Giancarlo Guizzardi Ontological Foundations for Structural Conceptual Models

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Giancarlo GuizzardiOntological Foundations for
Structural Conceptual Models

• Kapitel 5 Parts and Wholes, vorgestellt von
  Birgit Demuth
• am 06.12.2006

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Starting Point

• Parthood
• can be traced back to the early days of
  philosophy
• relation in all conceptual/OO languages
• modeling primitive for semantic web languages???
• only intuitively understood
• still much disagreement in axiomatization of this
  notion
• fundamental part of any foundational ontology
• Mereology
• theory of parts (meros part, Lesniewsky 1927)
• multiple mereological theories
• Guizzardi
• we need a theory of parts and a theory of wholes
• roles that parts play within a whole (secondary
  characteristics)
• concentrate on part-whole relations between
  substantials

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Hierarchy of Mereological Theories

• General Extensional Mereology (GEM)
• Closure Minimal/Extensional Mereology (CMM/CEM)
• Extensional Mereology (EM)
• Minimal Mereology (MM)
• Ground Mereology (M)

Classical Merology
Extensional Mereology
Core Concepts
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Core Concepts

• Ground Mereology (M)
• core of any theory of parts
• Based on (strict) partial ordering
• proper part relation
• x is not a part of itself
• if x is part of y then y is not part of x
• If x is part of y and y is part of z then x ix
  part of z
• Minimal Mereology (MM) M
• Weak supplementation principle Whenever an
  object has a proper part, it has more than one.

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Further Relations in Theories of Parts

• Overlapping
• Two objects overlap if they have a part in common
• Proper overlapping
• When two objects overlap but neither is a part
  of the other
• Disjointness
• Two objects are disjoint iff they have no parts
  in common.
• Atomism
• A mereological atom is an entity that has no
  proper parts.

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Extensional Mereology

• Extensional Mereology (EM) MM
• Strong supplementation principle If an object y
  is not a part of another object x then there is a
  part of y which does not overlap with x.
• Extensionality principle Two objects are
  identical iff they have the same (proper) parts.
• Closure Minimal/Extensional Mereology (CMM/CEM)
  EM/MM
• Closure operations
• Sum (mereological fusion, juxtaposition)
  ? union
• Product (superposition)
  ? intersection
• Difference
  ? set difference
• Complement
  ? complement of a set
• Uniqueness condition If two objects x and y
  overlap then there is a unique z that is composed
  of the common parts of x and y.

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Classical and Atomistic Mereologies

• General Extensional Mereology (GEM) (CMM/)CEM
• Unrestricted fusion/mereological sum z is the
  sum of the arbitrary non-empty set of objects
  such that a predicate F holds for all objects.
• __________________________________________________
  ___
• Atomism is orthogonal to any of the mereologies?
• Atomistic Mereologies
• admit finite models (decompositionof parts come
  to an end)
• important simplifications can be made to many of
  the axioms

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Problems with Mereologies in Conceptual Modeling

• Mereologies in conceptual modeling
• Sometimes too weak , sometimes too strong
• Transitivity often fails in conceptual modeling
• Notion of atoms is too coarse
• We need notions of atoms relative to a given
  context or level.
• Extensionality principle problem in EM
• There are several distinct principle of identity
  from a humans viewpoint.
• ? distinction between essential parts and not
  essential parts
• Problems in GEM
• Ontological extravagance (Objects that have no
  place in human cognition)
• Ontologically exuberant (too many objects in the
  domain)

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Theory of Integral Wholes

• Transitivity Problem in Conceptual Modeling
• Parthood relation does not consider the different
  roles that parts plays in a whole, e.g.
• Enschede is part of The Netherlands (ok)
• The Netherlands is part of the European Union
  (ok)
• Enschede is part of the European Union (fails)
• ? Theory of Integral Wholes (Simons, 1987)
• Many formal definitions
• Transitivity holds generally within a context.

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Secondary Properties of Part-Whole Relations

• Aspects of part-whole relations which are not
  taken into account in classical mereological
  theories
• Shareability
• exclusive part (strong type)
• exclusive part (weak type, Guizzardi)
• Seperability
• modal property (lifespan)
• based on ontological dependencies
• essential and mandatory parts,
• inseparable parts and parts with mandatory wholes

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Exclusive Part

• Strong type
  Weak type
• Exclusive part (Guizzardi)
• An object x of type A is an exclusive (proper)
  part of another object y of type B iff y is the
  only B that has x as part.

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Essential Parts

• Existential dependence
• An object x is existentially dependent on another
  object y iff y must exist whenever x exists.
• Essential part
• An object x is an essential part of another
  object y iff
• y is existentially dependent of x
• x is part of y

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Mandatory Parts

• Generic dependence
• An object y is generically dependent of a
  universal U iff, whenever y exists it is
  necessary that an instance of U exists.
• Mandatory part
• An object x is a mandatory part of another object
  y iff
• y is generically dependent of a universal U that
  x instantiates
• y has as a part an instance of U

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Inseparable Parts and Mandatory Wholes

• Inseparable part
• An object x is an inseparable part of another
  object y iff
• x is existentially dependent on y
• x is a part of y
• Mandatory whole
• An object y is a mandatory whole for another
  object x iff
• x is generically dependent on an universal U that
  y instantiates
• x is part of an object instantiating U

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Discussion

• Lessons learned
• exclusiveness in a weaker form (considering
  multiple roles of an object)
• dependency of a whole of a part
  (essential/mandatory parts)
• the generic dependence notion (mandatory
  parts/wholes)
• Composition in UML can be defined by inseparable
  and exclusive part relation (my interpretation!)
• Composition (UML reference manual, p 264ff) A
  strong form of aggregation with strong
  ownership of parts by the composite ??? and
  coincident lifetimes of parts with the composite
  essential and inseparable parts???. A part may
  be belong to only one composite at a
  time.Mandatory whole???
• Guizzardiss UML diagrams and UML interpretations
  are sometimes confusing and in my point of view
  partially false ? for example 5.13(b), 5.14(b)

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Parthood relations summarized(my UML
interpretation)
The whole is dependent of the part
The part is dependent of the whole
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Related Work

• Related Work in conceptual and object-oriented
  modeling
• Approach of Odell and Bock, 1998, Six Different
  Kinds of Composition
• The BWW Approach (Bunge-Wand-Weber ontology,
  2001)
• Part-whole theories in linguistic and cognitive
  sciences
• see 5.5
• A taxonomy of part-whole relations by
  WinstonChaffinHerrmann, 1987
• Focusing on the linguistic term of part-of, for
  example
• slice-pie versus tree-forest (slice is the
  same kind of thing as their whole versus tree is
  different from forest)

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The End

• Thank you for discussions!