Knowledge-Representation-Cognitive-Science-at-Northwestern知識表示在西北認知科學(xué)課件

1、Knowledge RepresentationPraveen ParitoshCogSci 207: Fall 2019: Week 1Thu, Sep 30, 2019Knowledge RepresentationPraveSome RepresentationsSome Elements of a RepresentationRepresented world: about what? Representing world: using what? Representing rules: how to map? Process that uses the representation:

2、 conventions and systems that use the representations resulting from above. Analog versus SymbolicElements of a RepresentationReMarrs levels of descriptionComputational: What is the goal of the computation, why is it appropriate, and what is the logic of the strategy by which it can be carried out?

3、Algorithmic: How can this computational theory be implemented? In particular, what is the representation for the input and output, and what is the algorithm for the transformation? Implementation: How can the representation and algorithm be realized physically? Marrs levels of descriptionCoMarrs lev

4、els of description 2Computational: a lot of cognitive psychologyAlgorithmic: a lot of cognitive scienceImplementation: neuroscienceMarrs levels of description A closer lookA closer lookOverviewHow knowledge representation worksBasics of logic (connectives, model theory, meaning)Basics of knowledge r

5、epresentationWhy use logic instead of natural language?QuantifiersOrganizing large knowledge basesOntologyMicrotheoriesResource: OpenCyc tutorial materialsOverviewHow knowledge represenHow Knowledge Representation WorksIntelligence requires knowledgeComputational models of intelligence require model

6、s of knowledgeUse formalisms to write down knowledgeExpressive enough to capture human knowledgePrecise enough to be understood by machinesSeparate knowledge from computational mechanisms that process itImportant part of cognitive model is what the organism knowsHow Knowledge Representation WHow kno

7、wledge representations are used in cognitive modelsContents of KB is part of cognitive modelSome models hypothesize multiple knowledge bases.KnowledgeBaseInferenceMechanism(s)LearningMechanism(s)Examples,StatementsQuestions,requestsAnswers,analysesHow knowledge representations Whats in the knowledge

8、 base?Facts about the specifics of the worldNorthwestern is a private universityThe first thing I did at the party was talk to John.Rules (aka axioms) that describe ways to infer new facts from existing factsAll triangles have three sidesAll elephants are greyFacts and rules are stated in a formal l

9、anguageGenerally some form of logic (aka predicate calculus)Whats in the knowledge base?FPropositional logicA step towards understanding predicate calculusStatements are just atomic propositions, with no structurePropositions can be true or falseStatements can be made into larger statements via logi

10、cal connectives.Examples:C = “Its cold outside” ; C is a propositionO = “Its October” ; O is a propositionIf O then C ;if its October then its cold outsidePropositional logicA step towaSymbols for logical connectivesNegation: not, , Conjunction: and, Disjunction: or, Implication: implies, , Bicondit

11、ional: iff, -Universal quantifier: forall, Existential quantifier: exists, Symbols for logical connectiveSemantics of connectives For propositional logic, can define in terms of truth tablesABABFFFFTFTFFTTTABABFFFTTFTTSemantics of connectives For pImplication and biconditionalABABFFFTTFTTABABFFTFTTT

12、FFTTTAB ABAB (AB)(BA)Implication and biconditionalARules of inferenceThere are many rules that enable new propositions to be derived from existing propositionsModus Ponens: PQ, P, derive QdeMorgans law: (AB), derive ABSome properties of inference rulesSoundness: An inference rule is sound if it alwa

13、ys produces valid results given valid premisesCompleteness: A system of inference rules is complete if it derives everything that logically follows from the axioms.Rules of inferenceThere are maPredicate calculusSame connectivesPropositions have structure: Predicate/Function + arguments. R, 2 ; Term

14、s. Terms are not individuals, not propositionsRed(R), (Red R) ; A proposition, written in two ways(southOf UnicornCafe UniHall) ;a proposition(+ 2 2) ; Term, since the function + ranges over numbersQuantifiers enable general axioms to be written(forall ?x (iff (Triangle ?x) (and (polygon ?x) (number

15、OfSides ?x 3)Predicate calculusSame connectModel TheoryMeaning of a theory = set of models that satisfy it.Model = set of objects and relationshipsIf statement is true in KB, then the corresponding relationship(s) hold between the corresponding objects in the modeled worldThe objects and relationshi

16、ps in a model can be formal constructs, or pieces of the physical world, or whateverMeaning of a predicate = set of things in the models for that theory which correspond to it.E.g., above means “above”, sort ofModel TheoryMeaning of a theorCaution: Meaning pertains to simplest modelThere is usually

17、an intended model, i.e., what one is representing.A sparse set of axioms can be satisfied by dramatically simpler worlds than those intendedExample: Classic blocks world axioms have ordered pairs of integers as a model( ) block(on A B) p(A) = p(B) & h(A) = h(B)+1(above A B) p(A) = p(B) & h(A) h(B)Mo

18、ral: Use dense, rich set of axiomsCaution: Meaning pertains to sMisconceptions about meaning“Predicates have definitions”Most dont. Their meaning is constrained by the sum total of axioms that mention them.“Logic is too discrete to capture the dynamic fluidity of how our concepts change as we learn”

19、If you think of the set of axioms that constrain the meaning of a predicate as large, then adding (and removing) elements of that set leads to changes in its models.Sometimes small changes in the set of axioms can lead to large changes in the set of models. This is the logical version of a discontin

20、uity.Misconceptions about meaning“PRepresentations as SculpturesHow does one make a statue of an elephant?Start with a marble block. Carve away everything that does not look like an elephant.How does one represent a concept?Start with a vocabulary of predicates and other axioms. Add axioms involving

21、 the new predicate until it fits your intended model well.Knowledge representation is an evolutionary processIt isnt quick, but incremental additions lead to incremental progressAll representations are by their nature imperfectRepresentations as SculpturesHIntroduction to Cycs KR systemThese materia

22、ls are based on tutorial materials developed by Cycorp, for training knowledge entry people and ontological engineersFor this class, we have simplified them somewhat.In examinations, you will only be responsible for the simplified versionsIntroduction to Cycs KR systeNL vs. Logic: ExpressivenessNL:J

23、ims injury resulted from his falling.Jims falling caused his injury.Jims injury was a consequence of his falling.Jims falling occurred before his injury.Logic: identify the common concepts, e.g. the relation: x caused yWrite rules about the common concepts, e.g. x caused y x temporally precedes yNL:

24、 Write the rule for every expression?NL vs. Logic: ExpressivenessNLNL vs. Logic: Ambiguity and Precisionx is running-InMotion x is changing locationx is running-DeviceOperating x is operatingx is running-AsCandidate x is a candidatex is at the bank.river bank?financial institution?NL:AmbiguousLogic:

25、 Precisex is running.changing location?operating?a candidate for office?Reasoning: Figuring out what must be true, given what is known. Requires precision of meaning.NL vs. Logic: Ambiguity and PNL vs. Logic:Calculus of MeaningLogic: Well-understood operators enable reasoning:Logical constants: not,

26、 and, or, all, someNot (All men are taller than all women).All men are taller than 12”.Some women are taller than 12”. Not (All A are F than all B).All A are F than x.Some B are F than x. NL vs. Logic:Calculus of MeaniSyntax: Terms (aka Constants)A sampling of some constants:Dog, SnowSkiing, Physica

27、lAttributeBillClinton,Rover, DisneyLand-TouristAttractionlikesAsFriend, bordersOn, objectHasColor, and, not, implies, forAllRedColor, Soil-SandyTerms denote specific individuals or collections (relations, people, computer programs, types of cars . . . )Each Terms is a character string prefixed by Th

28、ese denote collectionsThese denote individuals : Partially Tangible IndividualsRelationsAttribute ValuesSyntax: Terms (aka Constants)ASyntax: PropositionsPropositions: a relation applied to some arguments, enclosed in parenthesesAlso called formulas, sentencesExamples:(isa GeorgeWBush Person)(likesA

29、sFriend GeorgeWBush AlGore)(BirthFn JacquelineKennedyOnassis)Syntax: PropositionsPropositioSyntax: Non-Atomic TermsNew terms can be made by applying functions to other things In the Cyc system, functions typically end in “Fn”Examples of functions:BirthFn, GovernmentFn, BorderBetweenFnExamples of Non

30、-Atomic Terms:(GovernmentFn France)(BorderBetweenFn France Switzerland)(BirthFn JacquelineKennedyOnassis)Non-atomic Terms can be used in statements like any other term(residenceOfOrganization (GovernmentFn France) CityOfParisFrance)Syntax: Non-Atomic TermsNew tWhy Use NATs?UniformityAll kinds of fru

31、its, nuts, etc., are represented in the same, compositional way: (FruitFn PLANT) *Inferential EfficiencyForward rules can automatically conclude many useful assertions about NATs as soon as they are created, based on the function and arguments used to create the NAT.what kind of thing that NAT repre

32、sentshow to refer to the NAT in English Why Use NATs?UniformityWell-formedness: ArityArity constraints are represented in CycL with the predicate arity:(arity performedBy 2)Represents the fact that performedBy takes two arguments, e.g.: (performedBy AssassinationOfPresidentLincoln JohnWilkesBooth)(a

33、rity BirthFn 1)Represents the fact that BirthFn takes one arguments, e.g.:(BirthFn JacquelineKennedyOnassis) Well-formedness: ArityArity coWell-Formedness: Argument TypeArgument type constraints are represented in CycL with the following 2 predicates:1 argIsa (argIsa performedBy 1 Action) means that

34、 the first argument of performedBy must be an individual Action, such as the assassination of Lincoln in: (performedBy AssassinationOfPresidentLincoln JohnWilkesBooth)2 argGenl(argGenl penaltyForInfraction 2 Event) means that the second argument of penaltyForInfraction must be a type of Event, such

35、as the collection of illegal equipment use events in:(penaltyForInfraction SportsEvent IllegalEquipmentUse Disqualification)Well-Formedness: Argument TypeWhy constraints are importantThey guide reasoning(performedBy PaintingTheHouse Brick2)(performedBy MarthaStewart CookingAPie)They constrain learni

36、ngWhy constraints are importantTCompound propositionsConnectives from propositional logic can be used to make more complex statements(and (performedBy GettysburgAddress Lincoln)(objectHasColor Rover TanColor)(or (objectHasColor Rover TanColor)(objectHasColor Rover BlackColor)(implies (mainColorOfObj

37、ect Rover TanColor)(not (mainColorOfObject Rover RedColor) (not (performedBy GettysburgAddress BillClinton)Compound propositionsConnectivVariables and QuantifiersGeneral statements can be made by using variables and quantifiersVariables in logic are like variables in algebra Sentences involving conc

38、epts like “everybody,” “something,” and “nothing” require variables and quantifiers:Everybody loves somebody.Nobody likes spinach.Some people like spinach and some people like broccoli, but no one likes them both.Variables and QuantifiersGenerQuantifiersAdding variables and quantifiers, we can repre

39、sent more general knowledge.Two main quantifiers:1. Universal Quantifer - forAllUsed to represent very general facts, like:All dogs are mammalsEveryone loves dogs2. Existential Quantifier - thereExistsUsed to assert that something exists, to state facts like: Someone is bored Some people like dogsQu

40、antifiersAdding variables anQuantifiersUniversal Quantifier(forAll ?THING (isa ?THING Thing)Existential Quantifier:(thereExists ?JOE(isa ?JOE Poodle)Others defined in CycL:(thereExistsExactly 12 ?ZOS (isa ?ZOS ZodiacSign)(thereExistsAtLeast 9 ?PLNT (isa ?PLNT Planet)Everything is a thing.Something i

41、s a poodle.There are exactly 12 zodiac signsThere are at least 9 planetsQuantifiersUniversal QuantifieImplicit Universal QuantificationAll variables occurring “free” in a formula are understood by Cyc to be implicitly universally quantified. So, to CYC, the following two formulas represent the same fact:(forAll ?X(implies (isa ?X Dog)(is