrototype group prototype
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The predicate #$groupPrototype
is used to identify the individual prototype for a
particular group. (#$groupPrototype
GROUP PROTO) means that the prototype of GROUP is PROTO.
PROTO is an individual which is (or becomes), intentionally
or unintentionally, the model for the #$groupMembers of
GROUP, which share some feature(s) of the prototype. A group
may or may not have a prototype. A group has only one
prototype (if it has any). A prototype exists prior to other
members of the group; it may or may not itself be a member
of the group (by default, Cyc assumes it is). For example,
the prototype for the class of Saturn V rockets; or,
Casanova as the prototypical romantic adventurer.
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direct instance of:
#$FunctionalSlot
direct specialization of:
#$groupMembers
#$List lists
(mathematical concepts)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
A specialization of #$Tuple. Each instance of
#$List is a finite
structure with a first and last member-position, with each
member-postion other than the last having a successor
member-position. Lists, like other instances of #$Tuple, allow for
repetition of their members, so that the same item can
appear at multiple member-positions in a single list. A list
can be viewed formally as a function from a finite index set
of counting numbers, beginning with one, into the domain of
#$Things,
or perhaps some more restrictive domain. Unlike an instance
of #$Series (q.v.),
a list is purely abstract (i.e., not spatio-temporal), and
the only implied relation between an item and its successor
in a list is the successor relation of the list itself. #$List is, technically,
more specific than #$Tuple only in that the
index set for a list must be the counting numbers in their
usual order, rather than some other index set.
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direct instance of: #$StuffType
direct specialization of:
#$Tuple
direct generalization of:
#$ListWithoutRepetition
#$PathChain
#$TheList the list (relationship)
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
#$TheList
is a function that combines its arguments into a list. For
any ITEM(1), ..., ITEM(n), each of which is an instance of
#$Thing, (#$TheList ITEM(1) ...
ITEM(n)) gives the instance of #$List whose first member
is ITEM (1), ..., and whose last member is ITEM(n). Note
that in general ITEM(1), ..., ITEM(n) do not have to be
distinct, though they do if (#$TheList ITEM(1) ...
ITEM(n)) is an instance of #$ListWithoutRepetition.
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direct instance of: #$UnreifiableFunction #$IndividualDenotingFunction
#$VariableArityRelation
#$Individual
#$TheEmptyList the
empty list
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
#$TheEmptyList
denotes the empty list--the list that has no members at all.
Note that every list that has no members is the same as #$TheEmptyList,
i.e., #$TheEmptyList is
the only list whose length is 0. Note also that #$TheEmptyList is
a sublist of every list (see #$subLists). Note, finally,
that #$TheEmptyList is
not the same as #$TheEmptySet.
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direct instance of:
#$ListWithoutRepetition
#$Individual
#$ListWithoutRepetition lists
without repetition
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The collection of all those #$Lists, for each of
which, no element appears more than once in the list. A #$ListWithoutRepetition
is sometimes called an 'OSET'. Note that a #$ListWithoutRepetition
amounts to a finite #$TotalOrdering-Strict.
(In general a #$List
and #$Series may
have repeated elements.) See also #$SeriesWithoutRepetition.
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direct instance of:
#$ObjectType
direct specialization of:
#$WellOrdering #$List
#$listMembers list members
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$listMembers
LIST MEMBER) means that MEMBER is a member of LIST. For
example, if LIST = (#$TheList A B C B)
then LIST has exactly three members: A, B, and C. See #$SetOfListMembersFn.
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direct instance of: #$AsymmetricBinaryPredicate
#$EvaluatablePredicate
#$LengthOfListFn length
of list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$LengthOfListFn,
applied to a list, gives the length of the list, a
non-negative integer. Note that the length of LIST should
not in general be considered the same as the cardinality of
(#$SetOfListMembersFn LIST). For example, given that LIST =
(#$TheList A B
C B D), (#$LengthOfListFn
LIST) is 5 while the cardinality of (#$SetOfListMembersFn
LIST) is 4. When LIST is an instance of #$ListWithoutRepetition,
nevertheless, the length of LIST is identical to the
cardinality of (#$SetOfListMembersFn LIST).
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direct instance of: #$UnaryFunction #$EvaluatableFunction
#$Individual
#$FirstInListFn first
in list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$FirstInListFn,
applied to a list as in (#$FirstInListFn
LIST), results in the first item on the list. For each
nonempty #$List, (#$FirstInListFn
LIST) = (#$NthInListFn
LIST 1). (#$FirstInListFn
LIST) is undefined if LIST is #$TheEmptyList.
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direct instance of: #$UnaryFunction #$EvaluatableFunction
#$Individual
#$LastInListFn last
in list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$LastInListFn,
applied to a list as in (#$LastInListFn
LIST), results in the last item on the list. For each
nonempty #$List LIST,
(#$LastInListFn
LIST) = (#$NthInListFn
LIST (LengthOfListFn LIST)). (#$LastInListFn
LIST) is undefined if LIST is #$TheEmptyList.
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direct instance of: #$UnaryFunction #$EvaluatableFunction
#$Individual
#$RestOfListFn rest
of list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$RestOfListFn
applied to a list, as in (#$RestOfListFn
LIST), gives another list of all but the first item in LIST,
in the same order. To put it in another way, for each
nonempty #$List, (#$RestOfListFn
LIST) is the list obtained from LIST by taking away the
first member of LIST. If the first member of LIST is ITEM
and LIST = (#$JoinListsFn (#$TheList ITEM)
THE-LIST-OF-THE-REST), then (#$RestOfListFn
LIST) = THE-LIST-OF-THE-REST. Note that (#$RestOfListFn
LIST) is undefined if LIST is #$TheEmptyList
and that (#$RestOfListFn
LIST) is #$TheEmptyList if
the length of LIST is 1.
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direct instance of: #$UnaryFunction #$EvaluatableFunction
#$Individual
#$NthInListFn nth
in list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
This function picks a particular member of a list,
at a certain numbered position. For each LIST in #$List with length M
(i.e., (#$LengthOfListFn
LIST) = M), and for each #$PositiveInteger
N that is less than or equal to M, (#$NthInListFn
LIST N) is the member of LIST that occurs at the Nth
position of LIST. For example, given that LIST = (#$TheList A B C D A E
F), (#$NthInListFn
LIST 1) = A, (#$NthInListFn
LIST 2) = B, (#$NthInListFn
LIST 5) = A and (#$NthInListFn
LIST 7) = F. Note that when N is greater than the length of
LIST or LIST is #$TheEmptyList,
then (#$NthInListFn
LIST N) is undefined. Note also that the items on a list are
numbered 1, 2, 3, ..., not 0, 1, 2, ... .
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direct instance of: #$BinaryFunction #$EvaluatableFunction
#$Individual
#$PositionsInListFn positions
in list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$PositionsInListFn
applied to two lists, as in (#$PositionsInListFn
LIST1 LIST2), finds every occurrence of LIST1 as a sublist
of LIST2, and results in a list of all the positions in
LIST2 where a copy of LIST1 starts (i.e., a list of #$PositiveIntegers).
For any instances LIST1 and LIST2 of #$List, (#$PositionsInListFn
LIST1 LIST2) denotes the list LIST* of #$PositiveIntegers
defined below. Let L be the length of LIST1. The first
member of LIST*, if there is any, is the smallest positive
integer N1 such that LIST1 = (#$SublistFromToFn
LIST2 N1 N1+L). The second member of LIST*, if there is any,
is the second smallest positive integer N2 such that LIST1 =
(#$SublistFromToFn
LIST2 N2 N2+L). ... The last member of LIST* is the greatest
positive integer N such that LIST1 = (#$SublistFromToFn
LIST2 N N+L). Note that if LIST1 is not a sublist of LIST2
or LIST2 is #$TheEmptyList,
then (PositionsInListFn LIST1 LIST2) is #$TheEmptyList.
Note also that if LIST1 is #$TheEmptyList
while LIST2 is not, then (#$PositionsInListFn
LIST1 LIST2) returns a list of all the positions in LIST2
(e.g., if LIST2 = (#$TheList A B C), (#$PositionsInListFn
#$TheEmptyList
LIST2) = (#$TheList
1 2 3)).
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direct instance of: #$BinaryFunction #$EvaluatableFunction
#$Individual
#$ReverseListFn reverse
list fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$ReverseListFn
applied to a #$List,
as in (#$ReverseListFn
LIST), results in the same list, but in reverse order. For
example, if LIST is (#$TheList A B C A D),
then (#$ReverseListFn
LIST) = (#$TheList
D A C B A).
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direct instance of: #$UnaryFunction #$EvaluatableFunction
#$Individual
#$SublistFromToFn sublist
from to fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
The function #$SublistFromToFn
applied to a list and two numbers, as in (#$SublistFromToFn
LIST X Y), picks out the sublist of LIST from position X to
position Y, inclusive. For each nonempty #$List LIST, and for each
pair of positive integers M and N such that M is less than
or equal to N and such that N is less than or equal to the
length of LIST, (#$SublistFromToFn
LIST M N) denotes the sublist SUBLIST of LIST such that the
first member of SUBLIST is the Mth member of LIST and the
last member of SUBLIST is the Nth member of LIST. See
#$subLists. Note that (#$SublistFromToFn
LIST M N) is not defined if LIST is #$TheEmptyList or
M is greater than N or N is greater than the length of LIST.
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direct instance of: #$TernaryFunction #$EvaluatableFunction
#$Individual
#$JoinListsFn join
lists fn
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
This function attaches lists together to make
longer lists. For any instances LIST(1), ..., LIST(n) of #$List, (#$JoinListsFn
LIST(1) ... LIST(n)) denotes the list, i.e., the instance of
#$List, that is
obtained by concatenating LIST(1), ..., LIST(n) end to end
in the order from 1 to n. Note that LIST(1), ..., LIST(n) do
not have to be distinct.
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direct instance of: #$AssociativeRelation #$EvaluatableFunction
#$VariableArityRelation
#$Individual
#$Series series
A specialization of #$TemporalThing.
Each instance of #$Series is a complex
temporal thing in which two or more other things are ordered
in a linear fashion. Examples include a line of people at a
ticket booth (an instance of the specialization #$PhysicalSeries)
and a series of pitches in a baseball game (an instance of
the specialization #$EventSeries). In each instance of #$Series, there is some
relation by which its members are ordered (see the related
predicate #$seriesOrderedBy);
this relation often varies from series to series.
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direct instance of: #$FirstOrderCollection
direct specialization of:
#$TemporalThing
direct generalization of:
#$PhysicalSeries
#$PhysicalSeries physical series
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
A specialization of both #$Series and #$PartiallyTangible.
Each instance of #$PhysicalSeries
is a group of partially tangible objects ordered in a linear
fashion, most likely according to some spatial relationship.
Instances would include a group of people in line at a
ticket booth, or the vertebrae in one person's spine.
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direct instance of:
#$ExistingObjectType
direct specialization of:
#$Group #$PartiallyTangible #$Series
#$SeriesWithoutRepetition series
without repetition
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
A #$SeriesWithoutRepetition
is a #$Series in
which each member occurs only once.
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direct instance of:
#$Collection
direct specialization of:
#$Series
#$subSeries sub series
(#$subSeries SERIES
SUBSERIES) means that SUBSERIES is a sub-series of SERIES.
This means that all the members of SUBSERIES are
series-members (see the predicate #$seriesMembers) of
SERIES, that SERIES and SUBSERIES share the same ordering
principle, and that, if the first member of SUBSERIES is the
Mth member of SERIES, the Nth member of SUBSERIES is the (N
+ M - 1)th member of SERIES.
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direct instance of:
#$PartPredicate
#$ReflexiveBinaryPredicate #$AntiSymmetricBinaryPredicate
#$TransitiveBinaryPredicate
#$seriesMemberIsa series
member isa
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$seriesMemberIsa
SERIES COL) means that each of the #$seriesMembers of SERIES
SIT is an instances of the collection COL.
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direct instance of: #$BinaryPredicate
#$seriesLength series length
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$seriesLength
SER LEN) means that the series, SER, is LEN members long.
Note that some #$Series have an
unknown or infinite number of members.
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direct instance of:
#$FunctionalSlot
#$seriesOrderedBy series
ordered by
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
This predicate relates series to relations that
order them linearly. (#$seriesOrderedBy
SERIES PRED) means that PRED is a relation that imposes a
linear, or total, ordering (see #$TotalOrdering)
on the #$seriesMembers of SERIES. PRED is both a
#$TransitiveBinaryPredicate and a
#$AntiSymmetricBinaryPredicate, and each member of SERIES
stands in the relation PRED to all of the succeeding
members. For example, if SERIES is a line of cars driving
north, it might be ordered by #$northOf (and perhaps also by
ahead of ).
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direct instance of: #$BinaryPredicate
#$seriesOrderedByInverse series
ordered by inverse
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$seriesOrderedByInverse
SER PRED) means that PRED is the relation that imposes an
order on the members of SER. Each member of the series
stands in the relation PRED to the series members that come
before it. For example, if SER is a line of cars driving
south, the ordering relation might be #$northOf (or
''behind''). See also #$seriesOrderedBy.
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direct instance of: #$BinaryPredicate
#$Nth nth
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$Nth SER N)
denotes the Nth member of the series SER, provided that N is
an integer greater than or equal to 1 and less than or equal
to the #$seriesLength of SER.
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direct instance of: #$BinaryFunction #$ReifiableFunction
#$Individual
#$structureRelations structure relations
**COMMENT NOT REVIEWED**
**GAFs NOT REVIEWED**
(#$structureRelations
STRUCT REL) means that the situation or structure STRUCT has
REL as one of its associated relations between its
structure-members. This is very general and it could be an
abstract predicate, relation or function, defined on the structure-members.
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direct instance of: #$BinaryPredicate
direct specialization of:
#$parts
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