Modeling in Knowledge Representation: the Parthood Relation Stefano Borgo LOA, ISTC, CNR Carola Eschenbach Hamburg University Laure Vieu IRIT, CNRS

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Modeling in Knowledge Representation the
Parthood RelationStefano Borgo LOA, ISTC,
CNRCarola Eschenbach Hamburg UniversityLaure
Vieu IRIT, CNRS LOA, ISTC, CNR

• Doctorate Course
• 2006-2007

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Questioning Classical Extensional Mereology

• Some mereotopologies reject even weak
  supplementation (Lectures 34)
• Extensionality
• Loosing or acquiring parts identity across time
• Identity between my body and the collection of my
  organs
• Closure sum of my nose and Caesars toe Fusion
  even stranger scattered infinite sums
• First move mereotopology to identify wholes

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The transitivity puzzle

• Counter-examples to the transitivity of
  mereological parthood?
• My hand is part of me
• Im part of the ICT School Committee
• but
• My hand is not part of the Committee
• The handle is part of the door
• The door is part of the house.
• Is the handle part of the house?
• the handle of the house

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Solutions?

• Winston, Chaffin, Hermann 1987
• Not one, but several parthood relations
• component-integral object (handle-door,
  engine-car)
• member-collection (member-committee,tree-forest,
  cow-herd)
• portion-mass (slice-pie)
• stuff-object (steel-bike, sugar-bottle of syrup)
• feature-activity (paying-shopping)
• place-area (oasis-desert)
• Assumption that each relation is transitive and
  non-transitivities occur with mixed parthoods
• Simons, Varzi
• ?-Part(x,y) ?df P(x,y) ? ?(x,y)
• What is ???

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Linguistic parthood expressions

• the engine is part of the car
• the door has a handle
• this syrup is made of water and sugar
• the handle of the door
• a member of the committee
• the front of the car
• a cow from the herd
• give me ? water, dammi dellacqua
• there is ? sugar in this syrup
• a glass of water
• chairs, two chairs, one of the chairs
• Carola and Stefano

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Parthood relations that have been characterized

• Member / collection this cow / the cows, this
  cow / the herd not transitive
• count nouns / plurals collective terms.
• cumulativity
• atomic mereology constitution relation Link,
  Lønning
• Sub-collection / collection Benelux / EU (but
  not USA / NATO) transitive
• same theory and structure
• Portion-Whole ? water, a piece of cake
  transitive
• mass terms mass nouns, universal grinder
• cumulativity, dissectivity (?)
• (another) mereology substance universals
  Parsons, Pelletier
• Substance-Whole ? milk / this cappuccino
  transitive
• same theory and structure ( mereotopology?
  mereogeometry??)
• Piece-Whole the left half of this table
  transitive
• mereotopology
• Component-Integral Whole the handle / the door,
  the engine / my car
• function
• mereology (mereotopology) functional dependence
  lexical types Vieu
• 4 relations! complex pattern
  of transitivities

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Meronomies (partonomies)

• Taxonomic relation between universals
  (categories, lexical types)
• Set inclusion
• Meronomic relations
• Parthood between universals, not individuals
• Many interpretations
• all cars have an engine, all cars have wheels
• some engines have a carburettor
• all carburettors are part of an engine
• Which parthood?
• Transitivity??