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Doctorate Course 2006-2007

Modeling in Knowledge Representation: the Parthood Relation Stefano Borgo LOA, ISTC, CNR Carola Eschenbach Hamburg University Laure Vieu IRIT, CNRS & LOA, ISTC, CNR. Doctorate Course 2006-2007. Questioning Classical Extensional Mereology.

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Doctorate Course 2006-2007

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  1. Modeling in Knowledge Representation: the Parthood RelationStefano Borgo LOA, ISTC, CNRCarola Eschenbach Hamburg UniversityLaure Vieu IRIT, CNRS & LOA, ISTC, CNR Doctorate Course 2006-2007

  2. Questioning Classical Extensional Mereology • Some mereotopologies reject even weak supplementation (Lectures 3&4) • Extensionality • Loosing or acquiring parts: identity across time • Identity between my body and the collection of my organs • Closure: sum of my nose and Caesar’s toe Fusion: even stranger scattered infinite sums • First move: mereotopology to identify “wholes”

  3. The transitivity puzzle • Counter-examples to the transitivity of mereological parthood? • My hand is part of me • I’m 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

  4. 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 ??

  5. 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 memberof the committee • the frontof the car • a cow from the herd • give me water, dammi dell’acqua • there is sugar in this syrup • a glass of water • chairs, two chairs, one of the chairs • Carola and Stefano

  6. 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 caketransitive • mass terms: mass nouns, universal grinder • cumulativity, dissectivity (?) • (another) mereology + substance universals [Parsons, Pelletier…] • Substance-Whole:  milk / this cappuccinotransitive • same theory and structure (+ mereotopology? + mereogeometry??) • Piece-Whole: the left half of this tabletransitive • 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

  7. car … monospace pick-up car … wheel engine carburettor 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??

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