Copyright © 2002 Cycorp A Bundle of Assertions Think of a microtheory (mt) as a set of assertions. Each microtheory bundles assertions based on –a shared

Copyright © 2002 Cycorp

A Bundle of Assertions

• Think of a microtheory (mt) as a set of assertions.

• Each microtheory bundles assertions based on– a shared set of assumptions on which the truth of the assertions depends, or– a shared topic (world geography, brain tumors, pro football), or– a shared source: (CIA World Fact Book 1997, FM101-5, USA Today)

the Cyc KB, as a sea of assertions


Avoiding Inconsistencies

• The assertions within a microtheory must be mutually consistent– no monotonic contradictions allowed within a single microtheory

• Assertions in different microtheories may be inconsistent

the Cyc KB, as a sea of assertions

in MT1: tables, etc., are solidin MT2: tables are mostly space

in MT1: Mandela is an elder statesmanin MT2: Mandela is President of South Africain MT3: Mandela is a political prisoner


Every Assertion is in a Microtheory

• Every assertion falls within at least one microtheory

• Currently, every microtheory is a reified (named) term, such as #$HumanActivitiesMt or #$OrganizationMt

• Mts are one way of indexing all the assertions in Cyc


Better/faster/more scalable knowledge base building Better/faster/more scalable inferencing, too.

• To focus development of the Cyc knowledge base• To enable shorter and simpler assertions

Mandela is president vs. Mandela is president throughout 1995 in South Africa

Tables are solidvs. At granularity usually considered by humans, tables are solid

•To cope with global inconsistency in the KB, inevitable at this scale• Each mt is locally consistent (content in unrelated mts is not visible)• Good for handling divergence (different points of view, scientific theories, changes over time)

Why Have Microtheories?


Better/faster/more scalable knowledge base building Better/faster/more scalable inferencing, too.

• To focus development of the Cyc knowledge base• To enable shorter and simpler assertions

Mandela is president vs. Mandela is president throughout 1995 in South Africa

Tables are solidvs. At granularity usually considered by humans, tables are

solid

•To cope with global inconsistency in the KB, inevitable at this scale• Each mt is locally consistent (content in unrelated mts is not visible)• Good for handling divergence (different points of view, scientific theories, changes over time)

Why Have microtheories? (cont.)


•#$VocabularyMicrotheory -- each instance contains definitions of general concepts used in a knowledge domain •(e.g., #$TransportationVocabMt, #$ComputerSoftwareVocabMt)

• #$TheoryMicrotheory -- each instance contains general assertions in a knowledge domain (e.g., #$TransportationMt ,#$ComputerSoftwareMt).

• #$DataMicrotheory -- each instance contains assertions about specific individuals (e.g., #$TransportationDataMt, #$ComputerSoftwareDataMt)

Some types of microtheories#$Microtheory

#$TheoryMicrotheory

#$DataMicrotheory

#$CounterfactualContext

#$PropositionalInformationThing

genls

genl

s

genls

genls

#$VocabularyMicrotheory genl

s


Some types of microtheories#$Microtheory

#$TheoryMicrotheory

#$DataMicrotheory

#$CounterfactualContext

#$PropositionalInformationThing

genls

genl

s

genls

genls

#$VocabularyMicrotheory genl

s

•#$PropositionalInformationThing --each instance of this collection contains assertions representing the propositional content of some #$InformationBearingThing (such as a picture, text, or database table).

•#$CounterfactualContext -- each instance of this collection contains at least one assertion which is not generally taken to be true in the real world (e.g., #$TheSimpsonsMt, #$SQ77bMt)


Explicitly relates a microtheory to a formula that is true in that microtheory.

• (#$ist MT FORMLA) means that the Cyc formula FORMLA is true in the microtheory MT.

Microtheory predicates: #$ist

(#$ist #$CyclistsMt (#$isa #$Lenat #$Person))

(#$ist #$NaiveStateChangeMt (#$implies (#$and (#$isa ?FREEZE #$Freezing) (#$outputsCreated ?FREEZE ?OBJ)) (#$stateOfMatter ?OBJ #$SolidStateOfMatter)))


Relates two microtheories such that one of them inherits the assertions in the other; i.e., the first microtheory has access to the assertions in the second microtheory.

• (#$genlMt MT-1 MT-2) means that every assertion which is true in MT-2 is also true in MT-1.

• #$genlMt is transitive.

Microtheory predicates: #$genlMt

•(#$genlMt #$TransportationMt #$NaivePhysicsMt)

•(#$genlMt #$ModernMilitaryTacticsMt #$ModernMilitaryVehiclesMt)

•(#$genlMt #$EconomyMt #$TransportationMt)


#$genlMt

Microtheory predicates, cont’d.

#$BaseKB

#$NaiveSpatialMt

#$NaivePhysicsMt#$NaturalGeographyMt

genlMtgen

lMt

genl

Mt

#$MovementMt

genlM

t

genlMt

#$TransportationMt

genl

Mt


#$PredicateA sentence built from a predicate is either True or False.

• (#$mother #$ChelseaClinton #$HillaryClinton)

is True

• (#$physicalParts #$TheWhiteHouse

#$TheLincolnMemorial)

is False

Predicates are thus truth-functional relations.


Argument TypesExample 1

• (#$arg1Isa #$mother #$Animal) • (#$arg2Isa #$mother #$FemaleAnimal)

Thus ,

(#$mother #$ChelseaClinton #$HillaryClinton)

is a well-formed sentence because :

(#$isa #$ChelseaClinton #$Animal) and

(#$isa #$HillaryClinton #$FemaleAnimal)


Second-Order Predicates

• Sometimes we want to make statements about predicates themselves.

• This requires “second-order” predicates, which can take predicates as arguments.

Examples : #$arg1Isa, #$arity, #$isa• Thus in (#$arity #$mother 2), #$arity takes the predicate #$mother as its first argument.

• Some second-order predicates are used to relate CycL predicates to one another within a predicate hierarchy . . .


The Form and Content Of The Knowledge Base

• The main advantage of Cyc over other systems for representing knowledge is its use of a formal language in which inferential connections between concepts and statements are encoded in a machine accessible way.

• The content of the Knowledge Base comprises:– A vast taxonomy of concepts and relations– A rich formal representation of their interconnections


Arrangement, by Generality

Facts(Database)

Facts(Database)

UpperOntology

Core Theories

Domain-Specific Theories

Upper Ontology: Abstract Concepts

Core Theories: Space, Time, Causality, …


Facts: Instances

KnowledgeBaseLayers



Facts(Database)

Facts(Database)

UpperOntology

Core Theories


EVENT TEMPORAL-THING INDIVIDUAL THING


KnowledgeBaseLayers



Facts(Database)

Facts(Database)

UpperOntology

Core Theories



For all events a and b, a causes b implies a precedes b


Core Theories: Space, Time, Causality, …KnowledgeBaseLayers



Facts(Database)

Facts(Database)

UpperOntology

Core Theories




For any mammal m and any anthrax bacteria a, m’s being exposed to a causes m to be infected by a.




KnowledgeBaseLayers


Facts(Database)

Facts(Database)

UpperOntology

Core Theories




For any mammal m and any anthrax bacteria a, m’s being exposed to a causes m to be infected by a.

John is a person infected by anthrax.




Facts: Instances

KnowledgeBaseLayers



#$Thing

#$Intangible#$Individual

#$SetOrCollection#$TemporalThing

#$SpatialThing-Localized

#$ExistingStuffType

#$ExistingObjectType

#$Event

#$PartiallyTangible#$Collection

#$genls#$typeGenls#$disjointWith

Some Top Level Collections


#$Dog (the collection of all dogs)

#$isa: #$OrganismClassificationType #$BiologicalTaxon #$BiologicalSpecies #$DomesticatedAnimalType

#$genls: #$CanineAnimal


45 Collections of which #$Dog” is a Specialization

Agent Agent-Generic AirBreathingVertebrate Animal AnimalBLO BilateralObject BiologicalLivingObject CanineAnimal Carnivore CarnivoreOrder ChordataPhylum Coelomates Container-Underspecified Dog EukaryoticOrganism Eutheria FrontAndBackSidedObject Heterotroph HexalateralObject Homeotherm HumanScaleObject Individual IndividualAgent LeftAndRightSidedObject Location-Underspecified Mammal NaturalTangibleStuff NonPersonAnimal OrganicStuff Organism-Whole PartiallyTangible PerceptualAgent Region-Underspecified SentientAnimal SolidTangibleThing SomethingExisting SpatialThing SpatialThing-Localized System-Generic TemporalThing TerrestrialOrganism Thing TopAndBottomSidedObject Trajector-Underspecified Vertebrate


11 Collections of which#$Dog is an Instance

#$OrganismClassificationType #$ConventionalClassificationType #$ExistingObjectType #$TemporalStuffType #$ObjectType #$Collection #$SetOrCollection#$MathematicalThing#$MathematicalOrComputationalThing#$Intangible#$PartiallyIntangible#$Thing


Relations Between Temporal Things

– #$temporalBoundsIntersect

– #$temporallyIntersects

– #$startsAfterStartingOf

– #$endsAfterStartingOf

– #$endsAfterEndingOf

– #$startingDate

– #$temporallyContains

– #$temporallyCooriginating

– #$temporalBoundsContain

– #$temporalBoundsIdentical

– #$startsDuring

– #$overlapsStart

– #$startingPoint

– #$simultaneousWith

– #$after


Spatial Properties and Relations

• Surfaces, Portals and Cavities

• Shape Attributes (63)• Types of Spatial

Symmetry • Direction and

Orientation Vocabulary

• Relative Positions of Objects

• Nearness and Location• Being Between• ‘In-’ Predicates (~ 60)• Connections Predicates

(~ 65)• Mereological Relations


Senses of ‘In’• Does part of the inner

object stick out of the container?– None of it. -- Try

#$in-ContCompletely

– Yes -- Try

#$in-ContPartially

• If the container were turned around could the contained object fall out? – Yes -- Try

#$in-ContOpen

– No -- Try

#$in-ContClosed


Senses of ‘In’ Is it attached to the

inside of the outer object?– Yes -- Try

#$connectedToInside

Can it be removed, if enough force is used,

without damaging either object?

– Yes -- Try #$in-Snugly or #$screwedIn

Does the inner object stick into the outer

object?

– Yes -- Try #$sticksInto


Senses of ‘Part’

– #$parts– #$intangibleParts– #$subInformation– #$subEvents– #$physicalDecompositions– #$physicalPortions

– #$physicalParts– #$externalParts– #$internalParts– #$anatomicalParts– #$constituents– #$ingredients


Some Events Types

• #$PhysicalStateChangeEvent

• #$TemperatureChangingProcess

• #$BiologicalDevelopmentEvent

• #$ChangingDeviceState

• #$CuttingNails

• #$Cracking

• #$Carving

• #$ShapeChangeEvent

• #$MovementEvent

• #$GivingSomething

• #$DiscoveryEvent

• #$Buying

• #$Thinking

• #$Baking

• #$Singing

• #$PumpingFluid


Roles and ActorSlots(the world’s largest collection)

• Agency or initiating an event

• Objects acted on or changed

• Objects created or destroyed

• Facilitating objects or stuff in an event

• Slots of motion and location

• Instruments• Beneficiary/maleficiary• Specialized actor roles,

like #$plaintiffs


Roles and ActorSlots

“Moe clobbered Curly with the British scepter.”


Roles and ActorSlots“Moe clobbered Curly with the British scepter.”

• Relations between an event and its participants

• Cyc has over 200 role and ActorSlot predicates

Clobbering14

#$performedBy

Curly TheUKScepter

Moe

#$victim #$deviceUsed


• This represents a particular clobbering event, not clobberings in general.

Clobbering14

performedBy

Curly TheUKScepter

Moe

victims instruments

Roles and ActorSlots“Moe clobbered Curly with the British scepter.”


Roles in events and subevents

• A product of one subevent of the Krebs Process is the input to another.

• Hence, different ActorSlot predicates.

SubProcessBSubProcessA

#$inputsDestroyed#$outputsCreated

Krebs Process


Information

• Information-Bearing Things– Books, web-page copies, radio broadcasts,

utterances

• Abstract strings, characters• Propositional Content• Conceptual Works


What is “Moby Dick” ?


“‘ T i s M o b y D i c k !”

(#$thereExists ?SEE (#$and (#$isa ?SEE Seeing) (#$objectPerceived ?SEE #$MobyDick) (#$perceiver ?SEE #$CaptainAhab)))

AbstractInformationStructure(AIS)

PropositionalInformationThing(PIT)

InformationBearingThing(IBT)



(and (isa ?SEE Seeing) (objectPercieved ?SEE MobyDick) (perceiver ?SEE CaptainAhab))






(and (isa ?SEE Seeing) (objectPercieved ?SEE MobyDick) (perceiver ?SEE CaptainAhab))

#$AbstractInformationStructure(AIS)

#$Proposition and #$PropositionalInformationThing

(PIT)

#$InformationBearingThing(IBT)

#$ConceptualWork(CW)




ConceptualWork(CW)





ConceptualWork(CW)

instantiationOfCW






ConceptualWork(CW)

textOfIBT instantiationOfCW

InfoStructureOfCW

#$infoStructureRepresents

ContainsInfo-Propositional-CW

PITOfIBTFn


Emotion

• Feeling Attributes Types– #$Abhorrence– #$Adulation– #$Relaxed-Feeling– #$Gratitude– #$Anticipation-Feeling– Over 120 of these

• Relations Pertaining to emotions

– #$contraryFeelings– #$feelsTowardsObject– #$appropriateEmotion – #$feelsTowardsPersonType– #$actionExpressesFeeling


Propositional Attitudes Relations Between Agents and Propositions

• #$goals• #$intends• #$desires• #$hopes• #$expects• #$beliefs

• #$opinions • #$knows• #$rememberedProp• #$perceivesThat• #$seesThat• #$tastesThat


Biology

• Organisms classified by:– Taxon

– Habitat

– Source of Nutrients

• Some scientific, #$ChordataPhylum, some not, #$Worm

• Organism Anatomy– Gross Anatomy

– Cell biology

– Physiological Processes

• Life stages


Materials

• Common Substances• Attributes of Materials• States Of Matter• Solutions

• Electrical Conductivity • Thermal Conductivity• Structural Attributes• Tangible Attributes


Devices

• Specializations Of #$PhysicalDevice

• Device States• Device Actions• Device Predicates• Device Purposes


Food

• Food Types • Edibility • Preparing food• Consuming food • Hunger


Weather

• Weather Attributes– #$ClearWeather– (#$LowAmountFn

#$Raininess)• Weather Events– #$TornadoAsEvent– #$SnowProcess

• Weather Objects– #$CloudInSky– #$TornadoAsObject


Geography

• Geopolitical Entities• Addresses• Specific Ethnic and Language information• Borders• Districts, States, etc. • Seas, islands, straits,etc.


Inference uses Deduction:Rules + Facts

Deduction - rule fact(s) new fact(#$loves #$Hamlet #$Gertrude)

“Rules” - general, variables(#$implies (#$mother ?PERSON ?MOTHER) (#$loves ?PERSON ?MOTHER))

“Facts” - specific, no variables(#$mother #$Hamlet #$Gertrude)


The Resolution Principle

(#$and (#$knows #$Hamlet ?WHO) (#$loves #$Hamlet ?WHO))

(#$implies (#$mother ?PERSON ?MOTHER) (#$loves ?PERSON ?MOTHER))

Query Rule

Resolution Principle : “Unify, Substitute, Merge”


The Resolution Principle: Unify




Query Rule

Pivot Literals




Most General Unifier#$Hamlet / ?PERSON?WHO / ?MOTHER


Query Rule

The Resolution Principle: Unify

(#$loves #$Hamlet ?WHO))=(#$loves #$Hamlet ?WHO))


The Resolution Principle: Substitute



Most General Unifier#$Hamlet / ?PERSON?WHO / ?MOTHER

Resolution Principle : “Unify, Substitute, Merge”Query Rule


(#$implies (#$mother #$Hamlet ?WHO) (#$loves #$Hamlet ?WHO))

Substituted Query Substituted Rule


The Search Tree

Query/root

Possible Answers:Branches/Child nodes

“Who does Hamlet know and love?”


Justifying the Answers

Query

Goal!

Logical Deduction

with the Most General Unifier


The Halting Problem

millions of facts+ tens of thousands of rulesinfinite possibilities


Depth-first Search TraversalStart

here


Depth-first Search Traversal

??



??

??



??

**??

GOAL!GOAL!



??

??

**??


Depth-first: advantage and disadvantage

+ Algorithmically efficient- No end


Breadth-first Search: advantage and disadvantage

0-step

1-step

2-step

n-step

+ Deal with simplest proofs first- Infinite fan-out is common


Cyc is Life in the Big City

Searching in Cyc:~100,000 constants

~1 million assertions


Inference is Resource-bounded

Resource Bounds :– quit after NUMBER of answers– quit after TIME seconds– ignore any proof using more than

BACKCHAIN rules– ignore any proof using more than DEPTH steps


Inference Uses Mts for Consistency

WorldMythologyMt

•(genls Vampire IntelligentAgent)

•(isa LochNessMonster Reptile)

MainstreamAmericanCultureMt

•(genls Vampire MythologicalThing)

•(isa LochNessMonster MythologicalThing)

In the Mainstream AmericanCultureMt, •Vampire is a kind of mythological thing.•The Loch Ness Monster is a mythological thing.

In the WorldMythologyMt,•Vampire is a kind of intelligent agent.•The Loch Ness Monster is a reptile.


Mts Inherit from More General Mts Using #$genlMt

UniversalVocabularyMt


UnitedStatesSocialLifeMt

genlMt

HumanActivitiesMt

genlMt

genlMt

genlMt

WorldMythologyMt


Inference is performed Within Mts

UniversalVocabularyMt


UnitedStatesSocialLifeMt

genlMt

HumanActivitiesMt

genlMt

genlMt

genlMt

WorldMythologyMt

ASK in each Mt: (genls Vampire IntelligentAgent)

Results in each Mt:• True • Not Proven

Documents

Copyright © 2002 Cycorp A Bundle of Assertions Think of a microtheory (mt) as a set of assertions. Each microtheory bundles assertions based on –a shared