The Graph Theoretical Library (Edited)

The Graph Theoretical Library (Edited)
The Graph-Theoretic Library and The Role of Conceptual Data Modeling in Cultural Heritage Institutions
Ethnomathematics 1991 2002 1981
Ethnomathematics Ethnomathematics is the study of the mathematical practices of specific cultural groups in the course of dealing with their environmental problems and activities • The prefix “ethno” refers to identifiable cultural groups, such as national-tribal societies, labor groups, children of a certain age bracket, professional classes, etc. and includes their ideologies, language, daily practices, and their specific ways of reasoning and inferring. • “Mathema” here means to explain, understand and manage reality specifically by ciphering, counting, measuring, classifying, ordering, inferring and modeling patterns arising in the environment. • The suffix “tics” means art or technique.
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
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
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
What publishers can do: group their publications by date
What publishers can do: group their publications by date What publishers can do: group & order publications by editorial choice
What libraries can do: group related but editorially distinct publications by publisher and date
What libraries can do: supply a subject term for an article
What libraries can do: supply a subject term for an article What libraries can do: supply a controlled name for a person, corporation, etc. mentioned in or having to do with an article
The subject portion of this network of bibliographic entities and relationships may seem hierarchical when viewed in isolation, (but anomalies begin to appear).
Less hierarchical appearing are the naming sections of the network of bibliographic entities and relationships
When the entities and relationships are taken all together, the network structure of this mildly complex conceptual data model of a serial publication is readily apparent.
The ability to represent this serial publication diagrammatically is dependent on FRBR theory’s ability to prescribe diagram elements and construction rules in a conceptually valid fashion. If significant aspects of the publication’s structure and content cannot be expressed in the diagram, it is an indication that the theory needs work. Just as in architectural or engineering design, management of complex data model diagrams may require computerized assistance.
The ability to accept and use diagrammatic representations of FRBR theoretical elements may be dependent on that party’s position on the Description/Design Issue. Catalogers may already be accustomed to a descriptive stance due to personal inclination reinforced by professional training. Software developers must take a design stance towards their work, and are already conversant with diagrammatic representation. Whether either group will be able to reason theoretically using diagrams (á la Feynman) is an open question.
Working With Paper Tools: Exemplars • Exemplars† - A set of “typical” Resource and content description scenarios, solutions to which encourage (a.) selection of the best Paper Tool from available choices, (b.) the refinement of Resource description skills, and (c.) the creation of conceptual and logical data models that reflect Paper Tool capabilities – A manuscript (individual and related multiples, published but host to history, imaginary) – A monograph in one edition (individual and related multiples) – A monograph in multiple editions (individual and related multiples) – A publication in multiple media – A continuing publication (individual and related multiples publications, special editions) network – A library multimedia resource and resource description network – A World Wide Web page and its underlying multimedia resource network †Kuhn’s The Structure of Scientific Revolutions & Kaiser’s Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics
Archiveland, Libraryland, Webland and Beyond: A Modern Mathematical Tale • It is possible to adopt an Ethnomathematically informed perspective on Cultural Heritage Resource description: • Resource description in general and cataloging in particular involves the construction of descriptive structures - entities with attributes - and the definition of relationships between entities • These descriptive structures can be represented in graph form - as sets of nodes and links that represent Resources and Resource relationships • Resource description graphs display varying degrees of complexity in terms of node and link quantities and types - Graph-theoretical expressions of complexity can be given meaning from a Resource description and cataloging theory point of view
We All Speak Prose Here: Graph Structures In Resource Description And Access • Define increasingly complex graph structures that could represent bibliographic Resource descriptions • Indicate which combinations of graph structures characterize different Cultural Heritage institutions • Identify a number of graph characteristics that could support a dimensional view on Resource description graphs
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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