Categories and Objects

categories are an important aspect of general knowledge reasoning

strict kind categories – an object is a triangle iff it is a polygon with 3 sides
natural kind categories – have no clear cut definition

there are 2 choices for representing categories in first-order logic:

§  predicates (e.g. basketball(X))

§  objects (e.g. reify the category as an object, basketballs. and thus allows us to say member(X, basketballs) “X is a member of the category basketballs”)

categories can belong to sub-categories

taxonomy/taxonomic hierarchy – organization of categories and its subclasses
inheritance – an object or sub-category inherits the properties of the upper category 

disjoint – 2 or more categories are disjoint if they have no members in common
exhaustive decomposition – for example, if an animal is not male then it must be female
partition – a disjoint exhaustive decomposition

example of disjoint, exhaustive decomposition, and partition

Disjoint({Animals, Vegetables})ExhaustiveDecomposition({Americans,Canadians,Mexicans},NorthAmericans)Partition({Males,Females}, Animals)

Physical Composition

the idea that one object can be part of another

example of physical composition

part_of(bucharest, romania)part_of(romania, eastern_europe)part_of(eastern_europe, europe)part_of(europe, earth) part_of(x,y) ʌ part_of(y,z) → part_of(x,z)part_of(x,x)

composite objects – characterized by structural relations among parts

measurements – objects have height, mass, cost, and so on. the values that we assign for these properties are called measures

Substances vs Objects

individualization – division into distinct objects

Suppose I have some butter and an aardvark. I can say I have one aardvark, but there is no obvious number of butter. Any part of butter object is also a butter object. However if we cut an aardvark in half we don’t get 2 aardvarks unfortunately

count nouns – nouns that can be counted
mass nouns – nouns that cannot be counted

intrinsic properties – properties that belong to the very substance of the object, rather than the object as a whole (e.g. density, boiling point, flavor, color, ownership, etc)
extrinsic properties – properties that are not retained under subdivision (e.g. weight, length, shape, function, etc)

a class of objects that includes in its definition only intrinsic properties is then a substance or a mass noun
a class of objects that includes in its definition any extrinsic properties is a count noun

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