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Knowledge Repr e sent at i on. Outline. G e n e ral o n to l og y Ca t e g o r i e s a n d ob j e c t s E ve n t s a n d p r o cess e s Re a s on i n g s y s t e m s I n t e rnet s h op pi n g w o rld S u mm ary. Ontologies.

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Knowledge repr e sent at i on

KnowledgeRepresentation


Outline

Outline

  • General ontology

  • Categoriesandobjects

  • Eventsandprocesses

  • Reasoningsystems

  • Internetshoppingworld

  • Summary


Ontologies

Ontologies

  • Anontologyisa “vocabulary”anda “theory”ofa

  • certain“partofreality”

  • Special-purposeontologiesapplytorestricted

  • domains(e.g.electroniccircuits)

  • General-purposeontologieshavewider applicabilityacross domains,i.e.

  • Mustincludeconceptsthatcovermanysubdomains

  • Cannot use special“short-cuts”(suchas ignoringtime)

  • Mustallowunificationofdifferent typesofknowledge

  • GPontologiesare usefulinwideningapplicability

  • ofreasoningsystems,e.g.byincludingtime


Ontological engineering

Ontological engineering

  • Representingageneral-purposeontologyisa

  • difficulttaskcalledontology engineering

  • ExistingGPontologieshavebeencreatedin

  • differentways:

  • Byteamoftrainedontologists

  • Byimportingconceptsfromdatabase(s)

  • Byextracting informationfromtextdocuments

  • Byinvitinganybodytoenter commonsenseknowledge

  • Ontologicalengineeringhasonlybeenpartially successful,andfewlargeAI systemsare basedonGPontologies(usespecial purposeontologies)


Elements of a general ontology

Elements of a general ontology

  • Categories ofobjects

  • Measuresofquantities

  • Compositeobjects

  • Time,space,andchange

  • Eventsandprocesses

  • Physicalobjects

  • Substances

  • Mentalobjectsandbeliefs


Top level ontology of the world

Top-level ontology of the world

Anything

AbstractObjects

Events

SetsNumbers

RepresentationObjects

Intervals

Places

PhysicalObjects

Processes

Categories

Sentences

Measurements Moments

Things

Stuff

Times

Weights

Animals

Agents Solids

LiquidGas

Humans


Upper ontology

Upper Ontology

  • The general framework of concepts is called an upper ontology because of the convention of drawing graphs with the general concepts at the top and the more specific concepts below them

  • Of what use is an upper ontology?

    • Consider the ontology for circuits that we studied

    • It makes many simplifying assumptions: time is omitted completely; signals are fixed and do not propagate; the structure of the circuit remains constant.

    • more general ontology would consider signals at particular times, and would include the wire lengths and propagation delays.

    • This would allow us to simulate the timing properties of the circuit, and indeed such simulations are often carried out by circuit designers.


Categories and objects

Categories and objects

  • Categoriesareusedtoclassifyobjects

  • accordingtocommonpropertiesordefinitions

  • xxTomatesRed(x)Round(x)

  • Categoriescanberepresentedby

  • Predicates:Tomato(x)

  • Objects:TheconstantTomatoesrepresentssetof

  • tomatoes(reification)

  • Roles ofcategoryrepresentations

x1Tomatoes

Instancerelations(is-a):

Taxonomicalhierarchies(Subset):TomatoesFruit

Inheritanceofproperties

(Exhaustive)decompositions


Categories using fol

Categories using FOL


Properties of categories

Properties of categories

  • We say that two or more categories are disjoint if they have no members in common.

  • exhaustive decomposition

  • A disjoint exhaustive decomposition is known as a partition.

  • The following examples illustrate these three concepts:

  • The predicates us to define these concepts are

  • For example, a bachelor is an unmarried adult male:


Objects and substance

Objects and substance

  • Needtodistinguishbetweensubstanceand

  • discreteobjects

  • Substance(“stuff”)

  • Massnouns - notcountable

  • Intrinsicproperties

  • Partofasubstance is(still)thesamesubstance

  • Discreteobjects(“things”)

  • Count nouns - countable

  • Extrinsicproperties

  • Partsare (generally)not ofsamecategory


Composite objects

Composite objects

  • Acompositeobjectisanobject thathasother

  • objectsasparts

  • ThePartOfrelationdefinestheobject containment,andistransitiveandreflexive PartOf(x,y)PartOf(y,z)PartOf(x,z)

  • PartOf(x,x)

  • ObjectscanbegroupedinPartOfhierarchies,

  • similartoSubsethierarchies

  • Thestructureofthecompositeobject

  • describeshowthepartsarerelated


Composite objects1

Composite objects

  • For example, a biped has two legs attached to a body:

  • For example, we might want to say “The apples in this bag weigh two pounds.”

  • we need a new concept, which we will call a bunch.

  • For example, if the apples are Apple1, Apple2, and Apple3, then

    BunchOf({Apple1,Apple2,Apple3})

    ∀x x∈ s ⇒ PartOf (x, BunchOf (s))

    ∀ y [∀x x∈ s ⇒ PartOf (x, y)] ⇒ PartOf (BunchOf (s), y)

  • logical minimization, which means defining an object as the smallest one satisfying certain conditions.


Measurements

Measurements

  • Needtobeabletorepresentpropertieslike height,mass,cost,etc.Valuesforsuch propertiesare measures

  • Unitfunctionsrepresentandconvertmeasures

  • Length(L1)Inches(1.5)Centimeters(3.81)

  • lCentimeters(2.54l)Inches(l)

  • Measures canbeusedtodescribeobjects

  • Mass(Tomato1)Kilograms(0.16)

  • ddDaysDuration(d)Hours(24)

  • Non-numericalmeasurescanalsoberepresen- ted,butnormallythereisanorder(e.g.>).Usedinqualitativephysics


Me as u r e me n ts

Measurements

  • Comparative difficulty

    e1 ∈ Exercises ∧ e2 ∈Exercises ∧ Wrote(Norvig, e1) ∧ Wrote(Russell, e2) ⇒ Difficulty(e1) > Difficulty(e2)

    e1 ∈ Exercises ∧ e2 ∈Exercises ∧ Difficulty(e1) > Difficulty(e2) ⇒ ExpectedScore(e1) < ExpectedScore(e2)


Objects things and stuff

Objects: Things and stuff

  • The real world can be seen as consisting of primitive objects (e.g., atomic particles) and composite objects built from them.

  • There is, however, a significant portion of reality that seems to defy any obvious individuation—division into distinct objects. We give this portion the generic name stuff.

  • count nouns, such as aardvarks, holes, and theorems, and mass nouns, such as butter, water, and energy.

  • To represent stuff properly, we begin with the obvious. We need to have as objects in our ontology at least the gross “lumps” of stuff we interact with.

    b∈ Butter ∧ PartOf (p, b) ⇒ p ∈Butter

    b∈ Butter ⇒ MeltingPoint(b,Centigrade(30))

  • Intrinsic properties and extrinsic properties


Event calculus

Event calculus

  • Eventcalculus:Howtodeal withchangebasedon

  • representingpointsoftime

  • Reifiesfluentsandevents

  • Afluent:At(Bilal,Berkeley)

  • The fluentistrue attimet:T(At(Bilal,IQRA),t)

  • Eventsareinstancesofeventcategories

  • E1FlyingsFlyer(E1,Bilal)Origin(E1,SF)Destination(E1,KHI)

  • EventE1 tookplaceoverintervali

  • Happens(E1,i)

  • Timeintervalsrepresentedby(start,end)pairs

  • i=(t1,t2)


Event calculus predicates

Event calculus predicates

  • T(f, t)

  • Happens(e,i)

  • Initiates(e,f, t)

Fluentfistrueattimet

Evente happensover intervali

Eventecausesfluentftostartatt

  • Terminates(e,f, t)Eventecausesftoceaseatt

  • Clipped(f,t)

  • Restored(f,i)

Fluentfceases to betrue inint.i

Fluentfbecomestrueinintervali


Events

Events

  • We assume a distinguished event, Start , that describes the initial state by saying which fluents are initiated or terminated at the start time.

  • We define T by saying that a fluent holds at a point in time if the fluent was initiated by an event at some time in the past and was not made false (clipped) by an intervening event.

  • A fluent does not hold if it was terminated by an event and not made true (restored) by another event.

    • Happens(e, (t1, t2)) ∧ Initiates(e, f, t1) ∧ ¬Clipped(f, (t1, t)) ∧ t1 < t ⇒ T(f, t)

    • Happens(e, (t1, t2)) ∧ Terminates(e, f, t1)∧ ¬Restored (f, (t1, t)) ∧ t1 < t ⇒ ¬T(f, t)

      where Clipped and Restored are defined by

    • Clipped(f, (t1, t2)) ⇔ ∃ e, t, t3 Happens(e, (t, t3)) ∧ t1 ≤ t < t2 ∧ Terminates(e, f, t)

    • Restored (f, (t1, t2)) ⇔ ∃ e, t, t3 Happens(e, (t, t3)) ∧ t1 ≤ t < t2 ∧ Initiates(e, f, t)


Processes

Processes

  • The events we have seen so far are what we call discrete events

  • Categories of events with sub-intervals are called process categories or liquid event categories


Time intervals

Time intervals

  • Timeintervalsarepartitionedintomoments(zero duration)andextendedintervals Partition(Moments,ExtendedIntervals,Intervals)

  • iiIntervals(iMomentsDuration(i)  0)

  • FunctionsStartandEnddelimitintervals

  • iInterval(i)Duration(i) (Time(End(i))Time(Start(i)))

  • Mayuse e.g.January1, 1900asarbitrarytime0

  • Time(Start(AD1900))=Seconds(0)


Relations between time intervals

Relations between time intervals

j

Meet(i,j)

i

Before(i,j)

After(j,i)

j

i

Can beexpressedlogically,e.g.

i,jMeet(i,j)Time(End(i)) Time(Start(j))

j

During(i,j )

i

Overlap(i,j)

Overlap(j,i)

j


Mental events and mental objects

Mental events and mental objects

  • Needto representbeliefsinselfand other agents, e.g.for controllingreasoning,or for planningactions thatinvolveothers

  • Howare beliefsrepresented?

  • Beliefsare reifiedasmentalobjects

  • Mentalobjectsare representedasstringsin alanguage

  • Inferencerulesforthislanguagecan bedefined

  • Rulesfor reasoningabout logicalagents’ use theirbeliefs

  • a,p,qLogicalAgent(a)Believes(a,p)

  • Believes(a,"pq")Believes(a,q)

a,p

LogicalAgent(a)Believes(a,p)

Believes(a,"Believes(Name(a),p)")


Mental events

Mental events

  • propositional attitudes that an agent can have toward mental objects: attitudes such as Believes, Knows, Wants, Intends, and Informs

  • For example, suppose we try to assert that Lois knows that Superman can fly:

    Knows(Lois, CanFly(Superman))

  • if it is true that Superman is Clark Kent, then we must conclude that Lois knows that Clark can fly:

    (Superman = Clark) ∧ Knows(Lois , CanFly(Superman)) |= Knows(Lois, CanFly(Clark ))

  • This property is called referential transparency


Modal logic

Modal Logic

  • Modal logic is designed to address this problem.

  • Regular logic is concerned with a single modality, the modality of truth, allowing us to express “P is true.”

  • Modal logic includes special modal operators that take sentences (rather than terms) as arguments.

  • For example, “A knows P” is represented with the notation KAP, where K is the modal operator for knowledge. It takes two arguments, an agent (written as the subscript) and a sentence.


Semantic networks

Semantic networks

  • Graphrepresentationofcategories,objects,

  • relations,etc. (i.e.essentiallyFOL)

  • Natural representation ofinheritance anddefault values

∀x x∈ Persons ⇒ [∀ y HasMother(x, y) ⇒

y ∈ FemalePersons] .

∀x x∈ Persons ⇒ Legs(x, 2) .


Semantic network

Semantic Network

Human

Being

Is a

Boy

Is a

Is a

Needs

Goes to

Woman

Joe

School

Is a

Food

Has

a child

Kay


Other reasoning systems for categories

Other reasoning systems for categories

  • Descriptionlogics

  • Derivedfromsemanticnetworks,butmoreformal

  • Supportssubsumption,classificationand consistency

  • Circumscriptionanddefaultlogic

  • Formalizes reasoning about defaultvalues

  • Assumesdefaultinabsence ofother input;mustbe

  • able toretractassumptionifnewevidenceoccurs

  • Truthmaintenancesystems

  • Supportsbeliefrevisioninsystemswhereretracting beliefis permitted


Internet shopping world

Internet shopping world

  • Anagentthatunderstandsandactsinan

  • internetshoppingenvironment

  • ThetaskistoshopforaproductontheWeb,

  • giventheuser’s productdescription

  • Theproductdescriptionmaybeprecise,inwhich casetheagentshouldfindthebest price

  • Inothercases thedescriptionisonlypartial,and theagenthastocompareproducts

  • Theshoppingagentdependsonhavingproduct

  • knowledge,incl.category hierarchies


Peas specification of shopping agent

PEAS specification of shopping agent

  • Performance goal

  • Recommendproduct(s)to match user’sdescription

  • Environment

  • Allofthe Web

  • Actions

  • Followinglinks

  • Retrieve page contents

  • Sensors

  • Webpages:HTML,XML


Outline of agent behavior

Outline of agent behavior

  • Startathomepageof knownwebstore(s)

  • Musthaveknowledge ofrelevantwebaddresses,

  • suchas www.amazon.cometc.

  • Spreadout fromhomepage,followinglinksto

  • relevantpagescontainingproductoffers

  • Mustbeabletoidentifypagerelevance,using productcategoryontologies, aswell parsepagecontentsto detectproductoffers

  • Havinglocatedoneormoreproductoffers,

  • agentmustcompareandrecommendproduct

  • Comparisonrange fromsimplepricerankingto

  • complextradeoffsin severaldimensions


Following links

Following links

  • The agent will have knowledge of a number of stores, for example:

    Amazon ∈OnlineStores ∧ Homepage(Amazon, “amazon.com”) .

    Ebay ∈OnlineStores ∧ Homepage(Ebay, “ebay.com”) .

    ExampleStore ∈OnlineStores ∧ Homepage(ExampleStore, “example.com”)

  • a page is relevant to the query if it can be reached by a chain of zero or more relevant category links from a store’s home page, and then from one more link to the product offer.

    Relevant(page, query) ⇔ ∃ store, home store ∈OnlineStores ∧ Homepage(store, home) ∧ ∃url , url 2 RelevantChain(home, url 2, query) ∧ Link(url 2, url) ∧ page = Contents(url )

    RelevantChain(start , end, query) ⇔ (start = end) ∨ (∃ u, text LinkText(start, u, text ) ∧ RelevantCategoryName(query, text ) ∧ RelevantChain(u, end, query)) .


Following links1

Following Links


Comparing offers

Comparing offers

∃ c, offer c∈ LaptopComputers ∧ offer ∈ ProductOffers ∧

Manufacturer(c,IBM ) ∧ Model (c, ThinkBook970 ) ∧

ScreenSize(c, Inches(14)) ∧ ScreenType(c, ColorLCD) ∧

MemorySize(c,Gigabytes(2)) ∧ CPUSpeed (c,GHz (1.2)) ∧

OfferedProduct(offer, c) ∧ Store(offer , GenStore) ∧

URL(offer , “example.com/computers/34356.html”) ∧

Price(offer , $(399)) ∧ Date(offer ,Today)


Summary

Summary

  • Anontologyisanencodingofvocabularyand relationships.Special-purposeontologiescanbe effectivewithinlimiteddomains

  • Ageneral-purposeontologyneedstocoverawide varietyofknowledge,andisbasedoncategories andan eventcalculus

  • Itcovers structuredobjects,timeandspace, change,processes, substances,andbeliefs

  • Thegeneralontologycansupportagent reasoningina widevarietyofdomains,including theInternetshoppingworld


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