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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




  • General ontology

  • Categoriesandobjects

  • Eventsandprocesses

  • Reasoningsystems

  • Internetshoppingworld

  • Summary



  • 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












Measurements Moments






Agents Solids



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






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


    ∀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.



  • 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


  • 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)


Evente happensover intervali


  • Terminates(e,f, t)Eventecausesftoceaseatt

  • Clipped(f,t)

  • Restored(f,i)

Fluentfceases to betrue inint.i




  • 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)



  • 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








Can beexpressedlogically,e.g.

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


During(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)




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



Is a


Is a

Is a


Goes to




Is a



a child


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

  • 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, “”) .

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

    ExampleStore ∈OnlineStores ∧ Homepage(ExampleStore, “”)

  • 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 , “”) ∧

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



  • 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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