Concept Modeling in a World of Models by Arne Slvberg

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Concept Modeling in a World of ModelsbyArne
Sølvberg

• a world of models
• concepts and language
• concept models
• behaviour models
• model administration

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BW, W, AW
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Different life before and after W?

• BW- increasing number of people change from
  manual work to abstract work, abstract models are
  acquired through education
• W - a world of models, texts and pictures in
  cyberspace, used in relative ignorance
• AW - CSCW, democratic models, a life in
  abstractions, the reality is in the model and the
  model is perceived as the reality

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Information System and its UoD

• An information system is
• a body of signs, and
• the associated processes for storing and
  transforming the signs,
• and for exchanging signs with the exterior of
  the IS.
• The Universe of Discourse (UoD) is
• the domain of individuals referred to by the IS
• Each sign reflects some property of the UoD,
• or represent some property of the IS itself.

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Two research tasks, to find

• concepts for reflecting those features of the UoD
  that we want to represent in an information
  system.
• concepts for reflecting the features that are
  relevant to the formal processing of signs, as
  they are represented by data and programs in a
  computer

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Concept modeling and IS modeling

• concept modeling refers to the UoD, which is
  the world external to the information system.
• IS modeling refers to the modeling of the
  information systems itself, its processes and
  signs and their relations to the external world.
• concept modeling is part of IS modeling.

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Concept and term

• The concept is the unit of thought.
• The term is the unit of language.
• Theories, e.g., Newtons theory of motion, are
  structures of thoughts, and concepts like force
  and mass are the units of these thoughts
• Conceptual knowledge comes wrapped in signs,
  which are the linguistic expressions of knowledge
• In order to get access to the ideas of other
  people we have to understand the conceptual
  structures that are employed, and understand the
  relationship between the signs and the ideas that
  they stand for.

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The Triangle of Meaning
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Framework for IS modeling

• concept model
• data model
• workflow model
• (software model)

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Model quality evaluation framework
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Concept classification (thesaurus style)

• things and their physical parts, e.g. bird, car,
  mountain
• materials, e.g., water, steel, oxygen
• activities or processes, e.g., painting, golf
• events or occurrences, e.g., birthday, war,
  revolution
• properties or states of persons, things,
  materials or actions, e.g., elasticity, speed
• disciplines or subject fields, e.g., theology,
  informatics
• units of measurement, e.g., hertz, volt, meter

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Concept classification (science style)

• individual concepts
• class concepts
• relation concepts
• quantitative concepts
• specific versus generic concepts
• (linguistic versus non-linguistic concepts)

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Six classes of concepts
1 Individual Concepts (Newton, x) 2 Class
Concepts (copper, living, person)
/ Non-comparative (spouse,
between) 3 Relation Concepts -----
Comparative (?, better adapted than)
\ Operations (?, ) / Terms
(John, is a) 4 Linguistic concepts ----
Datatypes (name, integer) \
Datatype-extensions (personnel records,
project file) / Identifiers
(social-security-number) 5 Attribute
concepts ---- Descriptive concepts (first
name) \ Quantitative Concepts
(temperature, length) / State
(waiting for input) 6 Behaviour concepts ----
Event (input arrived) \ Process
(transform input to output)
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Basic notions in concept models

• intension
• extension
• reference
• class
• relation
• type
• attribute

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Intension, extension and reference

• The referents of a concept C are all individuals
  past,present and future which are classified as
  C-individuals
• the intension I(C) characterizes common
  properties of a concept Cs referents
• the extension E(C) are the referents that we know
  to exist past, present and future

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Class concept

• class is a set whose members share common
  properties
• two concepts are equal if they have the same
  intension and the same extension
• linguistic class concepts are formed from terms
• e.g., assume John is a person, and John is a
  name, then we have two concepts person and
  name where John?E(person) and John?
  E(name)
• for a computer the UoD consists of the linguistic
  units

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Relation concepts

• individual relation concepts
• class relation concepts, which are (unordered)
  sets of ordered sets (of ordered pairs)
• order concepts, which are ordered sets of ordered
  sets (of ordered pairs)
• operation concepts, which from members of a set
  yield another member of the same set

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Type

• type as a particular kind of set, e.g., x is
  of the type integers
• type as the relation concept type-of,
  relates concepts of different specificity, e.g.
  x is an integer, horse is a type of animal
• (type may be viewed to be the weak total order
  ? in the power set of the UoD)

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Individual concepts and class conceptsLinguistic
and non-linguistic concepts
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Attributes relate linguistic and non-linguistic
concepts
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Icons for relation concepts
Operation/ comparison
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Models of the bicycle-concept
generic individual concept
Class-level concept model
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Essential and contextual relations
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Nary relation concepts
supply
supply
supplies
part
project
project
supplier
part
supplier
1. Reification of nary relationship
2. nary relationship concept treated as a class
concept
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Corresponding concepts same designator
relation concept in extensional form
relation concept as mapping

• The term father designates two concepts
• the relation concept father-of, and
• the class concept fathers, that is, persons
  who are fathers

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Relation concept names
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E(parent) and E(child) are inverses
inverse
Definition by name
Definition by operation
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Operator and comparator concepts
Mutually exclusive subsets
Partition
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Non-commutative operations
ancestor
parent
Relational composition
Recursion
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Relation concepts uncle and aunt
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Family relation concepts
sis ter
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Relation properties
non-reflexive
irreflexive
reflexive
Reflexivity
asymmetric/ antisymmetric
symmetric
non-symmetric
Symmetry
transitive
non-transitive
intransitive
Transitivity
connex
Connexity

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Relation properties of various kinds of siblings
reflexive symmetric non-transitive
reflexive symmetric transitive
reflexive symmetric non-transitive
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Different sibling concepts
father
child
mother
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Concept of collections sets of sets
(calendar year,person)
same age
(equivalence relation)
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The concept of family
inverse
child
parent
sib ling
spouse
family
A family consists of persons who are related to
each other (parent, child, spouse,sibling) such
that each family-relation is connex, and every
person can belong to more than one family, e.g.,
spouses may share their children, but always have
different parents, and two families
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Data concepts

• data item the specific individual linguistic
  concept, the term, the value
• variable the generic individual linguistic
  concept
• data type a linguistic class concept, usually
  called type
• data set the extension of a linguistic class
  concept (a subset of the extension of a type)
• data base a set of data sets
• operation concepts selection, projection,
  reduction, nesting, unnesting, packing, unpacking

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Conceptual modeling through document analysis(1)
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Conceptual modeling through document analysis(2)
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Example

• Model-based classification
• Find words which correspond to a model concept
• make simple NL-sentences
• translate sentences to XML

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Behaviour models

• basic constructs state, event and process
• data processes are operations on data
• information processes deal with the interplay
  between data and people
• workflow processes take into account the
  human-human aspects in, e.g., negotiations, and
  the use of resources (software, people,
  databases) in process enactment.

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Facts and Ideas

• Facts are what is known -or assumed - to belong
  to reality
• Ideas are formally expressed as concepts,
  formulas (e.g., statements) and theories, which
  are systems of formulas
• Models are ideas

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Facts are usually distinguished in the following
kinds

• state - the properties of a thing at some time
• event - a change of state over a time interval
• process - a time-course of events
• phenomenon - an event or a process such as it
  appears to a human subject
• concrete system - a physical thing or entity,
  e.g., an electric field

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Workflow model, example
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Actor symbols and tool symbols
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Workflow essentials
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Model administration

• multi-site / multi-designer / multi-user
• product models
• model fragments
• versions and variants
• repositories

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Support system for co-operative system
development (system IGLOO)
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Internals of the product server
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Summing up

• IS formal theory needed to bring the IS field
  from pseudo-science to science
• democratic modeling facilities are needed
• conceptual modeling is at the core of this
  challenge