Chapter 3

Knowledge Representation

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Knowledge Representation

• 'A representation is a set of conventions about how to describe a class of things.' (Winston 1992:16).

• 'Good representations make important objects and relations explicit, expose natural constraints, and bring objects and relations together' (ibid: 45)

• The representation principle:– Once a problem is described using an appropriate

representation, the problem is almost solved.

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Starting with an Example

• The Farmer, The Fox, The Goose and The Grain:– The farmer must get a fox, a goose and a sack of grain across a

river, however his boat is small and he can only carry one thing at a time. His problem is that if he leaves the fox with the goose the goose will be eaten, and if he leaves the goose with the grain, the grain will be eaten…

• A good representation makes it easier for us to solve the problem:1. Draw possible safe combinations in a diagram.2. Arrange appropriate combinations in order.3. Link appropriate arrangements to represent boat trips.4. Problem is solved!

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Grain

FoxFarmerGoose

FarmerGooseGrain

Fox

FarmerFoxGooseGrain

FoxGrain

FarmerGoose

FarmerFoxGrain

Goose

Goose

FarmerFoxGrain

FarmerGoose

FoxGrain

FarmerGooseFoxGrain

Fox

FarmerGooseGrain

FarmerFoxGoose

Grain

Categories of Knowledge

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Procedural Knowledge

Knowing how to do something:

• Fix a watch• Install a window• Brush your teeth• Ride a bicycle

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Declarative Knowledge

• Knowledge that something is true or false

• Usually associated with declarative statements– Don’t put your finger in the boiled water

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The Pyramid of Knowledge

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Knowledge Types Example

• 711279762168321543

• Group numbers by twos. Ignore any two-digit number less than 32. Substitute the rest by ASCII equivalent

• GOLD +

• The price of the gold is rising, SO buy.

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Knowledge Representation Techniques

• Object-Attribute-Value Triple• Rules• Semantic nets• Frames• Logic oPropositional logicoFirst-order logic

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Object-Attribute-Value Triple

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OAV Triple(Object with multiple attribute)

OAV with Certainty Factor

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Fuzzy FactsCrisp fact: Tom’s height is 6 feet.Fuzzy fact: Tome’s height is tall (CF:0.5)

IF The person's height is tall THEN The person's weight is heavy

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Knowledge Representation Techniques

• Object-Attribute-Value Triple• Rules• Semantic nets• Frames• Logic oPropositional logicoFirst-order logic

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Rules and Facts

• Rules:– IF the car doesn’t run and the fuel gauge reads empty

THEN fill the gas tank.– IF there is flame, THEN there is a fire.– IF there is smoke, THEN there may be a fire.– IF there is a siren, THEN there may be a fire.

• Facts: – The car doesn’t run– There is a flame– There is smoke– There is a siren

• The meaning of firing a rule: – Condition is true => Generating the conclusion

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Example: Reasoning with rules

Conclusion

REASONING

Long-term Memory

Production Rule

Short-term Memory

Fact

يادآوري

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Types of Rules

• Relationship Rules: – if the battery is dead, then the car will not start

• Recommendation Rules:– If the car will not start, then take a cab

• Directive Rules:– If the car will not start AND the fuel system is OK, then

check out the electrical system

• Strategy Rules:– If the car will not start, then first check out the fuel

system then check out the electrical system

• Heuristic Rules:– If the car will not start AND the car is a 1957 Ford,

then check the float

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Types of Rules

• Pattern matching rules (Rules with variables):– If ?x is employee AND ?x age > 65, then ?x can be

retired

• Uncertain Rules– If the car will not start, then the probability

that the electrical system operate normally is 50%.

• Meta Rules– If the car will not start AND the electrical

system operating normally, then use rule concerning the fuel system

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Knowledge Representation Techniques

• Object-Attribute-Value Triple• Rules• Semantic nets• Frames• Logic oPropositional logicoFirst-order logic

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Semantic Networks

Two Types of Nets:

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Semantic Networks

• A classic representation technique for propositional information

• Rooted from Human Associative Memory

• Semantic nets consist of nodes (objects, concepts, situations) and arcs (relationships between them).

• The OAV triple can be used to characterize all the knowledge in a semantic net.

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Common Types of Links

• IS-A – relates generic nodes to generic nodes

• A-KIND-OF – relates an instance or individual to a generic class

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Semantic Net Example

Living Organism

Plant Animalisa isaisa

isa isaisa

isa isaisa

isa

isa isa

akoako

Fly

Swim Penguin EagleSparrow

walk

Cat family

Morris

Locomotion

Locomotion

Eats

House Cats Mice

rodents

Fred

Mammal

…

Bird

…

Locomotion

Eats

ako: a kind of

Inheritance(OO)

Exception handling(override)

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Semantic Net Example

Dog

d b

ako

Bite

assailant (attacker)

Mail-carrier

m

ako ako

victim

“The dog bit the mail carrier”

ako: a kind of

b: يك عمل گاز گرفتن

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Semantic Net Example

John g

Give

agent

Book

b

ako akoobject

Mary

beneficiarygive(John, Mary, book)

“John gives Mary a book”

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Semantic Net Example

Mammal

Person

Owen

Nose

Red Liverpool

isa

ako

has-part

uniform color tea

m

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PROLOG and Semantic Nets

• UniformColor(Owen,Red).• Team(Owen, Liverpool).• AKO(Owen, Person).• HasPart(Person, Nose).• ISA(Person, Mammal).

Mammal

Person

Owen

Nose

Red Liverpool

isa

ako

has-part

uniform color tea

m

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Problems with Semantic Nets

• One problem with semantic nets is lack of standard definitions for link names (IS-A, AKO, etc.).

– Solution: OAV

• To represent definitive knowledge, the link and node names must be rigorously defined.

– Solution: Extensible markup language (XML) and ontologies.

• Problems also include combinatorial explosion of searching nodes.

– Ex. What’s the name of Pluto planet’s football team?

• Inability to define knowledge the way logic can

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Knowledge Representation Techniques

• Object-Attribute-Value Triple• Rules• Semantic nets• Frames• Logic oPropositional logicoFirst-order logic

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Frames

• Semantic nets provide 2-dimensional knowledge; frames provide 3-dimensional.

– Semantic Nets + Procedures = Frames

– Data (Properties) + Procedures = objects (like in OO)

• A frame is a group of slots and fillers that defines a stereotypical object that is used to represent generic / specific knowledge.

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A Car Frame

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Frame Examples

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Frame Examples(in combination with semantic nets)

Animals

AliveFlies

TF

Birds

LegsFlies

2T

Mammals

Legs 4

Penguins

Flies F

Cats Bats

LegsFlies

2T

Opus

NameFriend

Opus

Bill

NameFriend

Bill

Pat

Name Pat

AKO

isa

isa

AKO AKO

isa

isa isa

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Knowledge Representation Techniques

• Object-Attribute-Value Triple• Rules• Semantic nets• Frames• Logic oPropositional logicoFirst-order logic

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Propositional logic

• Logical constants: true, false • Propositional symbols: P, Q,... (atomic sentences)• Sentences are combined by connectives:

and [conjunction] or [disjunction] implies [implication / conditional] is equivalent [biconditional] not [negation]

• Literal: atomic sentence or negated atomic sentenceP, P

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Truth Tables

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Implies (P Q)

• When is PQ true? Check all that apply P=Q=true P=Q=false P=true, Q=false P=false, Q=true

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Implies (P Q)

• When is PQ true? Check all that apply P=Q=true P=Q=false P=true, Q=false P=false, Q=true✔

✔

✔

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Examples of PL sentences

• (P Q) R “If it is hot and humid, then it is raining”

• Q P “If it is humid, then it is hot”

• Q “It is humid.”

• We’re free to choose better symbols, btw:Ho = “It is hot”Hu = “It is humid”R = “It is raining”

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PL: Advantages and Disadvantages

• Advantages– Simple KR language sufficient for some problems– Lays the foundation for higher logics (e.g., FOL)– Reasoning is decidable, though NP complete, and efficient

techniques exist for many problems• Disadvantages

– Not expressive enough for most problems– Hard to identify “individuals” (e.g., Mary, 3)– Can’t directly talk about properties of individuals or relations

between individuals (e.g., “Bill is tall”)– Generalizations, patterns, regularities can’t easily be

represented (e.g., “all triangles have 3 sides”)

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First-order logic

• Whereas propositional logic assumes the world contains facts,

• first-order logic (like natural language) assumes the world contains

• Objects: people, houses, numbers, colors, baseball games, wars, …– Relations: red, round, prime, brother of, bigger

than, part of, comes between, …– Functions: father of, best friend, one more than,

plus, …

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Syntax of FOL: Basic elements

• Constants KingJohn, 2, NUS,... • Predicates Brother, >,...• Functions Sqrt, LeftLegOf,...• Variables x, y, a, b,...• Connectives , , , , • Equality = • Quantifiers ,

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Atomic sentences

• Atomic sentence:predicate (term1,...,termn)

• Term: function (term1,...,termn) or constant or variable

• E.g., – Brother(KingJohn,Richard) – > (Length(LeftLegOf(Richard)), Length(LeftLegOf(KingJohn)))

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Complex sentences

Complex sentences are made from atomic sentences using connectives•

S, S1 S2, S1 S2, S1 S2, S1 S2,

• E.g. Sibling(KingJohn,Richard) Sibling(Richard,KingJohn) >(1,2) ≤ (1,2) >(1,2) >(1,2)

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Universal quantification

<variables> <sentence>• Everyone at IAUDA is smart:• x At(x,IAUDA) Smart(x)

• equivalent to the conjunction of instantiations of PAt(KingJohn,IAUDA) Smart(KingJohn)

At(Richard,IAUDA) Smart(Richard) At(Maryam,IAUDA) Smart(Maryam) ...

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Existential quantification

• <variables> <sentence>

• Someone at IAUDA is smart:• x At(x,IAUDA) Smart(x)

• equivalent to the disjunction of instantiations of PAt(KingJohn,IAUDA) Smart(KingJohn)

At(Richard,IAUDA) Smart(Richard) At(Maryam,IAUDA) Smart(Maryam) ...

Assignment 1:Knowledge Representation

• Due date: 93/12/21• Email to: azrabiee@gmail.com• Email Subject: ES_Assignment 1