The Graph Theoretical Library (Edited)

The Graph-Theoretic Libraryand The Role of Conceptual Data Modeling in

Cultural Heritage Institutions

Ethnomathematics

2002

1981

1991

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

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

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The Garden and GrovesBassin d’ApollonBosquet de l’EnceladeJardin du RoiSalle des MarronniersBosquet de la ColonnadeBosquet des DômesBassin du MiroirTapis vertBosquet de la GirandoleBosquet du DauphinBassin et parterre de LatoneSalle de BalBosquet des Bains d’ApollonParterre d’EauPièce d’Eau des SuissesBosquet des Trois FontainesBassin de NeptuneBassin du DragonOrangerie Parterre Sud Parterre NordBosquet de l’Arc de Triomphe

In townKing’s Kitchen Garden Academy of Equestrian Arts tel: 01 39 02 07 14

Tourist Office 2 bis, avenue de Paris78000 Versaillestel: 01 39 24 88 88

Baroque Music Centre (Hôtel des Menus Plaisirs)

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

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

From the Palace of Versailles to the end of the Grand Canal (3.5 km)60min. on foot

Horse-drawn carriagesFrom Tuesdays to SundaysTelephone: 01 30 97 04 40Fax: 01 30 97 04 44

Mini-trainA mini-train runs every day to the Trianon except in exceptional circumstances. Seats reserved for people with restricted mobility.Duration: 15min.

Telephone: 01 39 54 22 00Fax: 01 39 55 07 25

Electric carsSeveral visit circuits.Information: 01 39 66 97 66

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

Map X Y PicturePlanCB_07 85 354 IMG_1084.jpgPlanCB_07 64 310 IMG_1087.jpg

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The Garden and GrovesBassin d’ApollonBosquet de l’EnceladeJardin du RoiSalle des MarronniersBosquet de la ColonnadeBosquet des DômesBassin du MiroirTapis vertBosquet de la GirandoleBosquet du DauphinBassin et parterre de LatoneSalle de BalBosquet des Bains d’ApollonParterre d’EauPièce d’Eau des SuissesBosquet des Trois FontainesBassin de NeptuneBassin du DragonOrangerie Parterre Sud Parterre NordBosquet de l’Arc de Triomphe

In townKing’s Kitchen Garden Academy of Equestrian Arts tel: 01 39 02 07 14

Tourist Office 2 bis, avenue de Paris78000 Versaillestel: 01 39 24 88 88

Baroque Music Centre (Hôtel des Menus Plaisirs)

1

3 4

5 6

2

7

9 10

8

11

1312

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171819

20 21 22

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

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

From the Palace of Versailles to the end of the Grand Canal (3.5 km)60min. on foot

Horse-drawn carriagesFrom Tuesdays to SundaysTelephone: 01 30 97 04 40Fax: 01 30 97 04 44

Mini-trainA mini-train runs every day to the Trianon except in exceptional circumstances. Seats reserved for people with restricted mobility.Duration: 15min.

Telephone: 01 39 54 22 00Fax: 01 39 55 07 25

Electric carsSeveral visit circuits.Information: 01 39 66 97 66

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

But Wait: What if you want to better document or to relate significant aspects

of the creative expressions to one another, and not

just to the map?

Thinking About Versailles

A Further Simplifying Abstraction: The Versailles Graph

We can create a mathematical expression of the relationships between the Versailles Gardens and the creative expressions inspired by them.



This set of creative expressions would be called a Graph.



We construct a set of nodes (AKA vertices) and a set of edges (AKA links) that define one or more types of relationship between the nodes.

This set of creative expressions would be called a Graph.




In this example, the nodes represent locations within the gardens. The links represent a “next_to” relationship between two garden locations.




A graph may be visualized as a network of dots and lines (sometimes arrowed)



A graph diagram can be manipulated to show relationships more clearly

Thinking About Mazes

A Simplifying Abstraction: From Maze to Maze Graph

Data Modeling in General

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

Thinking About Mazes and Formal Gardens

Abstract, Refine, Generalize, Pose Questions


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


Is there a set of vertices and edges (a subgraph shape) within the Versailles graph

that matches the Hampton Court Maze?

• 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


Vertex/Node


A Resource


A NamedResource(Resource Plus

Minimal Description: ID and Name)

A “Backbone” for Optional Resource

Descriptions

A Resource




Optional Resource Descriptions


Descriptions

A Resource




Optional Resource Descriptions


Descriptions

Four Different Kindsof Descriptions are

Associated With This Resource

A Resource


It’s Convenient to Group Descriptions Logically, Changing the Shape of the

Resource Holder as Needed(e.g., library vs. archive vs. museum)

Resource ModelingVia 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 ModelingVia 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 ModelingUsing 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 PhysicsFeynman 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.

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• 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 A Paper Tool

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

Author:

Title:

Content type:

Provenance:

Subject:

Lee, T. B.

Cataloguing has a future

Spoken word

Audio disc

Metadata

Donated by the author

Carrier type:

From flat-file record ...

Author:

Title:

Content type:

Provenance:

Subject:

Lee, T. B.Cataloguing has a future

Spoken word

Audio disc

MetadataDonated by the author

Carrier type:

... to relational record

Name:Biography:...

Name authority

Term:Definition:...

Subject authority

Bibliographic description

Title:

Provenance:

Lee, T. B.

Cataloguing has a futureAudio disc

Metadata

Donated by the author

Carrier type:

... to FRBR record

Name:Biography:...

Name authority

Term:Definition:...

Subject authority

Item

Manifestation

Author:

Content type:

Subject:

Spoken wordExpression

Work

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

2

Provenance: Donated by the authorItem Information

Title:Carrier type: Audiodisc

Cataloguing has a futureManifestation Information

Content type:Expression Information

Spoken Word

Author:Subject:

Work InformationLee. T. B.Cataloging -- Philosophy

All four kinds of FRBR data are nested in a standard information carrier that is “attached” to the Resource

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A catalog card

Expression

Manifestation

Item

Work

FRBR Paper Tool Primer & Example

The basic diagram element represents a resource and the overall description of that resource

Expression

Manifestation

Item

Work


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

Expression

Manifestation

Item

Work


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

Expression

Manifestation

Item

Work


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

Expression

Manifestation

Item

Work


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

Expression

Manifestation

Item

Work


If a color square is solid, that means that a full resource description is present.

Expression

Manifestation

Item

Work


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

Expression

Manifestation

Item

Work


Has Part

Has Part

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.

Expression

Manifestation

Item

Work


Has Part

Has Part

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.

Expression

Manifestation

Item

Work


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.

In addition to routine issue publication, a number of articles have been selected by the editors for a special issue on Cosmology, as well as for an ongoing “Best Of” collection of articles.

Found on your bookshelf or your hard drive

Some Resources are not described as completely as others

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

What publishers can do: group their publications by date

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

What publishers can do: group their publications by date

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

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

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

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

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

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

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

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

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

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

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

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

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

• 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

Working With Paper Tools:Exemplars

†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


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Graph Type Graph Diagram Comments

Null

A null graph consists of a set of nodes without relationships: {{A B C D E F}, {Ø}}.

* Retrieval sets from Online Public Access Catalogs can be represented as null graphs, accept Boolean operations - and be ordered temporarily for display purposes.

Tree(AKA A Connected

Acyclic Graph)

* Nontrivial trees have at least two end nodes.* The deletion of any tree link disconnects the tree.* There is only one travel path between any two nodes in a tree.* Trees are minimally - most economically - connected structures.* A forest is a graph whose components are treesFrom Buckley & Lewinter (2003)

Directed Tree(Hierarchy)

Hierarchies are represented by tree graphs with arrowed links that specify the direction of a relationship.* A polyhierarchy is a forest of hierarchies(?)


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Graph Type Graph Diagram Comments

k-Partite

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

This example illustrates a library graph separated into a bipartite graph by “subject_of” relationships (dashed links in diagram) that link Subject Heading Resource nodes (“S1”) and Managed Named Resource nodes (“A”).

Network

Multiple relationships (directional or nondirectional) can exist between nodes.

One or more travel paths can exist 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

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Shelf Null - - -

Bin Null, Subgraphs - -

ArchiveNull,

Subgraph Hierarchy

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LibraryNull,

Subgraph Hierarchy, k-Partite

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Web

Null, Subgraph Hierarchy, k-Partite,

De-Facto & 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

The Graph Theoretical Library (Edited)

Technology

Transcript of The Graph Theoretical Library (Edited)