ISO/IEC JTC 1/SC34 N0344

ISO/IEC JTC 1/SC34

Information Technology --

Document Description and Processing Languages

TITLE: Reference Model for ISO 13250 Topic Maps (RM4TM)
SOURCE: Steven R. Newcomb, Sam Hunting and Jan Algermissen
PROJECT: Topic Map Models
PROJECT EDITORS: Michel Biezunski, Martin Bryan, Steven R. Newcomb
STATUS: Editor's Draft, Revision 1.0
ACTION: For review and comment
DATE: 12 November 2002
SUMMARY:
DISTRIBUTION: SC34 and Liaisons
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Ms. Sara Hafele Desautels, ISO/IEC JTC 1/SC 34 Secretariat
American National Standards Institute
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Tel: +1 212 642-4937
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E-mail: sdesaute@ansi.org

12 November 2002

JTC 1/SC 34 N 344

Reference Model for ISO 13250 Topic Maps (RM4TM)

Version 1.0, 2002/11/12
(The current editors' working copy is available at http://www.isotopicmaps.org/rm4tm/.)


0    Introduction

This Reference Model for ISO 13250 Topic Maps (RM4TM) provides a framework for the definitions of Topic Map Applications (TM Applications). Diverse topic maps that conform to diverse TM Applications that are defined in keeping with this framework can be interpreted and amalgamated automatically by independently implemented systems, without losing information, and with predictable results.

Many of the key advantages of the Topic Maps paradigm derive from the achievement of its primary objective, the "Subject Location Uniqueness Objective", which is to make everything known about every subject in a topic space accessible from a single location within that space. The achievement of the Subject Location Uniqueness Objective means that the efficiency with which users can find information is maximized, not only because the subject's single location, once found, acts as a comprehensive catalog of the things that are known about it, but also because the subject's location can be found in terms of any of its relationships to other subjects.

This RM4TM facilitates the development of TM Applications and systems that can achieve the Subject Location Uniqueness Objective with respect to all subjects, including those that are only implicit in interchangeable topic map instances, as well as with respect to subjects that are relationships (and aspects of relationships) among other subjects.

Moreover, this RM4TM facilitates the development of TM Applications and implementations that can amalgamate the topic spaces represented by topic maps that conform to diverse Topic Maps Applications into a single resulting topic space in which each subject has a single location, there is no redundant information, and all of the information represented by the comprising topic maps is preserved.

This RM4TM provides definition requirements for user-defined Topic Map Applications that allow such definitions to serve as contracts between topic map creators, users, and system implementers, such that when the interchange or amalgamation of topic maps fails due to nonconformance to the definition of a Topic Maps Application, the nonconforming aspects of the topic maps or system implementations can be identified.


1   Scope

This RM4TM defines:

  1. an abstract graph structure for the representation of relationships between subjects;

  2. rules for defining Applications of the Topic Maps paradigm; and

  3. rules for processing the information contained in topic maps.

Note 1: 

See Annex A for a brief informal overview of this RM4TM.



2   Glossary
Editor's Note 1: 

(The glossary hasn't been drafted yet.)


3   Topic map graphs

3.1   The common structural abstraction for topic maps

This RM4TM defines an abstract structure, called a "topic map graph", in terms of which all kinds of topic maps can be uniformly interpreted, regardless of their governing TM Applications, and regardless of the TM Application-defined interchange syntaxes in which they may be representable.

The "topic map graph" form of any given topic map represents all of the subjects that participate in the topic map explicitly, even if they were only implicitly represented in the interchangeable form of the given topic map.

The following subclauses name and define the rules and cases to which topic map graph components and entire topic map graphs must conform in order to be considered "well formed", and the additional rules to which topic map graphs must conform in order to be considered "fully merged". Topic map graphs that are under construction may or may not be well-formed, but only well-formed topic map graphs are eligible to become fully merged, in addition to being well-formed.


3.2   Topic map graphs consist of nodes and arcs.

A topic map graph consists of nodes and arcs. In a well-formed topic map graph, every arc is a typed, oriented connectedness of two nodes, and every node is one of the two endpoints of zero or more arcs.

Note 2: 

This RM4TM uses the neologism "connectedness" in order to avoid implying that TM Applications must be implemented in such a way that arcs are represented as a data structure. For example, The arc abstraction can be fully honored by the property values of the nodes that serve as its endpoints.



3.3   Arcs
Note 3: 

The reader's understanding of the remainder of this clause 3 is likely to be aided by referring to the informative "Assertion Diagrams" Annex B.


An "arc" in a topic map graph is a two-ended connectedness between nodes that satisfies all of the following criteria:


3.3.1   Four arc types

There are four arc types, named "AT", "AC", "CR", and "Cx". The significance of each type of arc is different.


3.3.2   Names of arc types and arc endpoint types

The first letter of an arc type's name is the name of one of its endpoint types. The second letter of the arc type's name is the name of its other endpoint type. That is, an AT arc has two endpoints, one of endpoint type "A" and the other of endpoint type "T".

Note 4: 

In a well-formed topic map graph, only a-nodes serve as "A" endpoint types, only c-nodes serve as "C" endpoint types, only r-nodes serve as the "R" endpoint types, and only t-nodes serve as the "T" endpoint types. There is no such thing as an "x-node", because all kinds of nodes are eligible to serve as the x endpoints of Cx arcs. The exceptional character of the x endpoints of Cx arcs is the reason why "x" is the only endpoint type name that is always rendered in lower case.



3.3.3   Eight forms of connectedness are possible

In all instances of each type of arc, the significance of a node's service as one of the endpoints is different from the significance of a node's service as the other endpoint. Given two nodes, N1 and N2, there are eight possible forms of connectedness between them, since there are four types of arcs. They are enumerated in the following subclauses.


3.3.3.1   Form 1: "A" to "T"

The connectedness of N1 and N2 is an instance of an AT arc type in which N1 is the A endpoint, and N2 is the T endpoint.


3.3.3.2   Form 2: "T" to "A"

The connectedness of N1 and N2 is an instance of an AT arc type in which N1 is the T endpoint, and N2 is the A endpoint. (This is the reverse of Form 1.)


3.3.3.3   Form 3: "A" to "C"

The connectedness of N1 and N2 is an instance of an AC arc type in which N1 is the A endpoint, and N2 is the C endpoint.


3.3.3.4   Form 4: "C" to "A"

The connectedness of N1 and N2 is an instance of an AC arc type in which N1 is the C endpoint, and N2 is the A endpoint. (This is the reverse of Form 3.)


3.3.3.5   Form 5: "C" to "R"

The connectedness of N1 and N2 is an instance of a CR arc type in which N1 is the C endpoint, and N2 is the R endpoint.


3.3.3.6   Form 6: "R" to "C"

The connectedness of N1 and N2 is an instance of an CR arc type in which N1 is the R endpoint, and N2 is the C endpoint. (This is the reverse of Form 5.)


3.3.3.7   Form 7: "C" to "x"

The connectedness of N1 and N2 is an instance of a Cx arc type in which N1 is the C endpoint, and N2 is the x endpoint.


3.3.3.8   Form 8: "x" to "C"

The connectedness of N1 and N2 is an instance of a Cx arc type in which N1 is the x endpoint, and N2 is the C endpoint.

Note 5: 

The above list of Forms of Connectedness can be represented in tabular form as follows:

N1 N2
1
A T
T A
A C
C A
C R
R C
C x
x C
2
3
4
5
6
7
8

Note 6: 

The above enumeration of the Forms of Connectedness serves two purposes in this RM4TM:

  1. It establishes a name ("Form n", where n is an integer in the sequence 1..8) for each of the Forms of Connectedness that an arc can represent, as a convenience for use elsewhere in this document, and possibly in the definitions of TM Applications.

  2. It establishes that the orientation of the connectedness represented by an arc is an essential aspect of the definition of "arc" in this RM4TM. For purposes of a TM Application's definition of a "situation feature" (see 3.4.2), for example, it is insufficient merely to say that two nodes are connected by a certain type of arc. The specification of the arc must also include information as to which node serves as which endpoint type. In order to represent connectedness equivalent to the connectedness represented by an RM4TM arc in some "directed graph" paradigms, at least two directed graph arcs must be used, plus whatever additional machinery may be required to associate the two directed graph arcs in order to represent that both represent different directional aspects of the same connectedness. By contrast, RM4TM arcs are nondirectional, but oriented.



3.4   Nodes and subjects

3.4.1   One subject for each node

In topic map graphs, only nodes can represent subjects, and every node represents a single subject.


3.4.2   Situations and subjects

A node serves as one endpoint of zero or more arcs.

Note 7: 

A node that serves as the endpoints of no arcs at all is not well-formed unless it has at least one built-in SIDP value. (See 3.4.2.)


A node that is the endpoint of zero arcs is said to be "isolated." In a well-formed topic map graph, only "built-in" nodes (see Clause 4) can be isolated.

A node that is the endpoint of one or more arcs is said to be "situated." A node's "situation" is its service as one of the endpoints of all of the "connected paths" through the graph to all other nodes accessible via such paths. (Given node n[0], a "connected path" is a finite alternating sequence n[0], arc[1], n[1], arc[2], n[3]... n[n] such that each arc[i] in the sequence connects node[i-1] and node[i].)

Except for the built-in values of the properties of built-in nodes, all of the values of the properties of nodes are determined by their situations. Thus, except for the built-in subjects of built-in nodes, the subjects of all nodes are entirely determined by their situations.

Except for the restrictions on the subjects of nodes that have special functions within assertion subgraphs (see 3.6.2.2), TM Applications are free to define "situation features" (features of the situations of nodes) and how those features, when they occur, affect the values of the properties of the nodes whose situations include those situation features. The values of all properties can be affected by such situation features, including both Subject Identity Discriminating Propertes (SIDPs) and Other Properties (OPs), in accordance with the specifications provided in the definition of the TM Application that defines the properties and the situation features (see 4.7.2.2).

Note 8: 

The situation of a node in a topic map graph is always and only as visible as the values of its properties make it. See Clause 4.


Note 9: 

The definition of a situation feature can include, but is not limited to, the situated node's status as a role player in one or more assertions. The definition of a situation feature can also include the situated node's status as another kind of assertion component node, such as an r-node component of one or more assertions (see 3.6.2.2).



3.5   Well-formed nodes

3.5.1   Six cases of well-formed nodes

A node that satisfies all the criteria in the subclauses of one of the six cases described in the following subclauses is well formed. A node that does not satisfy the criteria of one of the six cases is not well formed.


3.5.1.1   Well-formed node Case 1

3.5.1.1.1   Defining Characteristics of Case 1 nodes

3.5.1.1.1.1   The node serves as no endpoint of any arc.

3.5.1.1.1.2   The node has at least one built-in SIDP value (see Clause 4).

3.5.1.1.2   Node type name of Case 1 nodes

Case 1 nodes do not have a node type name.


3.5.1.1.3   Subjects of Case 1 nodes

The subjects of Case 1 nodes are not constrained by this RM4TM.


3.5.1.2   Well-formed node Case 2

3.5.1.2.1   Defining characteristics of Case 2 nodes

3.5.1.2.1.1   The node serves as one or more of the x endpoints of any number of well-formed Cx arcs.

3.5.1.2.1.2   The node does not serve as any other endpoint type of any instance of any arc type.

3.5.1.2.1.3   The node either has at least one built-in SIDP value, or its situation as a role player causes at least one SIDP value to be conferred upon it.

3.5.1.2.2   Node type name of Case 2 nodes

Case 2 nodes do not have a node type name.


3.5.1.2.3   Subjects of Case 2 nodes

The subjects of Case 2 nodes are not constrained by this RM4TM.


3.5.1.3   Well-formed node Case 3 ("a-node")

3.5.1.3.1   Defining characteristics of Case 3 nodes

3.5.1.3.1.1   The node serves as zero or more of the x endpoints of any number of Cx arcs.

3.5.1.3.1.2   The node serves as the A endpoint of two or more AC arcs.

3.5.1.3.1.3   The node may or may not serve as the A endpoint of one AT arc.

3.5.1.3.1.4   The node does not serve as any other endpoint of any instance of any arc type.

3.5.1.3.2   Node type name of Case 3 nodes

A Case 3 node is called an "a-node" (where "a" stands for "assertion").


3.5.1.3.3   Subjects of Case 3 nodes

The subject of an a-node is always the relationship that is specified via the assertion for which it serves as the unique nexus. The relationship is an instance of the type of relationship which is the subject of the node that serves as the T endpoint of the AT arc of which the a-node is the A endpoint, if any. If the a-node is not the A endpoint of an AT arc, the type of the relationship is unspecified.


3.5.1.4   Well-formed node Case 4 ("c-node")

3.5.1.4.1   Defining characteristics of Case 4 nodes

3.5.1.4.1.1   The node serves as zero or more of the x endpoints of any number of Cx arcs.

3.5.1.4.1.2   The node serves as the C endpoint of a single AC arc.

3.5.1.4.1.3   The node serves as the C endpoint of a single CR arc.

3.5.1.4.1.4   The node may or may not serve as the C endpoint of a single Cx arc.

3.5.1.4.1.5   The node does not serve as any other endpoint of any instance of any arc type.

3.5.1.4.2   Node type name of Case 4 nodes

A Case 4 node is called a "c-node" (where "c" stands for "casting").

Note 10: 

The term "casting" is consistent with the theatrical metaphor invoked by the term "role player". In an assertion, the role players are like the actors in a stage play. Each c-node represents the "casting" of an actor (a role player) in a specific role (a role type) in a specific stage production (a specific assertion), which may or may not be a production of a specific stage play (a specific assertion type). See 3.6.1.



3.5.1.4.3   Subjects of Case 4 nodes

3.5.1.4.3.1   Case 4 nodes with role players

If a c-node serves as the C endpoint of a Cx arc, then its subject is the playing of a specific role type by a specific subject in a specific relationship.


3.5.1.4.3.2   Case 4 nodes without role players

If a c-node does not serve as the C endpoint of a Cx arc, then its subject is the fact that a specific role type in a specific relationship is not played by any subject.


3.5.1.5   Well-formed node Case 5 ("r-node")

3.5.1.5.1   Defining characteristics of Case 5 nodes

3.5.1.5.1.1   The node serves as zero or more of the x endpoints of any number of Cx arcs.

3.5.1.5.1.2   The node serves as the R endpoint of one or more CR arcs.

3.5.1.5.1.3   The node does not serve as any other endpoint of any instance of any arc type.

3.5.1.5.2   Node type name of Case 5 nodes

A Case 5 node is called an "r-node" (where "r" stands for "role type").


3.5.1.5.3   Subjects of Case 5 nodes

The subject of an r-node is a role type that can be played by subjects in relationships. The subjects of the c-nodes that serve as the C endpoints of the CR arcs whose R endpoints are the r-node are the role-player castings of role players that play the role type.


3.5.1.6   Well-formed node Case 6

3.5.1.6.1   Defining characteristics of Case 6 nodes ("t-node")

3.5.1.6.1.1   The node serves as zero or more of the x endpoints of any number of Cx arcs.

3.5.1.6.1.2   The node serves as the T endpoint of one or more AT arcs.

3.5.1.6.1.3   The node does not serve as any other endpoint of any instance of any arc type.

3.5.1.6.2   Node type name of Case 6 nodes

A case 6 node is called a "t-node" (where "t" stands for assertion "type").


3.5.1.6.3   Subjects of Case 6 nodes

The subject of a t-node is a class of relationship, including the roles that can be played in instances of the class, and the values that are conferred on the properties of role players by virtue of their situations as players of specific roles in instances of the class. The subjects of all of the a-nodes that serve as the A endpoints of all of the AT arcs of which a t-node serves as the T endpoint are instances of the class of relationship that is the subject of the t-node.

Note 11: 

The above well-formedness requirements for nodes can be summarized in tabular form as follows:


Table 1:  The Six Cases of Well-formed Nodes
Form of
Connectedness
(node N2)
node N1
N1 Case 1
N1 Case 2
N1 Case 3
N1 Case 4
N1 Case 5
N1 Case 6
8
.........
C
x
7
.........
x
C
6
.........
C
R
5
.........
R
C
4
.........
A
C
3
.........
C
A
2
.........
A
T
1
.........
T
A
node type
name
(if any).
Subject
constraint
(if any).
Subject is:
requires
built-n
SIDP
value(s)?
0 0 0 0 0 0 0 0 (none) (unconstrained) yes
0 1+ 0 0 0 0 0 0 (none) (unconstrained) no
0 0+ 0 0 0 2+ 0 1? "a-node" assertion no
0 0+ 1? 0 1 1 0 0 "c-node" casting no
0 0+ 0 1+ 0 0 0 0 "r-node" role type no
0 0+ 0 0 0 0 1+ 0 "t-node" assertion type no
Legend:
0 In order to conform to the well-formed node case described on this row, node N1 is not permitted to serve as the arc endpoint designated by this column.
0+ In order to conform to the well-formed node case described on this row, node N1 may serve as zero or more of the arc endpoints designated by this column.
1 In order to conform to the well-formed node case described on this row, node N1 must serve as exactly one of the arc endpoints designated by this column.
1? In order to conform to the well-formed node case described on this row, node N1 may serve as exactly one of the arc endpoints designated by this column.
1+ In order to conform to the well-formed node case described on this row, node N1 must serve as at least one of the arc endpoints designated by this column.
2+ In order to conform to the well-formed node case described on this row, node N1 must serve as at least two of the arc endpoints designated by this column.

3.6   Assertions

3.6.1   Introduction to assertions

Assertions are subgraphs of topic map graphs. In a well-formed topic map graph, every arc is a specific component of a single assertion, so well-formed topic map graphs consist entirely of assertions (except, possibly, for isolated "built-in" nodes).

Each assertion represents (asserts the existence of) a single strongly-typed relationship among the subjects that are its "role players". Each role player is a subject that plays a specific role in the relationship. The roles ("role types") themselves are subjects, and so is the type of relationship of which the relationship is an instance.

The design of assertions in this RM4TM enables diverse multiple topic map graphs to be amalgamated into a single topic map graph, such that:

Note 12: 

In order to maintain the integrity of merged topic maps, it is necessary to establish a common structure for all assertions. In this RM4TM, the decisions as to which aspects of the structure of assertions should be "reified" as nodes, and which aspects should remain "unreified" as arcs, were made by distinguishing between the aspects of assertions that are substantive with respect to the relationships that they assert (and that could conceivably, therefore, need to become role players in other assertions about those relationships), as opposed to the aspects of assertions that nobody would want to make other assertions about unless they were discussing the design of assertions in general. In the structure of assertions set forth in this RM4TM, the former aspects are represented by a-nodes and c-nodes, while the latter aspects are represented as the four types of arcs (the "eight forms of connectedness").



3.6.2   Inventory of the components of assertions

An assertion is a subgraph of a topic map graph that consists of certain arcs and the nodes that serve as their endpoints, constructed in conformance to the rules set forth in this clause. Every node, regardless of its node type, is eligible to be a role player (i.e., to serve as the x endpoint of a Cx arc) in any number of assertions. Every arc is a component of a single assertion. The entire significance of every arc is its service as a unique component of a single assertion.


3.6.2.1   Inventory of the arcs in an assertion

The inventory of arcs that an assertion may have are defined in the subclauses that follow.


3.6.2.1.1   One or zero AT arcs
Note 13: 

The assertion type of an assertion may be specified or unspecified.



3.6.2.1.2   Two or more AC arcs
Note 14: 

In every assertion, there must be at least two role types, and therefore there must be at least two casting nodes.



3.6.2.1.3   Exactly as many RC arcs as there are AC arcs
Note 15: 

Every casting node must have a role type, as well as belong to a single assertion.



3.6.2.1.4   At least one Cx arc
Note 16: 

Every assertion must have at least one role player.



3.6.2.2   Inventory of the nodes in an assertion

3.6.2.2.1   Nodes whose subjects are never dependent on their situation with respect to a given assertion:

3.6.2.2.1.1   Assertion type nodes (t-nodes; i.e., T endpoints of AT arcs)

3.6.2.2.1.2   Role type nodes (r-nodes; i.e., R endpoints of CR arcs)

3.6.2.2.2   Nodes whose subjects are always dependent on their situation with respect to a given assertion:

3.6.2.2.2.1   Assertion nodes (a-nodes; i.e., A endpoints of AT and AC arcs)

An assertion always includes a single well-formed a-node which serves as its unique nexus. The a-node's subject is the relationship that the assertion represents.


3.6.2.2.2.2   Casting nodes (c-nodes; i.e., C endpoints of AC, CR, and Cx arcs)

An assertion always includes at least two c-nodes. The subject of every c-node is that a specific role player (or that no role player at all) plays a specific role type in a specific assertion.


3.6.2.2.3   Nodes whose subjects may or may not be dependent on their situation with respect to a given assertion (role player nodes):

The governing TM Application defines situation features and their effects on the values of the SIDPs of role players. Except in cases where a subject (specified by a set of SIDP values) has been defined by the governing TM Application as being built into a node, a node's subject depends entirely on the features of its situation (its "situation features" - see 3.4.2), on account of which the governing TM Application requires values to be conferred on the values of one or more of its SIDPs. Therefore, the situations of nodes as players of certain roles in instances of certain assertion types may or may not determine their subjects.

Note 17: 

For example, the subject of a node may be determined by its situation as a role player in a single assertion, even though it is also a role player in many others. For another example, the subject may be collectively determined by multiple assertions, perhaps by virtue of playing a role type or set of role types in a set of assertions, or perhaps by playing a role in an assertion in which another roleplayer's subject is collectively determined.



3.6.2.3   What's in and what's not in an assertion

The assertion of which a given a-node is the unique nexus includes all of the nodes and arcs enumerated in the following subclauses, and it does not include any other nodes and arcs:


3.6.2.3.1   All of the AC arcs of which the given a-node serves as the A endpoint.

3.6.2.3.2   The well-formed c-nodes that serve as the C endpoints of the AC arcs identified in 3.6.2.3.1.

3.6.2.3.3   The RC arcs that have the c-nodes identified in 3.6.2.3.2 as their C endpoints.

3.6.2.3.4   The well-formed r-nodes that serve as the R endpoints of the RC arcs identified in 3.6.2.3.3.

3.6.2.3.5   The Cx arcs that have the c-nodes identified in 3.6.2.3.2 as their C endpoints.

3.6.2.3.6   The well-formed nodes that serve as the x endpoints of the Cx arcs identified in 3.6.2.3.5.

3.6.2.3.7   The AT arc, if any, of which the given a-node serves as the A end.

3.6.2.3.8   The well-formed t-node that serves as the T endpoint of the AT arc, if any, identified in 3.6.2.3.7.

3.6.3   Identity of assertions

Two assertions are always considered identical if they have the same assertion type, and the same role players (or the absences of role players) play the same roles. Two assertions are never considered identical, even if they have the same role players playing the same roles, if either or both of their assertion types are unspecified. This clause provides the operational definitions of these concepts.

The identity of the relationship instance that is the subject of an a-node is defined by that a-node's situation as the nexus of an assertion subgraph. For all a-nodes, every TM Application is required to define a situation feature and a set of one or more SIDPs that unambiguously, comprehensively and exclusively reflects the combination of the following:

Note 18: 

One of the key features of this RM4TM is that the merging process does not need to understand the semantics of assertion types in order to merge identical assertions. If two assertions have the same type, regardless of what it is, and the same role players playing the same role types, regardless of what they are, they can be seen to be identical and automatically merged.



3.6.4   Assertion semantics

3.6.4.1   Semantics of assertion typing

3.6.4.1.1   When the assertion type is specified

A "typed" assertion is an assertion that specifies its assertion type (i.e., that has an AT arc and t-node). The semantics of a typed assertion are determined by the subject of its t-node, which is the assertion type of which the typed assertion is an instance. The subject of the t-node incorporates the semantics of all of the role types that can have role players in instances of the assertion type, all of which must be specified in the definition of the subject of the assertion type, either by reference or inclusion.

The semantics of a typed assertion may determine or affect the subjects of some or all of its role players, i.e., the existence of such an assertion may affect the values assigned to the SIDPs of its role players (see 4.7.2).


3.6.4.1.2   When the assertion type is not specified

An "untyped" assertion is an assertion that does not specify its assertion type (i.e., that has no AT arc). The semantics of an untyped assertion are determined by its role types, i.e., by the subjects of its r-nodes. The semantics of its role types may be such that the players of the role types have values conferred on their OPs (Other Properties -- see 4.4). However, the role types of untyped assertions must not be defined in such a way as to require values to be conferred upon the SIDPs of their players (see 5.2.5.3.2).


3.6.4.1.3   The subjects of assertion types and role types are never affected by their instances

The existence of a given assertion never implies anything about the subject which is the assertion type (if any) of which the assertion is an instance, or about the subjects that are the assertion's role types. No values can be conferred upon the SIDPs of assertion types or role types by virtue of their situations, r