Ontology Applying logic to the real world. D Goforth - COSC 4117, fall 20062 Real world knowledge...

OntologyApplying logic to the real world

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Real world knowledge

general knowledge /common sense reasoning

domain expertise /specific knowlege

problem /facts

example: understand a news reportlanguage and world knowledge; specific situation and terminology interpret story

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Ontology: structure of knowledge E.g. java programming ontology –

object-oriented design: class/object inheritance and interfaces part-of hierarchy API message-passing sequential execution, threads

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Ontology: structure of knowledge general knowledge: what top-level

structure? Anything

(like class Object)

AbstractObject(eternal)

GeneralizedEvent(time-limited existence)

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Upper Ontology

General knowledge

Domain knowledge

Problem facts and questions

Ontology in Knowledge base

“Abstract objects”

“Generalized events”

Categories (ontology)

Logic (sentences)

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Representing Knowledge how ‘deep’?

shallow – as predicate: Terrier(x)

deep ‘reification’category with meaning structure: Terriers ⊆ Dogs,

Dogs ⊆ Mammals Member (x, Terriers)

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Categories like set theory – easy to reason with

in FOL subcategories / subsets categories of categories intersections, unions, disjoint sets,

partitions

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Reasoning about categories disjoint subcategories – no common

objects NO: x Students, x Employed YES:x Mazdas, x Mercedes

x Mazdas ⇒ ~(x Mercedes) x Mercedes ⇒ ~(x Mazdas)

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Reasoning about categories exhaustive decomposition – all

objects of a category belong to at least one of the subcategories Namedstreets Cityroutes Numberedroads Cityroutes x Cityroutes ⇒ (x Namedstreets)

(x Numberedroads)(could be both named and numbered)

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Reasoning about categories Partitioning a category

subcategories are disjoint subcategories form exhaustive decompositione.g.,Players are teammates or opponents:Players = Teammates OpponentsTeammates Opponents = {}

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Physical objects properties

things – a pile of sand measurable / quantities

vs stuff - sand

intrinsic qualities

PhysicalObjects

StuffThings

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Situation calculus in specific domain

(TimedEvents vs AbstractObjects) some objects are ‘fluent’

functions and properties can change over time (position, orientation, etc)

some objects are ‘eternal’ existence and properties remain fixed

during period of reasoning (more efficient)(recall wumpus world example)

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GeneralizedEvents – the time problem

objects in this hierarchy have time property physical objects events processes intervals

‘fluent’ (“fleeting”) vs ‘eternal’ abstract objects

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Situation calculusuniverse is defined as

sequence of ‘situations’ ‘actions’ are like

inferences: preconditions – required

facts in current situation effects – facts that are

true in subsequent situation if action is applied

situa

tion

S 3

precondition effectaction

situa

tion

S 2

situa

tion

S 1

situa

tion

S 0

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Situation calculus - example blocks world

tabletop and three blocks actions and situations

A BC

eternal Table(x) Block(x)

fluent On(x,y,s) ClearTop(x,s)

s is situation variable

objects/terms in FOL

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Situation calculus - example actions are functions (objects) situations are objects

A BC

PutOn(x,y) preconditions:

ClearTop(x,s) ClearTop(y,s) V

Table(y) effect:

On(x,y,Result(PutOn(x,y),s))

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Situation calculus - example each situation is a function of the

previous one – Result function

A BC

Result(a,s) preconditions:

action a can be applied at s effect:

Result is next situation after a is applied at s

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T

Situation calculus - example e.g. KB:

function PutOn(x,y) ∀x (~∃y On(y,x,s)) ⇒ ClearTop(x,s) ∀x,y,s ClearTop(x,s) ^

(ClearTop(y,s) v Table(y) => On(x,y,Result(PutOn(x,y),s))

constants: A, B, C, T, S0, S1, S2,… Table(T), Block(A), Block(B), Block(C) On(A,B,S0), On(B,C,S0), On(C,T,S0)

ABC

S0

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T

Situation calculus - example action: PutOn(A,T)

preconditions: ClearTop(A,S0),Table(T) effect: On(A,T,Result(PutOn(A,T),S0))

BUT…what happens to other fluents?

some propagated, some not ABC

S1

A

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T

Situation calculus - example ‘On’ axiom: ∀x,y,z,a,s On(x,y,Result(a,s)) [ClearTop(x,s)^(ClearTop(y,s)vTable(y))^

a= PutOn(x,y)

v [ On(x,y,s)^~(a=PutOn(x,z))]

CS1

A

AB