Conceptual Modeling with Description Logics

1
Conceptual Modeling with Description Logics
Nadzeya Kiyavitskaya Department of Information
and Communication Technology University of
Trento June 2003
2
References

• A. Borgida, R. J. Brachman.
• Conceptual Modelling with Description Logics
• Description Logic Handbook
• edited by F. Baader, D. Calvanese,
• D.L. McGuinness, D. Nardi, P.F. Patel-Schneider
• Cambridge University Press, 2002
• pages 359-381

3
Outline

• Introduction
• Background
• Elementary DL modeling
• Individuals in the world
• Concepts
• Subconcepts
• Modeling relationships
• Modeling ontological aspects of relationships
• A conceptual modeling methodology
• The ABox modeling specific states of the world
• Conclusions

4
Introduction

• Main goals
• Understand the issues involved in developing
  ontology for some universe of discourse, which is
  to become a conceptual model or knowledge base
  represented and reasoned with Description Logics
• Review the purposes of conceptual modeling
• Illustrate on example an approach to conceptual
  modeling
• Consider ontological issues nature of
  individuals, concept specialization, non-binary
  relationships, materialization

5
Background

• Conceptual model is abstraction or
  simplification of reality
• Information modeling construction of
  computer-based symbol structures that model some
  part of the world
• Information bases generalized term from terms
  of databases and knowledge bases
• Universe of discourse (UofD) the part of real
  world being modeled by an information base
• Models abstract away irrelevant details, and
  allow more efficient examination of current, past
  and projected states of UofD
• Conceptual models are more expressive facilities
  for modeling application directly and naturally,
  for structuring information bases

6
Background (continue)

• Conceptual models are important in
• Artificial intelligence programs
• Design of database systems
• Requirements engineering
• Object-oriented software
• Important abstractions
• Aggregation - thinking of objects as wholes
• Classification - abstracting away the detailed
  differences between individuals
• Generalization - abstracting the commonalities of
  several classes into a superclass
• Benefits of abstraction
• It results in a structured information model,
  which is easier to build and maintain

7
Elementary Description Logics modeling

• Conceptual models ontology includes
• individual objects
• relationships
• classes
• Complex descriptions can be built from elementary
  ones atomic concepts and atomic roles -
  inductively with concept constructors
• Class (concept) a description gathering the
  common properties among a collection of
  individuals
• (unary predicate ranging over domain of
  individuals)
• Roles inter-relationships between individuals
• (binary relations over the domain of
  individuals)

8
Elementary Description Logics modeling (continue)

• Binary relationships are modeled using roles and
  attributes
• lentTo(BOOK23, GIANNI)
• hasBorrowed(GIANNI, BOOK23)
• Important to distinguish between
• Functional relationships (lentTo) called
  attributes or features
• Non-functional relationships (hasBorrowed)
• Attributes can be
• Total (ISBN-Nr)
• Partial (lentTo)
• Constructor the for total attributes
• (the p C) equivalent to conjunction of
• (all p C), (at-most 1 p), (at-least 1 p)

9
Elementary Description Logics modeling (continue)

• Individuals are grouped into classes (Book), that
  abstract out common properties
• Classes are modeled by concepts,
• the common properties are expressed as
  subsumption axioms
• Example
• Book (and Material (the callNr Integer))
• Books are materials, whose callNr is an integer
• Borrower (all hasBorrowed Book)
• Borrower is someone who can borrow a book
• Borrower (and (all hasBorrowed Book)
• (at-least 1 hasBorrowed) )
• Borrower is defined as someone who has borrowed
  books

10
Individuals in the world

• Individuals have an identity, which allows them
  to be distinguished from one another and counted
• Certain notion can be modeled as individual, or
  as concepts
• General heuristics
• If we expect notions to be counted, they must be
  modeled as individuals
• Notions that do not have an inception time are
  modeled as concepts
• Values vs. objects
• Individual objects John, Mary,
• Values strings, integers, lists, tuples,
• Individuals vs. references to them
• Individual Gianni
• Reference card holder number 32225
• Objects should remain related, if names are
  changed

11
Concepts

• Classes are modeled using atomic/primitive
  concepts
• Same individual may be instance of multiple
  classes, without one being necessarily subclass
  of another
• Important DL feature for classifying taxonomy -
  ability to distinguish between primitive and
  defined concepts
• Essential vs. incidental properties of concepts
• Option 1 being hardcover is part of the
  definition
• BookOnLoan (and Book (at-least 1 lentTo)
• (fills binding hardcover) )
• Option 2 being hardcover is an additional
  necessary condition
• BookOnLoan (and Book (at-least 1 lentTo))
• BookOnLoan (fills binding hardcover)
• Being hardcover is incidental property of
  the book on loan

12
Concepts (continue)

• Reified concepts and meta-roles capture
  aggregate information
• Creation of meta-individual in order to associate
  information with an entire concept, rather than
  with each of its individual instances
  (numberOfBooks)
• Concepts dependent on relationships
• Some concepts stand on their own (Book)
• Other concepts rely on the implied existence of
  some relation (Borrower)
• Corresponding binary relationship must be
  explicitly introduced

13
Subconcepts

• Specialized subconcepts representing subsets of
  individuals are also of interest
• Material could be Book, Journal, Videotape,
• Book may have subconcepts Monograph,
  EditedCollection, Proceedings,
• Borrowers may be Institutions or Individuals,
  with latter divided into Faculty, Student, Staff
• Disjointness of subconcepts
• Usually subclasses are disjoint from each other

14
Subconcepts (continue)

• Disjointness can be modeled
• By adding the complement of one concept to the
  necessary properties of the other
• Book not Journal
• By naming discriminator a special declaration
  operation for primitive subclasses
• Print (disjointPrim Material in group medium
  with discriminant paper)
• Video (disjointPrim Material in group medium
  with discriminant light)
• Audio (disjointPrim Material in group medium
  with discriminant sound)

15
Subconcepts (continue)

• Covering by subconcepts
• Circulating (or ShortTerm LongTerm)
• Circulating (or ShortTerm LongTerm)
• Defined vs. primitive concepts
• Circulating Material
• NonCirculating (and ShortTerm LongTerm)
• By joining covering and disjointness we get
  partitioning of a class by some group of
  subclasses
• Book (the format (one-of 'monograph
  'journal 'editedCollection))
• Monograph (and Book (fills format 'monograph))
• Journal (and Book (fills format 'journal))
• EditedCollection (and Book (fills
  format 'editedCollection))

16
Subconcepts (continue)

• Dynamics of (sub)concept membership
• Concepts may represent inherent properties of
  objects that do not change over time - rigid
  (Book)
• Concepts may represent more transient properties
  (MisplacedBook)
• Transient property can be a subconcept of rigid
  one but not vice versa
• The structure of the subconcept hierarchy
• A concept whose instances may cease to be
  instances at some point in the future (Student)
  cannot subsume a concept whose membership cannot
  change (Person)

17
Modeling relationships

• Binary relationships are modeled using roles and
  attributes
• Constraints expressed about relationships
• Cardinality constraints min and max number of
  objects
• Domain constraints kinds of objects
• Inverse relationships between roles need to be
  recorded
• Library (and (all hasOnLoan Material)
  (all hasAvailable Material) (all hasMissing
  Material) )
• Constructor to make roles non-overlapping
• (non-overlapping hasOnLoan hasAvailable)

18
Modeling relationships (continue)

• Reified relations - useful to define properties
  of properties
• Loan (and (the lentTo Borrower)
• (the onLoan Material)
• (the lentOn Date)
• (the dueOn Date)
• (the NrOfRenewals (max 3)))
• Relationship class Loan has attributes onLoan,
  lentTo, lentOn, dueOn
• Role hierarchies two roles on the same concept
  may be related by the constraint that every
  filler of the first role must be a filler of the
  second role (support a role taxonomy - subroles)
• hasOnShortTermLoan hasBorrowed

19
Modeling ontological aspects of relationships

• Important distinction between objects that may
  participate in a relationship and the objects
  that actually do take part in one or more
  relationships
• Objects participating in a relationship can be
  said to be playing certain roles
• DL allow to define relationship-roles roles
  associated with relationships
• LentObject (at-least 1 borrowedBy)
• Borrower (at-least 1 (inverse
  borrowedBy))
• Materialization relationship between a general
  notion and 0-to-N more specific notions

20
Modeling ontological aspects of relationships
(continue)

• Example
• Book (and . . .
• (all hasAuthors Person) (the hasTitle String))
• Books have information about authors, etc.
• BookEdition (and . . .
• (the publishedBy PublishingCompany)
• (the isbnNr IsbnNumber)
• (the format (one-of 'printed 'audio)))
• Editions of books are related to the book but
  have their own roles too
• BookCopy (and . . .
• (the callNr CallNumber)
• (the atBranch LibraryBranch))
• Book copies are related to book editions, and in
  turn have their own roles

21
Modeling ontological aspects of relationships
(continue)

• Materialization relationship can be modeled by
  creating subroles of general role
  materializationOf
• editionOf materializationOf
• copyOf materializationOf
• editionfOf and copyOf is a kind of
  materialization relationship
• BookEdition (the editionOf Book)
• BookCopy (the copyOf BookEdition)
• Book editions are materializations of books
• Book copies are materializations of book editions
• Often the properties of more abstract concept are
  inherited by the materialization
• BookEdition (same-as hasTitle
  (editionOf?hasTitle))

22
Modeling ontological aspects of relationships
(continue)

• Part-whole aggregation
• Kinds of wholes and their parts
• Complexes gt components
• Collections gt members
• Masses gt quantities
• Furthermore parts can be
• Portions (sharing intrinsic properties with the
  whole)
• Segments
• Nature of aspects between parts and wholes
• Existence whole may depend on particular
  individual for its existence and identity, or
  generically on a class of parts part may depend
  on the whole for existence, may belong
  exclusively to one whole or might be shared
• Properties may be inherited from the whole to
  part, or from the part to whole

23
Modeling ontological aspects of relationships
(continue)

• Part-whole aggregation
• Dealing with topics, exploiting various
  role-forming operators
• Role hierarchies
• Role inverse
• Transitive closure
• Special roles are introduced for the different
  kinds of part-whole relationships (hasDComponent,
  hasDMember, hasDsegment, hasDQuality, hasDStuff,
  hasDIngridient)
• Inheritance of properties is modeled in the
  manner of materialization
• But such representations may result in a quite
  expressive language for which subsumption is
  undecidable

24
Modeling ontological aspects of relationships
(continue)

• General constraints - characterize valid states
  of the world
• dueDate of a book must be later than lentOn date
• are not expressible in standard DLs, due to
  limited expressive power
• Views and contexts - various views of the
  information seen by different stakeholders and
  participants
• MaterialInLibrary in interest of staff to find
  a book
• MaterialOnLoan in interest of borrower
• Replacing binary relationship having attributes
  by two views is restricted to appear in at most
  one tuple
• every book can be loaned to at most one borrower

25
Conceptual modeling methodology

• Main steps of modeling
• Identify the individuals in the UofD
• Enumerate concepts that group these values
• Distinguish independent concepts from
  relationship-roles
• Develop a taxonomy of concepts
• Identify any individuals of interest in all
  states of the world
• Search for part-whole relationships between
  objects, creating roles for them
• Identify other properties of objects, and then
  general relationships, in which object
  participate
• Determine local constraints
• Determine more general constraints on
  relationships
• Distinguish essential from incidental properties
  of concepts, as well as primitive from defined
  concepts
• Consider properties of concepts to simplify
  taxonomy

26
The ABoxmodeling specific states of the world

• DL systems do not make close-world assumption gt
• Membership of individual in concepts
• definitely yes
• definitely no
• unknown
• Individuals may not recognized as satisfying
  definitions
• BOOK22 has author SHAKESPEARE, which is instance
  of Englishman gt BOOK22 is instance of class (all
  hasAuthor Englishman)
• To deal with clear distinction between the state
  of the world and our knowledge of it we need some
  form of epistemic operator (known)
• (and Book (at-most 0 isbnNr)) ?!
• UnknownIsbnBook (and Book
• (at-most 0 (known isbnNr)))

27
Conclusions

• Strengths of DLs in representing this conceptual
  model
• dealing with primitive and defined concepts,
  necessary and sufficient conditions for concept
  specification, and the treatment of roles as
  first-class citizens in subclasses and
  composition
• Weaknesses of DLs in representing this conceptual
  model
• difficulty in representing (structured) values,
  constraints related to the dynamic aspects of the
  domain, certain forms of inheritance, and
  meta-information
• The biggest problem in developing an appropriate
  conceptual model for a domain
• testing it for correctness and completeness