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UN/CEFACT Context Methodology
Technical Specification
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Working Draft
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DAG Chapter 6 Only
[15 April 2009]
UN/CEFACT Context Methodology Technical Specification
Copyright © UN/CEFACT 2009
. All Rights Reserved.
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Table of Contents
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STATUS OF THIS DOCUMENT ........................................................................... 2
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2 UN/CEFACT UNIFIED CONTEXT METHODOLOGY TECHNICAL
SPECIFICATION PROJECT TEAM PARTICIPANTS ............................................. 3
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INTRODUCTION..................................................................................................... 3
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OBJECTIVES ........................................................................................................... 4
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OVERVIEW .............................................................................................................. 5
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GRAPH THEORY FOUNDATION ....................................................................... 6
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6.1
Mathematical Directed Acyclic Graph ............................................................... 6
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6.1.1
Notations Used For DAG................................................................................ 6
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6.1.2
Key DAG Concepts ........................................................................................ 7
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6.2
Context Scheme Directed Acyclic Graph ........................................................... 7
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6.2.1
Notations Used For Context Scheme DAG .................................................... 8
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6.2.2
Context Scheme DAG Propeties ..................................................................... 8
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6.2.3
ContextNodes and DAG Edges ...................................................................... 8
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6.2.4 ContextValues within a Context Scheme DAG ........... Error! Bookmark not
defined.
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6.2.5
ContextPath ................................................................................................... 10
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6.2.6
Context Scheme DAG Lifecycle .................................................................. 15
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1 Status of this Document
UN/CEFACT Context Methodology Technical Specification
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. All Rights Reserved.
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2 UN/CEFACT Unified Context Methodology
Technical Specification Project Team
Participants
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3 Introduction
UN/CEFACT Context Methodology Technical Specification
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4 Objectives
UN/CEFACT Context Methodology Technical Specification
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5 Overview
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6 Graph Theory Foundation
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The foundation of this specification is a mathematical graph.
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Specifically, this specification is based on a Directed Acyclic Graph [DAG]. A DAG has
many applications in event processing, expression evaluation, game theory, sorting
algorithms, parser algorithms, etc.
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While a DAG is a mathematical construct, it defines no semantics. This specification
imposes semantics on a DAG to realize Context Schemes.
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6.1 Mathematical Directed Acyclic Graph
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This section provides a terse explanation of key DAG concepts and base terminology. For
in depth discussion of graphs, much has been written. Refer to the reference section of
the specification. We identify and discuss the base concepts of a DAG which are relevant
to this specification, which uses a mathematical DAG as its foundation.
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A Directed Acyclic Graph is a specific form of a graph. In a DAG, vertices (or nodes) are
directionally connected by edges (or lines) and following any edge along its direction,
from a given vertex, the same vertex can never be reached (no cycles, acyclic). Edges
directionally connect two vertices.
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6.1.1 Notations
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While there is no best drawing of a graph, they are usually represented using dots to
represent vertices and lines, or arcs, to represent edges. Arrows are usually used to show
orientation of directed edges.
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This specification uses this notation to exemplify graphs:
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A vertex is represented by ellipse:
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An edge is represented arrow, which identifies the direction. The end of the arrow
without the arrow head is the edge source and the end with the arrow is the edge target.
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Technically, a DAG is purely mathematical, and vertices within a DAG do not require a
value, or label, of any sort. However, a simple text label within a vertex is used to
exemplify a value of a vertex and facilitate the discussion:
X
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A sequence, or path, of connected vertices is represented in textual form by combining
text labels of vertices with the characters “->”, such as “X->Y->Z”.
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6.1.2 Key DAG Concepts
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A source node (or root node), is a vertex connected to zero edge sources (1, 2, 3, and 4).
A sink node (or leaf node), is a vertex connected to zero edge targets (4, 6, and 8). Note
that (4) is both a source node and a sink node. Vertexes, which are neither a source node
nor sink node (5) have no special term beyond just ‘vertex’.
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A directed path is a sequence of one or more vertices connected by edges (1, 4, 1->6, 2>5->7, 3->5->7->8, 5->7).
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Note that there is no requirement for a vertex to be connected by edges. A DAG may
have one or more source vertices and one or more sink vertices, but must have at least
one Vertex.
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6.2 Context Directed Acyclic Graph
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Industry has utilized graphs, in general, for approaches to knowledge and semantics for
years as a semantic network [SEMANTICNET]. This section specifies the terminology
and approach for leveraging the special form of a mathematical graph, a DAG, as the
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foundation for semantics to facilitate Context Schemes. Since a DAG is both acyclic and
directed, this dictates the approach at the semantic layer also.
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We refer to the use of a mathematical DAG for the foundation of Context Schemes as a
Contextual DAG, or CDAG.
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6.2.1 Notations
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6.2.1.1 CDAG Notation
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Notations for a CDAG utilize the notations for a mathematical DAG and is the primary
notation used in this section.
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6.2.1.2 UML
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This section utilizes UML as sketch where useful to facilitate the discussion. The
following UML packages are utilized:
un::unece::uncefact::ucm::dag
DAG classifiers
un::unece::uncefact::ucm::cdag
CDAG classifiers
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The CDAG package has dependency on the DAG package.
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6.2.2 CDAG Propeties
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<versioning, etc>
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6.2.3 ContextNode and ContextEdge as Node and Edge
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DAG nodes and edges have consistent entities in a CDAG.
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A ContextNode is a vertex in a mathematical DAG, while a ContextEdge is an edge in a
mathematical DAG. A CDAG contains one or more ContextNodes, and contains zero or
more ContextEdges.
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Further following a mathematical DAG, a source node (or root node), is referred to as a
RootContextNode and a sink node (or leaf node) is referred to as a LeafContextNode. A
ContextNode which is neither a RootContextNode nor LeafContextNode has no special
term beyond just ‘ContextNode’.
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6.2.4 ContextValue
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A CDAG introduces a ContextValue. A ContextNode contains one ContextValue.
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A ContextValue is abstract, and may be realized as either a code (in a code list) or some
form of identifier. Either way, the ContextValue has optional metadata for indicating
information about the code or identifier, such as the owning agency, version of the code
list, etc. This section does not elaborate on these realizations.
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We provide the following UML sketch depicting the core structural concepts of a CDAG.
Note that these relationships to not explicitly depict the base constraints of a DAG, such
as acyclicness. Key points about this sketch:
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ContextNode is not abstract since a given ContextNode is concrete as with
RootContextNode or a LeafContextNode
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ContextValue is abstract with concrete classifiers for code or identifier. Metadata
for these, such as the owning agency, are not shown for simplicity.
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1
Source
ContextEdge
Target
1
*
1
ContextDAG
1
*
1
ContextNode
1
1..*
RootContextNode
ContextValue
1
LeafContextNode
1
Code
Identifier
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6.2.5 ContextPath and Contextualizable
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A ContextPath is a directed path in a mathematical DAG. A ContextPath is a sequence of
one or more ContextNodes. A ContextNode may participate in more than one
ContextPaths.
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It is important to note that a CDAG by itself has no ContextPaths. A ContextPath is part
of a Contextualizable.
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6.2.5.1 Contextualizables and PathScope
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A Contextualizable is abstract, and is an entity that has one or more ContextPaths.
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A ContextPath identifies semantic relevancy of a Contexualizable. A CCTS BIE is a
Contextualizable.
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For example, a Customer Information CCTS ABIE (which is a Contextualizable) may be
defined specifically for the OrderToCash business process. To formally indicate this
relevancy, a BusinessProcesses->OrderToCash ContextPath must be defined and be part
of the CCTS ABIE Contextualizable.
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PathScope indicates the relevancy of an Contextualizable for a given ContextPath. There
are two kinds of PathScope:
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Implied
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Explicit
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Explicit indicates that the Contextualizable is relevant only as far as the sequence of
ContextValues defined in the ContextPath. It indicates nothing is being said about any
further children of the last ContextNode in the ContextPath. Implied indicates that the
Contextualizable is relevant to all ContextValues defined in the ContextPath and
downward to all children and subchildren within the CDAG.
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(Note that while a ContextPath does not have to include a SinkContextNode, if one is
included the PathScope has no meaning (and is actually not required). Note also that a
ContextPath must include one RootContextNode, so there are no PathScope values to
characterize relevancy “upward” in the graph.)
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In the following example there are 5 different ABIE definitions, which are identified with
a uuid attribute, all representing Customer Information. The ABIE 791 has been
associated to the CDAG by declaring a BusinessProcesses->OrderToCash ContextPath
(in red) with a PathScope “Explicit”, indicating this CustomerInfo ABIE is relevant to the
OrderToCash business process and nothing more. It is not necessarily indicating it has
semantic relevance to the Execution History, etc.
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«ACC»
CustomerInfo
-uuid : Integer = 789
+firstName
+lastName
+middleName
+customerNumber
«Based On»
«Based On»
«Based On»
«Based On»
«ABIE»
CustomerInfo
-uuid : Integer = 790
+firstName : String
+middleName : String
+lastName : String
+customerNumber : String
DesignToRelease
«ABIE»CustomerInfo
-uuid : Integer = 791
+firstName : String
+lastName : String
+customerNumber : String
«ABIE»
CustomerInfo
-uuid : Integer = 792
+customerNumber : String
«ABIE»CustomerInfo
-uuid : Integer = 793
+customerNumber : Integer
PathScope=
Explicit
CreateOrderForCustomer
BusinessProcesses
OrderToCash
Steps
GetAllCutomerOders
UpdateOrder
ExecutionHistory
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Adjusting the association and PathScope to the following example indicates that the
CustomerInfo ABIE has been associated to the CDAG by delaring a BusinessProcesses>OrderToCash->Steps ContextPath and “Implied” path scope, indicating that this
CustomerInfo ABIE is now relevant to all steps in the OrderToCash business process.
The Implied PathScope is essentially a convenience indicator which eliminates listing all
possible paths beyond a specific ContextNode.
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«ACC»
CustomerInfo
-uuid : Integer = 789
+firstName
+lastName
+middleName
+customerNumber
«Based On»
«Based On»
«Based On»
«Based On»
«ABIE»
CustomerInfo
-uuid : Integer = 790
+firstName : String
+middleName : String
+lastName : String
+customerNumber : String
DesignToRelease
«ABIE»CustomerInfo
-uuid : Integer = 791
+firstName : String
+lastName : String
+customerNumber : String
«ABIE»
CustomerInfo
-uuid : Integer = 792
+customerNumber : String
«ABIE»CustomerInfo
-uuid : Integer = 793
+customerNumber : Integer
PathScope=
Implied
CreateOrderForCustomer
BusinessProcesses
OrderToCash
Steps
GetAllCutomerOders
UpdateOrder
ExecutionHistory
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6.2.5.2 ContextPath and Semantic Precision via ContextValues
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A ContextPath represents variation semantic precision. By altering the ContextValues
(via their ContextNodes) within a ContextPath, a change in understanding granularity is
realized.
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Increasing ContextValues within a ContextPath in the direction of a ContextEdge
(extending the path) increases semantic precision, while decreasing ContextValues
(reducing the path) in the opposite direction of a ContextEdge decreases semantic
precision. Therefore, a RootContextNode within a ContextPath provides the most
imprecise point of understanding within the path, while the ‘ending’ ContextNode
provides the most precise understanding within the path.
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In the above CDAG examples, the BusinessProcesses RootContextNode is the most
imprecise point of understanding. It provides a general point of understanding for nothing
more than business processes. Taking into account the OrderToCash ContextNode as part
of a ContextPath, a more comprehensive and increase in precision of understanding is
achieved by realizing which specific business process is under consideration. Further, the
CDAG organizes steps and execution history in this process. Also taking into account
within a ContextPath the Steps and CreateOrderForCustomer ContextNodes, a significant
increase in precision of understanding realized as to the relevancy of the ABIE.
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In order to declare maximum semantic within a CDAG, a ContextPath must include one
SouceContextNode. This has the desirable, and required, side effect of avoiding
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ambiguity which would be imposed by including ContextNodes associated with multiple
ContextEdge targets. There is, however, no requirement to include a SinkContextNode.
Valid ContextPaths using the above example are:
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BusinessProcesses
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BusinessProcesses->OrderToCash
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BusinessProcesses->OrderToCash->ExecutionHistory
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BusinessProcesses->OrderToCash->Steps
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BusinessProcesses->OrderToCash->Steps->CreateOrderForCustomer
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However, the following ContextPaths using the above example are invalid:
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Steps
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OrderToCash->Steps->CreateOrderForCustomer
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ExecutionHistory
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UpdateOrder
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6.2.5.3 ContextPaths within Contexualizables
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A Contextualizable contains one or more ContextPaths representing union of its complete
semantic relevancy. ContextPaths may contain the same intersecting ContextValue
representing different semantics as in the following example CDAG:
US Tax Rates
North Carolina
Texas
Travis County
Austin
US State Capitals
Raleigh
Mecklenburg County
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In this example, a Population ABIE has been defined by restricting a Population ACC to
only include, and provide the typing for, the men and women property terms (no
children) which has the following two ContextPaths declared as shown, indicating
semantic relevance to Austin both for the context of state capitals via an Explict
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ContextPath, and also for semantic relevancy to Austin and Travis County for the context
of US Tax rates via an Implied ContextPath.
Contextualizable
+ContextPath : String
«ACC»
Population
-uuid : Integer = 789
+men
+women
+children
«Based On»
«ABIE»
Population
+ContextPath : String = US Tax Rate ->Texas ->Austin [Impled]
+ContextPath : String = US State Capitals ->Austin [Explicit]
-uuid : Integer = 792
+men : Integer
+women : Integer
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This example does not indicate that the ABIE is semantically relevant to Raleigh for any
context.
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6.2.6 CDAG Lifecycle
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7 X
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REFERENCES FOR SECTION 6
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DAG
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Directed Acyclic Graph, WikiPedia, http://en.wikipedia.org/wiki/Directed_acyclic_graph
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[SEMANTICNET]
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Semantic Network / Semantic Nets, WikiPedia, http://en.wikipedia.org/wiki/Semantic_network
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