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Modeling in Knowledge Representation: the Parthood Relation Stefano Borgo LOA, ISTC, CNR Carola Eschenbach 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 • Some mereotopologies reject even weak supplementation (Lectures 3&4) • 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” ICT School 2007 2

The transitivity puzzle • Counter-examples to the transitivity of mereological parthood? • My hand 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 ICT School 2007 3

Solutions? • Winston, Chaffin, Hermann 1987 • Not one, but several parthood relations: • 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) • What is ? ? ICT School 2007 4

Linguistic parthood expressions • • • the engine is part of the car the 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 dell’acqua there is sugar in this syrup a glass of water chairs, two chairs, one of the chairs Carola and Stefano ICT School 2007 5

Parthood relations that have been characterized • Member / collection: this cow / the 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 ICT School 2007 6

Meronomies (partonomies) • Taxonomic relation between universals (categories, lexical types) • • … “Parthood” Meronomies (partonomies) • Taxonomic relation between universals (categories, lexical types) • • … “Parthood” between universals, not individuals car Many interpretations: • • • car monospace Meronomic relations • • Set inclusion wheel all cars have an engine, all cars have wheels some engines have a carburettor all carburettors are part of an engine Which parthood? Transitivity? ? ICT School 2007 … pick-up engine carburettor 7