Knowledge Representation II Praveen Paritosh CogSci 207 Fall 2003 Week 2 Tue Oct 5 2004 Knowledge Representation II These slides draw heavily from Cycorp s tutorial materials They have been simplified for the purpose of this course Concepts and Categories Widely used ideas in accounts of mental representation How we talk about things in general apart from specific individuals Much controversy about what they really are and how they work Where do they come from How stable over time are they Common Assumptions in AI Concepts are organized into hierarchies similar to taxonomies Animals versus plants Animals Mammals Dogs Some concepts are grounded in perceptual apparatus Other concepts are constructed by combining more primitive concepts Our mental representation language is compositional Cyc as a cognitive model Goal is overall functional equivalence not axiom by axiom modeling Knowledge differs across people and in the same person across time Overlap must be high enough to reason as we do over the range of topics that we do Concepts and categories in Cyc are modeled as collections Collections and Individuals A collection is a kind or class Collections have instances Each collection is characterized by some feature s that all of its instances share Some collections Tower SpaceStation Director Movie Person Person AbrahamLincol n MarioAndretti Cher Instances of Person BillClinton Individuals An individual is a single thing not a collection Individuals do not have instances Individuals may have parts Some individuals EiffelTower Mir OrsonWelles UnitedStatesMarineCorps Cher Joe The Marine UnitedStatesMarineCorps An individual organization A single specific thing It has parts but not instances UnitedStatesMarine The collection of all human members of the UnitedStatesMarineCorps Has instances each of which is an individual marine UnitedStatesMarineCorps UnitedStatesMarine Joe Remember Collections can have instances but not parts Individuals can have parts but not instances Everything Is An Instance of Something Every collection is at minimum an instance of Collection Every individual is at minimum an instance of Individual Collection Tower Individual Individual Collection SpaceStation MilitaryPerson Mir EiffelTower OrsonWelles UnitedStatesMarineCorps Collections of Collections and Collections of Individuals Some collections whose instances are individuals Tower Person Dog Some collections whose instances are collections ArtifactType Collection Some collections with instances of both types ProprietaryConstant DocumentationConstant Disjoint Collections Collections which have no instances in common are disjoint Dog Cat disjointWith Dog Cat isa isa X Y means X is an instance of collection Y isa EiffelTower Tower isa Canada Country isa Cher Person isa UnitedStatesMarineCorps ModernMilitaryOrganization Y X genls genls X Y means Every instance of collection X is also an instance of collection Y genls Dog Mammal genls Tower FixedStructure genls ModernMilitaryOrganization Organization Sometimes expressed in Cyclish as Y is a genls generalization of X X is a spec specialization of Y Y X genls is transitive PhysicalDevice Animal ComputationalSystem Mammal Elephant Dog Computer ComputerNetwork A piece of the genls hierarchy Individual FixedStructure Tower BellTower Lighthouse Animal Mammal Elephant Dog The top of the hierarchy partial Thing Individual Intangible TemporalThing SpatialThing Localized PartiallyTangible SetOrCollection Event Collection ExistingStuffType genls typeGenls disjointWith ExistingObjectType isa is NOT transitive InfiniteSetOrCollection Collection PositiveInteger 5 Person Cher Remember Because every instance of a collection is also an instance of the collection s genls the following statements are true isa transfers through genls isa does NOT transfer through isa What can we conclude about Rover the dog isa Thing genls Collection BiologicalTaxon Individual BiologicalKingdom BiologicalClass Animal BiologicalSpecies Mammal Dog Rover A more complete list of collections of which Rover is an instance Agent Generic Agent AirBreathingVertebrate Animal AnimalBLO BilateralObject BiologicalLivingObject CanineAnimal Carnivore CompositeTangibleAndIntangibleObject Dog Eutheria Individual IndividualAgent LeftAndRightSidedObject Mammal NaturalTangibleStuff NonPersonAnimal OrganicStuff Organism Whole PartiallyIntangible PartiallyIntangibleIndividual PartiallyTangible PerceptualAgent SentientAnimal SomethingExisting SpatialThing SpatialThing Localized TemporalThing Thing Vertebrate Is genls reflexive Consider genls Dog Dog This means Every instance of Dog is an instance of Dog Yes Is isa reflexive Consider isa Dog Dog However consider NOT reflexive isa Collection Collection Not anti reflexive either Summary Collections vs Individuals isa vs genls genls is transitive genls is reflexive Microtheories People know millions of things What we know isn t globally consistent Fiction Alternate hypotheses possible worlds Alternate perspectives How do we keep everything straight 3607 instances of Microtheory as of 02 05 01 254 instances of GeneralMicrotheory A Bundle of Assertions the Cyc KB as a sea 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 Avoiding Inconsistencies the Cyc KB as a sea of assertions The assertions within a microtheory must be mutually consistent no monotonic contradictions allowed within a single microtheory Assertions in different microtheories may be inconsistent in MT1 tables etc are solid in MT2 tables are mostly space in MT1 Mandela is an elder statesman in MT2 Mandela is President of South Africa in 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 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 solid vs At granularity usually considered by humans tables are