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CS 2710, ISSP 2160

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CS 2710, ISSP 2160

Chapter 12

Knowledge Representation

- Last 3 chapters: syntax, semantics, and proof theory of propositional and first-order logic
- Chapter 12: what content to put into an agent’s KB
- How to represent knowledge of the world

- Some categories have strict definitions (triangles, squares, etc)
- Natural kinds don’t
- Define a cup (distinguishing it from bowls, mugs, glasses, etc)
- Bachelor: is the Pope a bachelor?
- But logical treatment can be useful (can extend with typicality, uncertainty, fuzziness)

- An ontology is similar to a dictionary but with greater detail and structure
- Ontology: concepts, relations, axioms that formalize a field of interest
- Upper ontology: only concepts that are meta, generic, abstract; cover a broad range of domain areas
- IEEE Standard Upper Ontology Working Group

Anything

AbstractObjects GeneralizedEvents

Sets Numbers RepresentationalObjects Interval Places PhysicalObjects Processes

Categories Sentences Measurements Moments things stuff

times weights animals agents solid liquid gas

Lower concepts are specializations of their parents

- I want to marry a Swedish woman
- Category of Swedish woman?
- A particular woman who is Swedish?

- Choices for representing categories: predicates or reified objects
- basketball(b) vs member(b,basketballs)
- Let’s go with the reified version…

- An object is a member of a category
- A category is a subclass of another category
- All members of a category have some properties (necessary properties)
- Members of a category can be recognized by some properties (sufficient properties)
- A category as a whole has some properties

- Before continuing: inspiration for creative reification!
- From Through the Looking Glass

- Two or more categories are disjoint if they have no members in common:
- Disjoint(s)( c1,c2 c1 s c2 s c1¹ c2 Intersection(c1,c2) ={})
Example:

Disjoint({animals, vegetables})

- Disjoint(s)( c1,c2 c1 s c2 s c1¹ c2 Intersection(c1,c2) ={})
- A set of s categories constitutes an exhaustive decomposition of a category c if all members of the set c are covered by categories in s:
- ExDecomp(s,c) ( i i c c2 c2 s i c2)
Example:

ExDecomp ({Americans, Canadians,Mexicans},NorthAmericans).

- ExDecomp(s,c) ( i i c c2 c2 s i c2)

- A partition is a disjoint exhaustive decomposition:
Partition(s,c) Disjoint(s) E.D.(s,c)

Example:

Partition({Males,Females},Persons)

- Is({Americans,Canadians, Mexicans},NorthAmericans)a partition?
- Categories can be defined by providing necessary and sufficient conditions for membership
x Bachelor(x) Male(x) Adult(x) Unmarried(x)

- partof(england,europe)
- All X,Y,Z ((partof(X,Y) ^ partof(Y,Z)) partof(X,Z))
- Heavy(bunchOf({apple1,apple2,apple3}))

- Often characterized by structural relations among parts.
E.g.

Biped(a)

- We covered Chapter 12 through 12.2.1