The Graph Theoretical Library

The Graph-Theoretic Library
and The Role of Conceptual Data Modeling in
Cultural Heritage Institutions

Ethnomathematics

1991

2002

1981

Ethnomathematics
Ethnomathematics is the study of the mathematical practices of
specific cultural groups in the course of dealing with their
environmental problems and activities
• The prefix “ethno” refers to identifiable cultural groups, such as
national-tribal societies, labor groups, children of a certain age
bracket, professional classes, etc. and includes their ideologies,
language, daily practices, and their specific ways of reasoning and
inferring.
• “Mathema” here means to explain, understand and manage reality
specifically by ciphering, counting, measuring, classifying, ordering,
inferring and modeling patterns arising in the environment.
• The suffix “tics” means art or technique.

Representing Versailles

A Simplifying Abstraction: From Versailles to
the Versailles Map of Creative Expressions
• You want to create multimedia records of your
experience of Versailles by identifying various
locations within the gardens, and creating and/or
collecting still and motion images of that point plus
the texts, musical performances, etc. that are evoked
by that point.

• How do you organize these collected resources?

The Estate of Versailles
Horse-drawn carriages
From Tuesdays to Sundays
i Information Telephone: 01 30 97 04 40
School groups cloakroom Fax: 01 30 97 04 44
Telephone Mini-train
Cafeteria, Restaurant A mini-train runs every day
Refreshments to the Trianon except in
Toilets exceptional circumstances.
For disabled persons Seats reserved for people
P Car parks with restricted mobility.
Boat hire Duration: 15min.
Bicycles Telephone: 01 39 54 22 00
Ice creams Fax: 01 39 55 07 25
Souvenirs Electric cars
Confectionery Several visit circuits.
Picnic area Information: 01 39 66 97 66



P

  Arboretum
de Chèvreloup

P

 

P
i

P  

P

P
’ 
Grille des Matelots
-
-
- -
-
-
- -
-
-
 Porte St-Antoine

On foot
1
From the Palace of Versailles
to the top of the Grand Canal
(1 km) 15min. on foot
2

3 4 From the Palace of Versailles
5 to the Trianon estate (1.5 km)
6
25min. on foot

7 8
to the end of the Grand Canal
9 10
(3.5 km)
60min. on foot

The Garden and Groves
1 Bassin d’Apollon
11
Grille de la Reine

---
2 Bosquet de l’Encelade

--
13
3 Jardin du Roi
12
G rille de Neptune 4 Salle des Marronniers

-
-
-
-
-
14 5 Bosquet de la Colonnade
6 Bosquet des Dômes
16
7 Bassin du Miroir
15 19 18 17 8 Tapis vert
20 21 9 Bosquet de la Girandole
22
Grille du Dragon 10 Bosquet du Dauphin

-
-
-
-
-
11 Bassin et parterre de Latone
A 13
12 Salle de Bal
 13 Bosquet des Bains d’Apollon
14 Parterre d’Eau

Map X Y Picture
15 Pièce d’Eau des Suisses
16 Bosquet des Trois Fontaines
17 Bassin de Neptune

-
-
-
-
-
23 P Grille d’Honneur 18 Bassin du Dragon
19 Orangerie
Grande Écurie 20 Parterre Sud
    21 Parterre Nord

PlanCB_07 85 354 IMG_1084.jpg
  22 Bosquet de l’Arc de Triomphe
24
In town
23 King’s Kitchen Garden
Bus 171
24 Academy of
Equestrian Arts
Versailles Rive Droite SNCF
25 tel: 01 39 02 07 14

PlanCB_07 64 310 IMG_1087.jpg Versailles Rive Gauche RER C
25 Tourist Office
2 bis, avenue de Paris

Conception Polymago. ©photos RMN.
78000 Versailles
tel: 01 39 24 88 88
26 Baroque Music
Centre
(Hôtel des Menus Plaisirs)

... ... ... ... Versailles Chantiers SNCF
26

A
13

The Estate of Versailles
Horse-drawn carriages
From Tuesdays to Sundays
i Information Telephone: 01 30 97 04 40
School groups cloakroom Fax: 01 30 97 04 44
Telephone Mini-train
Cafeteria, Restaurant A mini-train runs every day
Refreshments to the Trianon except in
Toilets exceptional circumstances.
For disabled persons Seats reserved for people
P Car parks with restricted mobility.
Boat hire Duration: 15min.
Bicycles Telephone: 01 39 54 22 00
Ice creams Fax: 01 39 55 07 25
Souvenirs Electric cars
Confectionery Several visit circuits.
Picnic area Information: 01 39 66 97 66

But Wait: What if you want 

P

to better document or to  

P

P
i
 
Arboretum
de Chèvreloup

relate significant aspects P  

P

P
’ 
Grille des Matelots
-
-
- -
-
-
- -
-
-
 Porte St-Antoine

of the creative expressions
On foot
1
to the top of the Grand Canal
(1 km) 15min. on foot
2

3 4 From the Palace of Versailles
5 to the Trianon estate (1.5 km)
6
25min. on foot

7 8
to the end of the Grand Canal

to one another, and not
9 10
(3.5 km)
60min. on foot

The Garden and Groves
1 Bassin d’Apollon
11
Grille de la Reine

---
2 Bosquet de l’Encelade

--
13
3 Jardin du Roi
12
G rille de Neptune 4 Salle des Marronniers

-
-
-
-
-
14 5 Bosquet de la Colonnade
6 Bosquet des Dômes
16

just to the map?
7 Bassin du Miroir
15 19 18 17 8 Tapis vert
20 21 9 Bosquet de la Girandole
22
Grille du Dragon 10 Bosquet du Dauphin

-
-
-
-
-
11 Bassin et parterre de Latone
A 13
12 Salle de Bal
 13 Bosquet des Bains d’Apollon
14 Parterre d’Eau
15 Pièce d’Eau des Suisses
16 Bosquet des Trois Fontaines
17 Bassin de Neptune

-
-
-
-
-
23 P Grille d’Honneur 18 Bassin du Dragon
19 Orangerie
Grande Écurie 20 Parterre Sud
    21 Parterre Nord
  22 Bosquet de l’Arc de Triomphe
24
In town
23 King’s Kitchen Garden
Bus 171
24 Academy of
Equestrian Arts
Versailles Rive Droite SNCF
25 tel: 01 39 02 07 14
Versailles Rive Gauche RER C
25 Tourist Office
2 bis, avenue de Paris

Conception Polymago. ©photos RMN.
78000 Versailles
tel: 01 39 24 88 88
26 Baroque Music
Centre
(Hôtel des Menus Plaisirs)

26
Versailles Chantiers SNCF

A
13

Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
Graph


Graph
We can create a
mathematical
expression of the This set of creative
relationships between expressions would be
the Versailles called a Graph.
Gardens and the
creative expressions
inspired by them.


Graph
We construct a set of
nodes (AKA vertices)
and a set of edges This set of creative
(AKA links) that define expressions would be
one or more types of called a Graph.
relationship between
the nodes.


Graph
We construct a set of In this example, the
nodes (AKA vertices) nodes represent
and a set of edges locations within the
(AKA links) that define gardens. The links
one or more types of represent a “next_to”
relationship between relationship between
the nodes. two garden locations.


Graph
We construct a set of
nodes (AKA vertices) A graph may be
and a set of edges visualized as a
(AKA links) that define network of dots and
one or more types of lines (sometimes
relationship between arrowed)
the nodes.


Graph

A graph diagram can
be manipulated to
show relationships
more clearly

Thinking About Mazes

A Simplifying Abstraction: From Maze to Maze
Graph

Data Modeling in General

• Definitions
• About data modeling
• Data models and “Paper Tools”
• Data modeling examples (many!)
• What to do now

Thinking About Mazes and
Formal Gardens
Abstract, Refine, Generalize, Pose Questions

Formal Gardens
Is the Hampton Court maze transformable
into a section of the Versailles Gardens?

Formal Gardens
Is there a set of vertices and edges (a
subgraph shape) within the Versailles graph
that matches the Hampton Court Maze?

Formal Gardens

• Um, probably

• Brute force approach (shape matching) foreclosed by
old brains and unwillingless to go insane

• Did not have a representation that could be used to
decide the question in a more elegant fashion

Data Modeling in General
• Definitions
– Conceptual Data Model: A description of a portion of an enterprise in terms of
the fundamental things of interest to it. They are fundamental in that most things
seen by business owners are examples of these.
– Logical Data Model: The organization of data for use with a particular data
management technology. For relational databases, these are tables and columns;
for object-oriented databases, object classes and attributes.
• The MARC bibliographic standard specifies a logical data model that uses tags and
delimiters to structure bibliographic data. In practice, the bibliographic conceptual
data model is tangled up in the logical data model
– Physical Data Model: The organization of data used to place it on specific
storage media. This level refers to “tablespaces” and “cylinders.”
– General Definition: The specification of a final conceptual data model and an
initial logical data model that together meet business requirements, prior to any
performance tuning.

About Data Modeling

• Why a Data Model is Important
• What Makes a Good Data Model?
• What Makes a Good Data Modeler?
• What is the Description/Design Question?

About Data Modeling
– Leverage: Small changes in the data model have major effects on the
system design and final implementation
– Conciseness: The relatively compact data model takes less time to
review that the functional specification, and in-depth understanding
easier to achieve
– Data Quality: Data quality problems are often traceable to
inconsistent data definition, interpretation, and enforcement
mechanisms

About Data Modeling
– It serves as a necessary complement to a function and process
model
• The database system design and implementation process described here can
involve three types of modeling
• A data model describes the information an enterprise must have on hand to
execute its functions
• A function model describes what an enterprise must do
• A process model describes how an enterprise must do it.
– Function and process models are regularly combined during the database
system design process
– It can function as a “Paper Tool” in service of theoretical and
practical ends

About Data Modeling
• What Makes a Good Data Model?
– Completeness
– Nonredundancy
– Enforcement of Business Rules
– Data Reusability
– Stability & Flexibility
– Elegance
– Communication
– Integration

About Data Modeling
• What is the Description/Design Question?
– Is data modeling best characterized as a descriptive activity, the
objective of which is to document some aspect of the real world?
– Is data modeling best characterized as a design activity, the objective
of which is to create data structures to meet a set of requirements?
– Does the history of the development and implementation of the FRBR
model reflect aspects of this controversy?

Portions quoted from Simsion, Graeme (2007). Data Modeling: Theory and Practice. p.3.

About Data Modeling
• How is the Description/Design Issue Manifest?
– Explicit arguments among practitioners and academics, as to
whether the description or design paradigm was correct.
– Clashes between practitioners who subscribed to the descriptive
paradigm, but had produced different models that were difficult
to reconcile.
– Disagreement over the appropriateness of data modelers
introducing new concepts and terminology rather than simply
documenting an established view of business entities.

Quoted from Simsion, Graeme (2007). Data Modeling: Theory and Practice. p.10.

About Data Modeling
• How is the Description/Design Issue Manifest (cont.)?
– Difficulty in teaching data modeling using texts and teaching
materials which treated it as a descriptive process.
– Experienced data modeling practitioners struggling to develop
models, and observing that data modeling in practice was much
more difficult than it should be if it was essentially concerned
with describing data requirements.
– Antipathy towards data modelers, who were frequently seen as
pursuing an ideal description of reality rather than contributing
in the most productive way to an information system design.

Quoted from Simsion, Graeme (2007). Data Modeling: Theory and Practice. p.10.

About Data Modeling
• Description/Design Issue Findings
– The description/design issue is considered an important
one by data modeling practitioners
• Evenly divided on opinion
– Data modeling extends into the implementation-oriented
Logical Data Model stage
– Database design methods used in practice support the
design paradigm
– Data modeling product variation supports a design
paradigm with many possible models, plus there are
effects of training and personal modeling stylees

From Simsion, Graeme (2007). Data Modeling: Theory and Practice. p.326-3xxx.

About Data Modeling
• Description/Design Issue Implications for FRBR
– Expect FRBR data modeling efforts to encounter similar
issues
– In compensation, develop an approach that allows theory
to guide (but not dictate) FRBR design efforts
• Design data structures that meet requirements
• Test data models - as Paper Tools - in theory-driven scenarios,
and allow each to mutually inform and creatively correct one
another
–Employ multiple sources for theory
–Employ data modeling conventions and patterns

From Simsion, Graeme (2007). Data Modeling: Theory and Practice. p.326-3xxx.

A Simplifying Abstraction:
Resource Diagram Drawing Conventions


Vertex/Node


A Resource


A Resource

A Named
Resource
(Resource Plus
Minimal Description:
ID and Name)

A “Backbone” for
Optional Resource
Descriptions


A Resource

A Named
Resource
(Resource Plus
ID and Name)

Optional Resource
Optional Resource
Descriptions
Descriptions


A Resource

Four Different Kinds
of Descriptions are A Named
Associated With This Resource
Resource (Resource Plus
ID and Name)

Optional Resource
Optional Resource
Descriptions
Descriptions


It’s Convenient to Group Descriptions
Logically, Changing the Shape of the
Resource Holder as Needed
(e.g., library vs. archive vs. museum)

Resource Modeling
Via a Diagrammatic Method
• Things of interest in the world can be treated as
Resources
– Resources are represented by dots
• Resources must be described in order to be findable,
navigable, and accessible
– Resource descriptions (in attribute form, apart from the minimum) are
represented by color-coded boxes
• Different types of Resource descriptions can be defined
for the same Resource
– Co-occurring Resource description boxes are attached to a backbone

Resource Modeling
Via a Diagrammatic Method
• Relationships can be defined between Resources
– Labeled lines can be drawn between related Resource descriptions
• Diagram drawing and manipulation rules reflect relevant
attributes of real world Resources and their relationships
– Only certain entities and relationships can be defined and described
• Extension and/or modification of the drawing rules can
reveal Resource attributes and relationships that are not
apparent or impossible using the usual approaches
– Memory or legacy record-keeping system overload/failure is
eliminated by changes in representation and/or record-keeping
systems

FRBR-Centric Resource Modeling
Using a Diagrammatic Method
(A FRBR “Paper Tool”)
• What is a paper tool?
• Who uses a diagrammatic method like this?
• Why use a paper tool to reason about bibliographic
(etc.) relationships among resources?
• How do we use it?

The Precedent From Physics
Feynman Diagrams & Diagramming Rules†

† http://www2.slac.stanford.edu/vvc/theory/feynman.html. Kaiser, David. Drawing Theories Apart: The Dispersion of
Feynman Diagrams in Postwar Physics. Chicago, IL: University of Chicago Press. 2005.

Working With A Paper Tool
• Paper Tool† - A collection of symbolic elements (diagrams,
characters, etc.), whose construction and manipulation follow
rules and constraints of one or more guiding theories
– Paper tool manipulation permits rapid, flexible, and creative exploration of
phenomena of interest
– Paper tool/user dialogs can generate unprecedented manipulations, and
change the interests and goals of a modeling effort
– One can work theoretically as well as practically with a paper tool
• Examples abound in the Sciences
• We can use a paper tool as a bookkeeping device during resource
description (cataloging) and for FRBR theory formation and testing
• Proper paper tool design aids in specification of appropriate data
structures that meet user requirements for discovery and access

† Klein, Ursula (2001) ‘Paper Tools in Experimental Cultures’, Studies in History and Philosophy of Science 32: 265–302.

Working With Paper Tools

• Why use a paper tool for reasoning about bibliographic (or any
other) relationships among resources?
– Efficient presentation of entities, attributes, relationships, and business
rules
– Diagram construction can be heavily constrained by (FRBR) theory
• What levels of descriptions are appropriate?
• What relationships exist between Resources and/or descriptions?
• What emergent structural properties emerge from a given Resource/
description?
– Can validate obvious and non-obvious aspects of resource descriptions ahd
relationships by creating and validating simple and complex model
diagrams

Representing Bibliographic
Information: Prior Art

From flat-file record ...

Author: Lee, T. B.
Title: Cataloguing has a future
Content type: Spoken word
Carrier type: Audio disc
Subject: Metadata
Provenance: Donated by the author

Bibliographic description Name authority
Author: Name: Lee, T. B.
Title: Cataloguing has a future Biography:
...
Subject authority
Subject:
Term: Metadata
Provenance: Donated by the author Definition:
...

... to relational record

Name authority
Name: Lee, T. B.
Biography:
Work ...

Author:
Subject authority
Subject:
Term: Metadata
Expression
Definition:
...
Manifestation
Item
Provenance: Donated by the author ... to FRBR record

Information: Prior Art
• Simplifying abstractions center on the catalog card
–The text-bearing card becomes the information-
bearing record
• Card text becomes Resource attributes
• Card text becomes Resource relationships
–Catalog record evolution reflects theoretical &
pragmatic concerns
• More diverse record types (Name & Subject
Authorities)
• Assumption of hierarchical Resource structure
• Related Term (RT) cross-referencing employed as a
pragmatic access strategy

Information
Work Information
Author: Lee. T. B.
W
Subject: Cataloging -- Philosophy

E
Expression Information
Content type: Spoken Word M

I
Manifestation Information
Carrier type: Audiodisc

Item Information
Provenance: Donated by the author
All four kinds of FRBR data
are nested in a standard
information carrier that is
2
A catalog card “attached” to the Resource

FRBR Paper Tool Primer &
Example
The basic diagram element
represents a resource and the
overall description of that
resource

Work
Expression

Manifestation

Item

Example
A black-filled circle means
that a resource and a resource
description are both present. A
clear circle means that no
resource is present

Work
Expression

Manifestation

Item

Example

Work
Expression

Manifestation The color squares designate different
Item descriptions of the resource. In this
case, they reflect FRBR rules for
resource description.

Example

Work
Expression
Connections between descriptions are
Manifestation
made according to the rules for the
Item
point of view being represented.

Example

Work
Expression
Squares placed next to one another are
Manifestation
linked together by the appropriate
Item relationship. No lines are visible.

Example

Work
Expression
If a color square is solid, that means
Manifestation that a full resource description is
Item present.

Example

Work
Expression

Manifestation If a color square is hollow, that means
Item that this description points to one or
more descriptions of the same type. It
acts as a container.

Example
A container description must be linked to one
or more descriptions of the same Type. (This is
a Business Rule at work.)

In this example, an Item (acting as a container)
is composed of two other Items.

Work
Expression

Manifestation

Item

Has Part

Has Part

Example
In Item can act as a container because it is a
type of Resource. In our modeling of
bibliographic information, a Resource can be
composed of other Resources.

Resource subtypes like Item may inherit this
ability, depending on business rules.

Work
Expression

Manifestation

Item

Has Part

Has Part

Example
A Mildly Complex Example

A serial publication consists of a number of articles (one is
two-part) gathered into issues under a single journal title. Some
author, publisher, and other role-based information is known.
Only two subject headings have been assigned so far.
Work

In addition to routine issue publication, a number of articles
Expression

have been selected by the editors for a special issue on
Manifestation

Cosmology, as well as for an ongoing “Best Of” collection of
Item

articles.

Found on your bookshelf or your hard
drive

Some Resources are not described as
completely as others

Same as before, but with a serial
number/ID and your own name for
the Resource of interest assigned

What
publishers
can do:
group their
publications
by date

What
publishers
can do:
group their
publications
by date

What
publishers
can do:
group &
order
publications
by editorial
choice

What
libraries can
do: group
related but
editorially
distinct
publications
by publisher
and date

What libraries
can do: supply a
subject term for
an article

What libraries
can do: supply a
subject term for
an article

What libraries can do: supply
a controlled name for a
person, corporation, etc.
mentioned in or having to do
with an article

The subject
portion of this
network of
bibliographic
entities and
relationships
may seem
hierarchical
when viewed
in isolation,
(but anomalies
begin to appear).

Less
hierarchical
appearing are
the naming
sections of the
network of
bibliographic
entities and
relationships

When the entities and relationships are taken all together, the
network structure of this mildly complex conceptual data
model of a serial publication is readily apparent.

The ability to represent this serial publication diagrammatically is
dependent on FRBR theory’s ability to prescribe diagram elements and
construction rules in a conceptually valid fashion.

If significant aspects of the publication’s structure and content cannot be
expressed in the diagram, it is an indication that the theory needs work.

Just as in architectural or engineering design, management of complex data
model diagrams may require computerized assistance.

The ability to accept and use diagrammatic representations of FRBR
theoretical elements may be dependent on that party’s position on the
Description/Design Issue.

Catalogers may already be accustomed to a descriptive stance due to
personal inclination reinforced by professional training. Software
developers must take a design stance towards their work, and are already
conversant with diagrammatic representation.

Whether either group will be able to reason theoretically using diagrams (á
la Feynman) is an open question.

Working With Paper Tools:
Exemplars
• Exemplars† - A set of “typical” Resource and content description
scenarios, solutions to which encourage (a.) selection of the best
Paper Tool from available choices, (b.) the refinement of Resource
description skills, and (c.) the creation of conceptual and logical data
models that reflect Paper Tool capabilities
– A manuscript (individual and related multiples, published but host to history,
imaginary)
– A monograph in one edition (individual and related multiples)
– A monograph in multiple editions (individual and related multiples)
– A publication in multiple media
– A continuing publication (individual and related multiples publications, special
editions) network
– A library multimedia resource and resource description network
– A World Wide Web page and its underlying multimedia resource network
†Kuhn’s The Structure of Scientific Revolutions & Kaiser’s Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics

Archiveland, Libraryland, Webland and
Beyond: A Modern Mathematical Tale
• It is possible to adopt an Ethnomathematically informed
perspective on Cultural Heritage Resource description:
• Resource description in general and cataloging in particular
involves the construction of descriptive structures - entities with
attributes - and the definition of relationships between entities
• These descriptive structures can be represented in graph form - as
sets of nodes and links that represent Resources and Resource
relationships
• Resource description graphs display varying degrees of complexity
in terms of node and link quantities and types
- Graph-theoretical expressions of complexity can be given meaning
from a Resource description and cataloging theory point of view

We All Speak Prose Here: Graph Structures In
Resource Description And Access

• Define increasingly complex graph structures that
could represent bibliographic Resource
descriptions
• Indicate which combinations of graph structures
characterize different Cultural Heritage institutions
• Identify a number of graph characteristics that
could support a dimensional view on Resource
description graphs

Graph Type Graph Diagram Comments

A B A null graph consists of a set of nodes without
relationships: {{A B C D E F}, {Ø}}.
D
Null C
* Retrieval sets from Online Public Access Catalogs can
E F be represented as null graphs, accept Boolean operations
- and be ordered temporarily for display purposes.

* Nontrivial trees have at least two end nodes.
A D E F * The deletion of any tree link disconnects the tree.
* There is only one travel path between any two nodes in
Tree B C a tree.
(AKA A Connected B C
* Trees are minimally - most economically - connected
Acyclic Graph)
structures.
D E F A
* A forest is a graph whose components are trees
From Buckley & Lewinter (2003)

A D E F

Hierarchies are represented by tree graphs with arrowed
Directed Tree B C
B C links that specify the direction of a relationship.
(Hierarchy) * A polyhierarchy is a forest of hierarchies(?)
D E F A


Graph Type Graph Diagram Comments

The graph is separable into k non-
overlapping sets, based on a specified
A S2 S1 relationship.

This example illustrates a library graph
B C S4 S5 S6 S3

k-Partite separated into a bipartite graph by
D E F S4 S4
“subject_of” relationships (dashed links in
diagram) that link Subject Heading
Resource nodes (“S1”) and Managed
Named Resource nodes (“A”).

Multiple relationships (directional or
A H I
nondirectional) can exist between nodes.
B C G J K N

Network One or more travel paths can exist
D E F L M between any two nodes.

Networks can be richly connected

Shelfland Binland, Libraryland, & Beyond:
A Cautionary Tale About Resource
Description & Access Subcultures

• Shelfland - Resources aggregated without any attempt
at organization by Resource characterstic.
• Binland - Resources aggregated by one or more
Resource characteristics. Bins may be nested in other
bins.
• Archiveland - A Binland operated by a responsible
party, following established Resource collection,
binning, and preservation procedures.

Shelfland Binland, Libraryland, & Beyond:
A Cautionary Tale About Resource
Description & Access Subcultures

• Libraryland - Resources organized into bins,
hierarchies, and de-facto networks following one or
more “authoritative” set of cataloging rules.
Structured or unstructured reference Resources are
used to support access
• Webland - Resources organized into bins, hierarchies,
de-facto and explicit networks. Organization is
variable, because a Webland can contain one or more
of all of the other lands

Support of Resource Description And Access
A B

Shelf
D

Null C
- - -
E F

A B
A B
B G

Null, D

Bin - -
D L
K
C C I

Subgraphs E F H
M
O

N
E F

A B

Null,
A D E F
A B
B G

D

Archive - -
L

Subgraph
D K B C
C C I B C
O

Hierarchy
E F H
M N D E F A
E F

Null, A B
A B
B
G
A D E F A S2 S1

Subgraph D

Library -
D L B C S4 S5 S6 S3
K B C
C C I B C

Hierarchy, E F H
M
O

N D E F A
D E F S4 S4

E F
k-Partite

Null,
Subgraph A B

Hierarchy,
A D E F A S2 S1 A H I
A B
B G

D

Web
L B C S4 S5 S6 S3 B C G J K N

k-Partite,
D K B C
C C I B C
O

De-Facto &
E F H D E F S4 S4 D E F L M
M N D E F A
E F

Explicit
Network

Binland, Libraryland, Webland, & Beyond:
Levels of Graph-Friendly Resource
Description

• Weblanders, who are the most free in defining Resource
graphs do not view Libraryland as a highly informative but
graph-constrained Resource space
• Confusion in attribute and relationship definitions while data
modeling combine with institutional hierarchical
assumptions

• Librarylanders do not view Archiveland as a highly
informative but graph-constrained Resource space

Binland, Libraryland, Webland, & Beyond:
Levels of Graph-Friendly Resource
Description
• Librarylanders do not view Webland as a graph-enhanced
Resource space
• Institutional missions and systems available for
representation strongly shape reflect different institutional
assumptions and governance
• Authoritative control and user direction vs. distributed
creation, ownership, dissemination, and discovery
• Permitted nodes, attributes, relationships, and parties

• Archivelanders, Librarylanders and Weblanders all have
trouble viewing Binland as an informative but most strongly
graph-constrained space!
• Resource descriptions with few attributes

Archiveland, Libraryland, Webland and
Beyond: A Modern Mathematical Tale
• Resource description graphs in Cultural Heritage institutions
can be related to institutional and other factors that have guided
the creation, etc. of those structures
• As in Abbott’s Flatland, lack of awareness of a common
underlying structure threatens understanding and action
• It endangers efforts to make Resource descriptions created at one
level accessible to other levels.
• It reduces opportunities for parties working at one level of
Resource description to share experience and tools across levels
• It denies end-users improved and varied access to Resources

• Enlightenment becomes the ability to engage in Resource-oriented,
graph-theoretical thinking independently of institutional level

Placing The FRBR Data Model In A
Widening Context
• What kinds of “things of interest” are FRBR entities?
– Of what types or subtypes are they?
• Who else is out there creating information about
things that are of interest to us
– Where do our paths cross?
• Design Decisions
– Model FRBR entities as subtypes of a larger, more familiar
type of entity, as Resources
– Descriptions of resources can themselves be resources
– Business Rules constrain a more flexible data structure

The Conceptual Data Model
• Model Presentation
–Data model to be presented from FRBR “up”
–Model elements are introduced one at a time, in an
order that promotes assimilation of new element
function and relationship to existing elements
–Statements about the model should take the form of
“Business Assertions” that employ:
• Entity Names
• Entity Attributes
• Relationships
• Business Rules - Constraints applied to the model


Institutionally
Managed Named
Resource

Work Expression Manifestation Of Manifestation Item
Expressed As Exempliﬁed By
Manifest As
Expression Of Example Of


Institutionally
Managed Named
Resource

Work Expression Manifestation Item
C D Expressed As C D Manifest As C D Exempliﬁed By C D
Expression Of Manifestation Of Example Of


Institutionally
Managed Named
Resource


IFLA’s FRBR theory asserts that a Resource may be viewed and described from one
up to to four levels of abstraction: Work, Expression, Manifestation, or Item.

The FRBR specification indicates which Institutionally Managed Named Resource
attributes and relationships (plus others specific to that level of abstraction) constitute
each of these levels of description of a given Resource.


Described By
Institutionally Managed Named Resource Description Institutionally
Describes Managed Named
Resource

View In View In View In View In

Viewed As Viewed As Viewed As Viewed As



Described By
Resource


Viewed As Viewed As Viewed As Viewed As


An Institutionally Managed Named Resource Description is (ultimately) a Type of
Resource. This entity makes it possible to describe an Institutionally Managed
Named Resource by associating it with one or more of an institution’s customary
views of that Resource.

No customary view has a privileged or compulsory relationship with the
Institutionally Managed Named Resource. Incremental or incomplete resource (set)
descriptions can be created.


Described By
View In Resource


Viewed As Viewed As Viewed As Viewed As Viewed As Viewed As Viewed As Viewed As
Contained In
Fonds Series Contained In File Work Expression Manifestation Item Other View

Contains C D Expressed As C D Manifest As C D Exempliﬁed By C D
Contains
Contained In Contains
Contained In
Contains Viewed As

Annotation


Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation

While the more abstract combinations of attributes and relationships that define an
institution’s customary view on a Resource may not be shareable with another
institution’s, overlaps at less abstract levels are possible.

A set of ISAD(G) archival Resource views has been added to the bibliographic
views in the model, along with a general Annotation view, and an Other View.


Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation

One of these Other Views could be one or more
Physical Preservation views: combinations of (a.) physical measurements of one
or more Resources, (b.) statistical analyses of those measurements, and (c)
observations and judgments made on the Resource by a Conservator, Archivist,
Curator, etc.

Question: Physical Preservation views would co-occur with which of the FRBR/

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation

Institutionally Managed Find & Navigate Named Resource Description

Responsible Party
Identifying Authority Resource Aboutness Resource Description
Resource Description Resource Description

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
governor of Other Relationship Resource Description
Family

Controlled Rule
Access Point Corporate basis for/ Relationship/Rule
Controlled Body Formal Rule basis of Assignment
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
basis of Other basis of
Corporate
Body Relationship
Subject
basis for/ "Name"
basis of "Identifier"
Concept Other
Organization
Identification
Event
Name Computation

Object Other Responsible
Identifier Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Described By

Institutionally Managed Find & Navigate Resource Descriptions aid in Resource
View In Resource


discovery by providing identifiers, assigning standardized names, subjects, and

resource relationships.
Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Event
Name Computation

Identiﬁer Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Described By
View In Resource


An Identifying Authority Resource Description
Contained In

Contains

consists of a name or an identifier. One or more of these
Contained In
Contains Viewed As

Annotation

must be assigned to a Named Resource.

Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Event
Name Computation

Identiﬁer Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Described By

A Resource Aboutness Resource Description provides a subject term for a
View In Resource


Named Resource. The term must be a Concept, an Event, an Object, a Place, or
Viewed As
Contained In
Viewed As Viewed As Viewed As Viewed As Viewed As Viewed As Viewed As

another Resource.

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Event
Name Computation

Identiﬁer Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Described By

A Responsible Party Resource Description identifies parties (Persons, Families,
View In Resource


Corporate Bodies, etc.) who may (a.) play one or more roles with respect to a

Named Resource, or be the subject of a Named Resource.
Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Event
Name Computation

Identiﬁer Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

An Other Relationship Resource Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/

Description consists of any “other” Type of
governor of Agency
Family

Controlled Rule
Subject

relationship that one Named Resource may
Preferred
Agency
Informal Rule
Variant basis for/
basis for/
Corporate

have with another Named Resource. At
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation

least one relationship (“Creator”) is
Event
Name Computation

Identiﬁer

required for a Named Resource.
Party

Place

Resource
Other Managed
Find & Navigate
Named Resource
Description

Managed Named Resource

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identification
Has
Known By Event Relationship
Name Computation

Assigned Object The Other Responsible
Identifier Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

Institutionally Managed Find & Navigate Named Resource Assignment
Identifying Relationship Relationship
Institutionally Managed Institutionally Managed Institutionally Managed Other Managed
From To
Named Resource Identifier Named Resource Subject Named Resource Named Resource Other Managed
& Name Assignment Assignment Relationship Assignment Assignment Named Resource
Naming


Described By
View In Resource


Contained In

Contains

A Managed Named Resource is a Named Resource
Contained In
Contains Viewed As

Annotation

that is managed (ID’d, named, described, etc.) by one
or more Responsible Parties playing one or more

Roles such as “Creator,” “Cataloger,” “Curator,”
Identifying Authority
Resource Description

Rule
Resource Aboutness

Rule
Responsible Party

Person

“Repository,” etc.
Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Name Computation

Identiﬁer Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

From To
Naming

This Resource

Described By

assignment
View In Resource


grouping collects Viewed As

Fonds
Contained In
Viewed As

Series Contained In
Viewed As

File
Viewed As

C
Work
D Expressed As
Viewed As

Expression
C D
Viewed As

Manifestation
C D
Viewed As

C
Item
D
Viewed As

Other View

all of the link
Contains Contains Manifest As Exemplified By
Contained In
Contains Viewed As

Annotation

information made
possible by Institutionally Managed Find & Navigate Named Resource Description

institutionally
Responsible Party

Rule Rule Person

Organization
Corporate

managed reference
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Controlled Body Formal Rule basis of

data.
Assignment
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identification
Has
Name Computation

Identifier Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

From To
Naming

Grouping Resource

Described By

assignments like this
View In Resource


makes it possible to Viewed As

Fonds
Contained In
Viewed As

Series Contained In
Viewed As

File
Viewed As

C
Work
D Expressed As
Viewed As

Expression
C D
Viewed As

Manifestation
C D
Viewed As

C
Item
D
Viewed As

Other View

refer to (i.e., create,
Contained In
Contains Viewed As

Annotation

update and delete)
ID’s, names, parties- Institutionally Managed Find & Navigate Named Resource Description

in-roles, and
Responsible Party

Rule Rule Person

Organization
Corporate

relationships without
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule

changing the content
Assignment
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate

of any Resource.
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Name Computation

Identiﬁer Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

From To
Naming

Notice that two of

Described By

these
View In Resource


Institutionally Viewed As

Fonds
Contained In
Viewed As

Series Contained In
Viewed As

File
Viewed As

C
Work
D Expressed As
Viewed As

Expression
C D
Viewed As

Manifestation
C D
Viewed As

C
Item
D
Viewed As

Other View

Managed Named
Contained In
Contains Viewed As

Annotation

Resource
Assignments are Institutionally Managed Find & Navigate Named Resource Description

applied to an even
Responsible Party

Rule Rule Person

Organization
Corporate

simpler type of
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule

resource than the
Assignment
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate

Managed Named
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Known By

Resource.
Event Relationship
Name Computation

Identiﬁer Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

From To
Naming

This indicates that

Described By

identifier, subject
View In Resource


heading, Viewed As

Fonds
Contained In
Viewed As

Series Contained In
Viewed As

File
Viewed As

C
Work
D Expressed As
Viewed As

Expression
C D
Viewed As

Manifestation
C D
Viewed As

C
Item
D
Viewed As

Other View

responsible party,
Contained In
Contains Viewed As

Annotation

and relationship
lists are created Institutionally Managed Find & Navigate Named Resource Description

and maintained by
Responsible Party

Rule Rule Person

Organization
Corporate

institutions but are
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule

useable by any
Assignment
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate

non-institutional
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Known By

party.
Event Relationship
Name Computation

Identiﬁer Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

As Subject

From To
Naming

Named Resource

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identification
Has
Name Computation

Identifier Party
Subject Of

Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

Part Of
As Subject

Institutionally Managed Assigned Institutionally Managed Institutionally Managed Other Managed
From To
& Name Assignment Assignment Relationship Assignment Assignment Named Resource Has Part
Naming

Other Named
Identifies Relating Resource
Relating
Or Names From To

Type Of

Has Subtype Of Type

Type
Relationship Type
Other Relationship
Other Type Role Subject
Subtype Relationship Rule Type
Of

Named Resource

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation

A
Named Resource is a Resource that must be of one or more

Resource Aboutness
Responsible Party

Types. Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject

A Named Resource may be composed of one or more other
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject

Named Resources.
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Name Computation

Identiﬁer Party
Subject Of

A Type may be differentiated into one or more Subtypes.
Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

Part Of
As Subject

From To
Naming

Other Named
Relating
Or Names From To

Type Of

Has Subtype Of Type

Type

Types of Types are here
Relationship Type
Other Relationship
Of

Identifier, names and creator information are the most basic Resource
Named Resource

Described By

characteristics that can be assigned, and appear at this very general level.
View In Resource


Viewed As Viewed As Viewed As

Assigning an identifier to a Resource makes it uniquely distinguishable from
Viewed As Viewed As Viewed As Viewed As Viewed As
Contained In

Contains

other Resources. Assigning an name to a Resource renders it discoverable (but
Contained In
Contains Viewed As

Annotation

not necessarily uniquely) with a text-based search.

Business Rules for this data model deliberately limit Responsible Party-in-role

Rule
Resource Aboutness

Rule
Responsible Party

Person

assignments for a Named Resource to a “Creator” role only. This follows from a governed by/
governor of
governed by/
governor of
Organization
Corporate
Body
Agency
Family Other Relationship Resource Description

design assertion that “someone” who assigns more than a “Creator” role to a
Controlled Rule
Preferred Subject
Agency

Resource is either managing that Resource or knows someone who is.
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Name Computation

Additional roles can be assigned, from the Managed Named Resources level on
Assigned
Identiﬁer
Object The
Subject Of
Other Responsible
Party

down.
Place

Resource
Other Managed
Find & Navigate
Named Resource
In Description
Relationship

Part Of
As Subject

From To
Naming

Other Named
Relating
Or Names From To

Type Of

Has Subtype Of Type

Type
Relationship Type
Other Relationship
Of

Named Resource

Described By
View In Resource


Contained In

Contains
Contained In
Contains Viewed As

Annotation


Responsible Party

Rule Rule Person

Organization
Corporate
governed by/ Body
governed by/
governor of Agency
Family

Controlled Rule
Preferred Subject
Agency
Informal Rule
Variant basis for/
basis for/
Corporate
Body Relationship
Subject
basis for/ "Name"
Concept Other
Organization
Identiﬁcation
Has
Known By

Finally(!), allowing a Named Resource to be composed of
Event Relationship
Name Computation

Identiﬁer Party
Subject Of

one or more Named Resources follows a conceptual data modeling convention Place

for entities that may be composed of parts (that may be composed of parts...).
Resource
Other Managed
Find & Navigate
Named Resource
In Description

Business Rules limit its use to theoretically relevant situations.
Relationship

Part Of
As Subject

From To
Naming

Other Named
Relating
Or Names From To

Type Of

Has Subtype Of Type

Type
Relationship Type
Other Relationship
Of

The Role of Conceptual Data Modeling
In Cultural Heritage Institutions
• Definitions
– Conceptual, Logical, Physical, General
• About data modeling
– Modeling process, model, modeler
• Data models as “Paper Tools”
– Efficient reasoning about simple and complex models
• Data modeling examples
– FRBR entities are defined in the context of a Resource
• What to do now
– Revisit current modeling efforts; secure professional
involvement in the modeling process; build, lease, buy
modeling tools, training, education, taking leadership

The Graph Theoretical Library

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