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



1991




         2002




1981
Ethnomathematics



1991




         2002




1981
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.
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
Apprehending Versailles
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?
Representing Versailles

A Simplifying Abstraction: From Versailles to
the Versailles Map of Creative Expressions
Representing Versailles
A Simplifying Abstraction: From Versailles to
the Versailles Map of Creative Expressions
                                                                                                                     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

                                                                                                                                                                                                         From the Palace of Versailles
                                                                               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
Representing Versailles
A Simplifying Abstraction: From Versailles to
the Versailles Map of Creative Expressions
                                                                                                           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
                                                                                                                                                                                               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

                                                                                                                                                                                               From the Palace of Versailles
                                                                     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
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
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.
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
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.
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
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.
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
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.
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
Graph


                               A graph diagram can
                               be manipulated to
                               show relationships
                               more clearly
Thinking About Versailles

A Further Simplifying Abstraction: The Versailles
Graph
Thinking About Mazes

A Simplifying Abstraction: From Maze to Maze
Graph
Thinking About Mazes

A Simplifying Abstraction: From Maze to Maze
Graph
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
Thinking About Mazes and
     Formal Gardens
Is the Hampton Court maze transformable
 into a section of the Versailles Gardens?
Thinking About Mazes and
     Formal Gardens
    Is there a set of vertices and edges (a
subgraph shape) within the Versailles graph
  that matches the Hampton Court Maze?
Thinking About Mazes and
     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
• Why a Data Model is Important
  – 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
• Why a Data Model is Important
  – 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
A Simplifying Abstraction:
Resource Diagram Drawing Conventions

                               Vertex/Node
A Simplifying Abstraction:
Resource Diagram Drawing Conventions

                               A Resource
A Simplifying Abstraction:
Resource Diagram Drawing Conventions

                                   A Resource

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




                     A “Backbone” for
                     Optional Resource
                       Descriptions
A Simplifying Abstraction:
Resource Diagram Drawing Conventions

                                   A Resource

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




                     A “Backbone” for
 Optional Resource
                     Optional Resource
   Descriptions
                       Descriptions
A Simplifying Abstraction:
     Resource Diagram Drawing Conventions

                                         A Resource

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




                           A “Backbone” for
       Optional Resource
                           Optional Resource
         Descriptions
                             Descriptions
A Simplifying Abstraction:
Resource Diagram Drawing Conventions




        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:
                                                ...
 Content type: Spoken word
 Carrier type:   Audio disc
                                               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:
  Content type: Spoken word
                                                 ...
Manifestation
 Title:          Cataloguing has a future
 Carrier type:   Audio disc
Item
 Provenance:     Donated by the author      ... to FRBR record
Representing Bibliographic
      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
Representing Bibliographic
                     Information
Work Information
    Author: Lee. T. B.
                                                                         W
    Subject: Cataloging -- Philosophy

                                                                          E
Expression Information
    Content type: Spoken Word                                            M

                                                                          I
Manifestation Information
    Title: Cataloguing has a future
    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
Representing Bibliographic
                     Information
Work Information
    Author: Lee. T. B.
                                                                         W
    Subject: Cataloging -- Philosophy

                                                                          E
Expression Information
    Content type: Spoken Word                                            M

                                                                          I
Manifestation Information
    Title: Cataloguing has a future
    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
Representing Bibliographic
                     Information
Work Information
    Author: Lee. T. B.
                                                                         W
    Subject: Cataloging -- Philosophy

                                                                          E
Expression Information
    Content type: Spoken Word                                            M

                                                                          I
Manifestation Information
    Title: Cataloguing has a future
    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
FRBR Paper Tool Primer &
                    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
FRBR Paper Tool Primer &
                    Example




Work
Expression

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




Work
Expression
                        Connections between descriptions are
Manifestation
                        made according to the rules for the
Item
                        point of view being represented.
FRBR Paper Tool Primer &
                    Example




Work
Expression
                       Squares placed next to one another are
Manifestation
                       linked together by the appropriate
Item                   relationship. No lines are visible.
FRBR Paper Tool Primer &
                    Example




Work
Expression
                        If a color square is solid, that means
Manifestation           that a full resource description is
Item                    present.
FRBR Paper Tool Primer &
                    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.
FRBR Paper Tool Primer &
                    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
FRBR Paper Tool Primer &
                    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
FRBR Paper Tool Primer &
                    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
The Graph Theoretical Library (Edited)
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
The Graph Theoretical Library (Edited)
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 Graph Theoretical Library (Edited)
The subject
portion of this
network of
bibliographic
entities and
relationships
may seem
hierarchical
when viewed
in isolation,
(but anomalies
begin to appear).
The Graph Theoretical Library (Edited)
Less
hierarchical
appearing are
the naming
sections of the
network of
bibliographic
entities and
relationships
The Graph Theoretical Library (Edited)
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
We All Speak Prose Here: Graph Structures In
     Resource Description And Access
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
We All Speak Prose Here: Graph Structures In
     Resource Description And Access

  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
We All Speak Prose Here: Graph Structures In
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 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

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The Graph Theoretical Library (Edited)

  • 1. The Graph-Theoretic Library and The Role of Conceptual Data Modeling in Cultural Heritage Institutions
  • 5. 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.
  • 14. 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?
  • 15. Representing Versailles A Simplifying Abstraction: From Versailles to the Versailles Map of Creative Expressions
  • 16. Representing Versailles A Simplifying Abstraction: From Versailles to the Versailles Map of Creative Expressions 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 From the Palace of Versailles 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
  • 17. Representing Versailles A Simplifying Abstraction: From Versailles to the Versailles Map of Creative Expressions 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 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 From the Palace of Versailles 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
  • 18. Thinking About Versailles A Further Simplifying Abstraction: The Versailles Graph
  • 19. Thinking About Versailles A Further Simplifying Abstraction: The Versailles 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.
  • 20. Thinking About Versailles A Further Simplifying Abstraction: The Versailles 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.
  • 21. Thinking About Versailles A Further Simplifying Abstraction: The Versailles 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.
  • 22. Thinking About Versailles A Further Simplifying Abstraction: The Versailles 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.
  • 23. Thinking About Versailles A Further Simplifying Abstraction: The Versailles Graph A graph diagram can be manipulated to show relationships more clearly
  • 24. Thinking About Versailles A Further Simplifying Abstraction: The Versailles Graph
  • 25. Thinking About Mazes A Simplifying Abstraction: From Maze to Maze Graph
  • 26. Thinking About Mazes A Simplifying Abstraction: From Maze to Maze Graph
  • 27. Thinking About Mazes A Simplifying Abstraction: From Maze to Maze Graph
  • 28. Data Modeling in General • Definitions • About data modeling • Data models and “Paper Tools” • Data modeling examples (many!) • What to do now
  • 29. Thinking About Mazes and Formal Gardens Abstract, Refine, Generalize, Pose Questions
  • 30. Thinking About Mazes and Formal Gardens Is the Hampton Court maze transformable into a section of the Versailles Gardens?
  • 31. Thinking About Mazes and Formal Gardens Is there a set of vertices and edges (a subgraph shape) within the Versailles graph that matches the Hampton Court Maze?
  • 32. Thinking About Mazes and 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
  • 33. 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.
  • 34. 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?
  • 35. About Data Modeling • Why a Data Model is Important – 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
  • 36. About Data Modeling • Why a Data Model is Important – 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
  • 37. About Data Modeling • What Makes a Good Data Model? – Completeness – Nonredundancy – Enforcement of Business Rules – Data Reusability – Stability & Flexibility – Elegance – Communication – Integration
  • 38. 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.
  • 39. 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.
  • 40. 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.
  • 41. 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.
  • 42. 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.
  • 43. A Simplifying Abstraction: Resource Diagram Drawing Conventions
  • 44. A Simplifying Abstraction: Resource Diagram Drawing Conventions Vertex/Node
  • 45. A Simplifying Abstraction: Resource Diagram Drawing Conventions A Resource
  • 46. A Simplifying Abstraction: Resource Diagram Drawing Conventions A Resource A Named Resource (Resource Plus Minimal Description: ID and Name) A “Backbone” for Optional Resource Descriptions
  • 47. A Simplifying Abstraction: Resource Diagram Drawing Conventions A Resource A Named Resource (Resource Plus Minimal Description: ID and Name) A “Backbone” for Optional Resource Optional Resource Descriptions Descriptions
  • 48. A Simplifying Abstraction: Resource Diagram Drawing Conventions A Resource Four Different Kinds of Descriptions are A Named Associated With This Resource Resource (Resource Plus Minimal Description: ID and Name) A “Backbone” for Optional Resource Optional Resource Descriptions Descriptions
  • 49. A Simplifying Abstraction: Resource Diagram Drawing Conventions It’s Convenient to Group Descriptions Logically, Changing the Shape of the Resource Holder as Needed (e.g., library vs. archive vs. museum)
  • 50. 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
  • 51. 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
  • 52. 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?
  • 53. 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.
  • 54. 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.
  • 55. 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
  • 56. Representing Bibliographic Information: Prior Art
  • 57. 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
  • 58. Bibliographic description Name authority Author: Name: Lee, T. B. Title: Cataloguing has a future Biography: ... Content type: Spoken word Carrier type: Audio disc Subject authority Subject: Term: Metadata Provenance: Donated by the author Definition: ... ... to relational record
  • 59. Name authority Name: Lee, T. B. Biography: Work ... Author: Subject authority Subject: Term: Metadata Expression Definition: Content type: Spoken word ... Manifestation Title: Cataloguing has a future Carrier type: Audio disc Item Provenance: Donated by the author ... to FRBR record
  • 60. Representing Bibliographic 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
  • 61. Representing Bibliographic Information Work Information Author: Lee. T. B. W Subject: Cataloging -- Philosophy E Expression Information Content type: Spoken Word M I Manifestation Information Title: Cataloguing has a future 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
  • 62. Representing Bibliographic Information Work Information Author: Lee. T. B. W Subject: Cataloging -- Philosophy E Expression Information Content type: Spoken Word M I Manifestation Information Title: Cataloguing has a future 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
  • 63. Representing Bibliographic Information Work Information Author: Lee. T. B. W Subject: Cataloging -- Philosophy E Expression Information Content type: Spoken Word M I Manifestation Information Title: Cataloguing has a future 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
  • 64. FRBR Paper Tool Primer & Example The basic diagram element represents a resource and the overall description of that resource Work Expression Manifestation Item
  • 65. FRBR Paper Tool Primer & 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
  • 66. FRBR Paper Tool Primer & Example Work Expression Manifestation The color squares designate different Item descriptions of the resource. In this case, they reflect FRBR rules for resource description.
  • 67. FRBR Paper Tool Primer & Example Work Expression Connections between descriptions are Manifestation made according to the rules for the Item point of view being represented.
  • 68. FRBR Paper Tool Primer & Example Work Expression Squares placed next to one another are Manifestation linked together by the appropriate Item relationship. No lines are visible.
  • 69. FRBR Paper Tool Primer & Example Work Expression If a color square is solid, that means Manifestation that a full resource description is Item present.
  • 70. FRBR Paper Tool Primer & 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.
  • 71. FRBR Paper Tool Primer & 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
  • 72. FRBR Paper Tool Primer & 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
  • 73. FRBR Paper Tool Primer & 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.
  • 74. Found on your bookshelf or your hard drive
  • 75. Some Resources are not described as completely as others
  • 76. Same as before, but with a serial number/ID and your own name for the Resource of interest assigned
  • 79. What publishers can do: group their publications by date What publishers can do: group & order publications by editorial choice
  • 80. What libraries can do: group related but editorially distinct publications by publisher and date
  • 82. What libraries can do: supply a subject term for an article
  • 83. 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
  • 85. The subject portion of this network of bibliographic entities and relationships may seem hierarchical when viewed in isolation, (but anomalies begin to appear).
  • 87. Less hierarchical appearing are the naming sections of the network of bibliographic entities and relationships
  • 89. 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.
  • 90. 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.
  • 91. 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.
  • 92. 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
  • 93. 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
  • 94. 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
  • 95. We All Speak Prose Here: Graph Structures In Resource Description And Access 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
  • 96. We All Speak Prose Here: Graph Structures In Resource Description And Access 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
  • 97. 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.
  • 98. 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
  • 99. We All Speak Prose Here: Graph Structures In 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
  • 100. 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
  • 101. 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
  • 102. 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
  • 103. 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
  • 104. 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