Knowledge Representation - Budditha Hettige...2019/11/02 · – Frames – Scripts – Ontology 3...

Knowledge Representation

Budditha HettigeDepartment of Computer Engineering

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Overview

• Introduction

• Logical Representation

– Propositional Logic

– Predicate Logic

• Procedural representation

• Network representation

• Structured representation

– Frames

– Scripts

– Ontology

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Introduction

• Knowledge Representation (KR) is an

approach to Artificial Intelligence

• The concept of KR is as old as AI

• KR formalisms allows to represent and

reasoning on knowledge

• There are so many types of knowledge

• Requires different ways to represent

knowledge

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Types of Knowledge

• Static knowledge

• Dynamic or active knowledge

• Surface knowledge

• Deep knowledge

• Procedural knowledge

• Declarative knowledge

• Meta knowledge

• Heuristic knowledge

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Major KR Techniques

• Logical Representation Schema

• Procedural representation

• Network representation

• Structured representation

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Logical representation

• Oldest form of knowledge representation

• Propositional and Predicate logic are so

popular in KR in Artificial Intelligence

• Precise representation and effective

reasoning mechanism

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Logic

• A formal system for describing knowledge

• Logic is a language

• Logic deals with

– Syntax

– Semantics

– Inference mechanism

• Ontological/Epistemological concern

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Ontology/Epistemology

Language Ontology Epistemology

Propositional logic Facts T/F/Unknown

Predicate logic Facts, objects,

relations

T/F/unknown

Temporal Logic Facts, objects,

relations, time

T/F/unknown

Fuzzy logic Degree of truth Degree of belief

0….1

Propositional logic

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Propositional logic

• Proposition is a statement (sentence) which is either true or false

• Propositional symbols such as P, Q are used to represent sentences

• The following logical connectives are used to combine propositions– ∩ conjunction (AND)

– ∪ disjunction (OR)

– ¬ not

– → implies

– ↔ equivalence or if and only if

Example

• P means “It is hot.”

• Q means “It is humid.”

• R means “It is raining.”

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

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

Budditha Hettige ([email protected]) 11

Example

• Examples of propositions:– The Moon is made of green cheese.

– Trenton is the capital of New Jersey.

– Toronto is the capital of Canada.

– 1 + 0 = 1

– 0 + 0 = 2

• Examples that are not propositions.– What time is it?

– x + 1 = 2

Source: (Richard Mayr University of Edinburgh, UK)

7/11/2015 Budditha Hettige ([email protected]) 12

Syntax

• Sequence of element of the vocabulary yields a formula

• The formula which abide the rules of propositional logic is called well formed formula (WFF)– A symbol is a sentence

– If S is a sentence, then S is a sentence

– If S is a sentence, then (S) is a sentence

– If S and T are sentences, then (S T), (S T), (S T), and (S ↔ T) are sentences

Budditha Hettige ([email protected]) 13

Logical connectives

• Disjunction

The disjunction of propositions p and q is

denoted by p ∨ q and has this truth table:


logical connectives

• The Conjunction of propositions p and q is

denoted by p ∧ q and has this truth table:


logical connectives

• Implication

– If p and q are propositions, then p → q is a

conditional statement or implication which is

read as “if p, then q” and has this truth table:


Implication

• In p → q, p is the hypothesis (antecedent

or premise) and q is the conclusion (or

consequence).

• Implication can be expressed by

disjunction and negation: p → q ≡ ¬p ∨ q


Different Ways of Expressing p

→ q

• if p, then q

• p implies q

• if p, q

• p only if q

• q unless ¬p

• q when p

• q if p

• q whenever p

• p is sufficient for q

• q follows from p

• q is necessary for p

a necessary

condition for p is q

• a sufficient condition

for q is p


Biconditional

• If p and q are propositions, then the biconditional proposition p ↔ q has this truth table

• p ↔ q also reads as

– p if and only if q

– p iff q.

– p is necessary and sufficient for q

– if p then q, and conversely

– p implies q, and vice-versa


Precedence of Logical Operators

1. ¬

2. ∧

3. ∨

4. →

5. ↔

• Thus p ∨ q → ¬r is equivalent to (p ∨ q) → ¬r.

• If the intended meaning is p ∨ (q → ¬r) then parentheses must be used.


Logical Equivalence

• Definition

– Two compound propositions p and q are logically equivalent if the columns in a truth table giving their truth values agree.

– This is written as p ≡ q.

• It is easy to show:Factp ≡ q if and only if p ↔ q is a tautology.


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Propositional logic …

• Assignment: each raw of a truth table

• Interpretation: what each assignment yields

• Model: an assignment that makes a true interpretation

• Counter example: an assignment that makes a false interpretation

• Tautology an expression whose interpretation is always true Example: p ∨ ¬p.

• Contradiction: an expression whose interpretation is always false Example: p ∧ ¬p.

• Equivalence - Two expressions with same interpretations

De Morgan’s Laws

• ¬(p ∧ q) ≡ ¬p ∨ ¬q¬(p ∨ q) ≡ ¬p ∧ ¬q

• Truth table proving De Morgan’s second

law.


Logical Equivalences


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Logical Equivalences contd.

• (P) P

• PQ QP

• P Q PQ

• (PQ) PQ

• (PQ) PQ

• P(QR) (PQ) (PR)

• P Q Q P

Logical Equivalences contd.


Conditional Biconditional

A Proof in Propositional Logic

• To prove: ¬(p ∨ (¬p ∧ q)) ≡ ¬p ∧ ¬q

¬(p ∨ (¬p ∧ q)) ≡ ¬p ∧ ¬(¬p ∧ q) by De Morgan’s 2nd law

≡ ¬p ∧ (¬(¬p) ∨ ¬q) by De Morgan’s first law

≡ ¬p ∧ (p ∨ ¬q) by the double negation law

≡ (¬p ∧ p) ∨ (¬p ∧ ¬q) by the 2nd distributive law

≡ F ∨ (¬p ∧ ¬q) because ¬p ∧ p ≡ F

≡ (¬p ∧ ¬q) ∨ F by commutativity of disj.

≡ ¬p ∧ ¬q by the identity law for F


Conjunctive and Disjunctive

Normal Form

• A literal is either a propositional variable, or the negation of one.

– Examples: p, ¬p.

• A clause is a disjunction of literals.

– Example: p ∨ ¬q ∨ r.

• A formula in conjunctive normal form (CNF) is a conjunction of clauses.

– Example: (p ∨ ¬q ∨ r) ∧ (¬p ∨ ¬r)

• Disjunctive normal form (DNF) by swapping the words ‘conjunction’ and ‘disjunction’ in the definitions above.

– Example: (¬p ∧ q ∧ r) ∨ (¬q ∧ ¬r) ∨ (p ∧ r).


Transformation into Conjunctive

Normal Form• Every propositional formula one can construct an equivalent

one in conjunctive normal form.

• Steps

1. Express all other operators by conjunction, disjunction

and negation.

2. Push negations inward by De Morgan’s laws and the

double negation law until negations appear only in

literals.

3. Use the commutative, associative and distributive laws

to obtain the correct form.

4. Simplify with domination, identity, idempotent, and

negation laws.


Transformation into CNF

Transform the following formula into CNF.¬(p → q) ∨ (r → p)

Express implication by disjunction and negation.¬(¬p ∨ q) ∨ (¬r ∨ p)

Push negation inwards by De Morgan’s laws and double negation.

(p ∧ ¬q) ∨ (¬r ∨ p)Convert to CNF by associative and distributive laws.

(p ∨ ¬r ∨ p) ∧ (¬q ∨ ¬r ∨ p)Optionally simplify by commutative and idempotent laws.

(p ∨ ¬r) ∧ (¬q ∨ ¬r ∨ p)and by commutative and absorbtion laws

(p ∨ ¬r)


Translating English Into Logic

The word “but” in English is often translated as ∧.

– Example: Today is is hot but it is not sunny.

– Because the second part of the sentence is a surprise, “but” is used instead of “and”.

– Example: Write each sentence in symbols, assigning propositional variables to statements as follows:

• P: It is hot.

• Q: It is sunny.

– It is not hot but it is sunny.


Translating English Into Logic

• Example:

You can use the microlab only if you are a cs major or not a

freshman.• P: You can use the microlab.

• Q: You are a cs major.

• R: You are a freshman.

– Rewrite the statement using logical connectives.

• Example:If it snows or rains today, I will not go for a walk.

– Rewrite this proposition using logical connectives and propositional variables


Deriving the Semantic Values

• If Peter and Susan leave, I will be upset

– KEY: p = Peter leaves; q = Susan leaves; r = I

will be upset.


Simplification

• Example: Simplify the formula

(P ∧ Q) ∨ ¬ (¬ P ∨ Q).

• Solution


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Propositional Logic..

• An argument consists of a set of propositions called premises and another proposition called conclusion as in the following statement

P1P2P3……Pn C

• If the above statement is a tautology, then the argument is called valid

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Reasoning – Example

((P Q)QP R) R

LHS – ((P Q)QP R) (using modus tolens) P(P R) (P R)P (P R)P (using modus ponens) R (i.e. RHS)

• Note that this can also be shown by using truth tables

• Better way would be use CNF and method of contradiction

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Conjunctive normal forms

• We can express propositional logic formulae as conjunct of disjunction (CNF)

• Procedure– Eliminate , replacing PQ with

(P Q)(Q P)

– Eliminate , replacing P Q with PQ

– Push negation in using• (P) P, (PQ) PQ, (PQ) PQ

– Distribute over (break at sign)

• With the use of CNF proof can be done by using the method of contradiction

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Example

• Consider the paragraph:If Sarath works hard and or lucky he can pass the exam. Sarath is curious but he is not lucky. If sarath is curious then he works hard.

• From this paragraph, check whether sarath can pass the exam.

• Let P- sarath works hard,

Q- Luck

S- sarath is curious

R- pass exam

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Example…Then the paragraph can be written in propositional logic as follows

(PQ) R ----(a)

SQ ----(b)

S P ----(c)Convert these into CNF

(a) Eliminate , we get (PQ)R

remove , then get (PQ)R

R(PQ)

(R P) (RQ)

break at sign

(R P) ----(a1)

(RQ) ----(a2)

(b) Only the last step apply

S ----(b1)

Q ----(b2)

( c) elimination

SP ----(c1)

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Example …..

Thus CNF are as follows(R P) ----(a1)

(RQ) ----(a2)

S ----(b1)

Q ----(b2)

SP ----(c1)

Suppose we want to show sarath can pass the exam.

For this purpose, assume its negation is true add it as a new CNF

to the system, i.e. R.

R ----(d1)

Then resolve the above and try to get a contradiction as follows

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Example …

R P R

P SP

S S

{ }

Therefore, we conclude that R is true

Limitations of Propositional logic

• Inability to generalize

• Inability to represent internal information

• Example: Suppose we have:• “All men are mortal.”

• “Socrates is a man”.

• Does it follow that “Socrates is mortal” ?

– This cannot be expressed in propositional logic.

– We need a language to talk about objects, their properties and their relations.


Predicate Logic

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First-order Logic

• This is also known as predicate logic• Address the issues of propositional logic• Predicates are defined as objects with

properties– E.g. fruit(mango).– fruit is name of the predicate and mango is a property

• Using a variable for a property we can achieve generalization

• Predicate name tells us about what the predicate represents

• Quantifiers can be used to define the scope of variables

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Syntax of first-order logic

• Sentence AtomicSentence |Sentence Connective Sentence |Quantifier Variable Sentence

| Sentence

• AtomicSentences Predicate(Term, ....)Term =Term

• Term Function (Term, …)

| Constant

| Variable

• Connectives |||

• Quantifier |

• Constant A|X1|Asoka| ….

• Variable a|x| ….

• Predicate Before|Hascolour|Raining|.....

• Functions Mother|….

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Quantifiers in FOL

• x universal quantifiers

– Read as for all x

• x – existential quantifier

– Read as for some, there exists

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Examples

• Everything is fine x fine(x)

• Something is expensive x expensive(x)

• All dogs are animal

– x dog(x) animal(x)

• Some dogs are friendly

– x dog(x) friendly(x)

• Nothing is fine x fine(x)

• Not everything is fine x fine(x)

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Order of quantifiers

• xy P(x,y) yx P(x,y)

• x y P(x,y) y x P(x,y)

• xy P(x,y) yx P(x,y)

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Inference in First-order logic

• Most useful rule is the modus ponens

– P(a), P(x) Q(x)├ Q(a)

• This happens through substitution for

variables and unification

Modus ponens Example

• If it is raining, I will meet you at the theater.

It is raining. Therefore, I will meet you at

the theater.

• Modus ponens can be stated formally as:


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Conversion procedure FOL to CNF

step 1: remove all “=>” and “” operators

(using P => Q ~P v Q and P Q P => Q ^ Q => P)

step 2: move all negation signs to individual predicates

(using de Morgan’s law)step 3: remove all existential quantifiers y

case 1: y is not in the scope of any universally quantified variable, then replace all occurrences of y by a skolem constant

case 2: if y is in scope of universally quantified variables x1, ... xi,then replace all occurrences of y by a skolem function

with x1, ... xi are its argument

step 4: remove all universal quantifiers x (with the understanding that all remaining variables are universally quantified)

step 5: convert the sentence into CNF (using distribution law, etc) step 6: use parenthesis to separate all disjunctions, then drop all v’s

and ^’s

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Example – FOL to CNF

• Consider the sentence “every one who loves all animals is loved by someone”x [y animal(y)loves(x,y)] [y loves(y,x)]

• Using S1 (note replacing P Q with PQ)

x [ y animal(y)loves(x,y)][y loves(y,x)]

• Using S2 push inwards

x [y (animal(y)loves(x,y))][y loves(y,x)]

x [y animal(y)loves(x,y))][y loves(y,x)]

x [y animal(y)loves(x,y))][y loves(y,x)]

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Example – FOL to CNF…

• Use S3 to rename variable not to appear twice

x [y animal(y)loves(x,y))][z loves(z,x)]• Use S4 to introduce constants to existential

quantifiers

x [animal(A)loves(x,A))]loves(B,x)Note: this A can be a F(x) and B is G(x) as they depend on x

x [animal(F(x))loves(x,F(x)))]loves(G(x),x)

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Example – FOL to CNF…

• Use S5

[animal(F(x))loves(x,F(x)))]loves(G(x),x)

• Use S6

[animal(F(x))loves(G(x),x)]

[loves(x,F(x)))loves(G(x),x)]

Proof by contradiction

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Resolution Proof - Example

• Consider the exampleEvery one who loves all animals is loved by someone.

Anyone who kills an animal is loved by no one

Jack loves all animals

Either Jack or Curiosity killed the cat, who is named Tuna

Did Curiosity kill the cat?

• Write these sentences in predicate logic (FOL)

• Covert them into corresponding CNF

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Writing in FOL

A. x [y animal(y)loves(x,y)] [y loves(y,x)]

B. x [y animal(y) kills(x,y)] [z loves(z,x)]

C. x animal(x) loves(Jack,x)

D. kills(Jack,Tuna) kills(Curiosity, Tuna)E. Cat(Tuna)

F. x cat(x) animal(x)

G. kills(Curiosity, Tuna) Note that we have assumed that Curiosity did not kills Tuna, as

we prove this using method of contradiction

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Corresponding CNF

A1 animal(F(x)) loves(G(x), x)

A2 loves(x,F(x)) loves(G(x), x)

B aniaml(y)kills(x,y) loves(z,x)

C aniaml(x)loves(Jack,x)

D kills(Jack, Tuna) kills(Curiosity, Tuna)

E cat(Tuna)

F cat(x) animal(x)

G kills(Curiosity, Tuna)

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Example of Automatic Theorem Proof:Did Curiosity kill the cat

• Jack owns a dog. Every dog owner is an animal lover. No animal lover kills an animal. Either Jack or Curiosity killed the cat, who is named Tuna. Did Curiosity kill the cat?

• These can be represented as follows:A. (x) Dog(x) ^ Owns(Jack,x)

B. (x) ((y) Dog(y) ^ Owns(x, y)) => AnimalLover(x)

C. (x) AnimalLover(x) => (y) Animal(y) => ~Kills(x,y)

D. Kills(Jack,Tuna) v Kills(Curiosity,Tuna)

E. Cat(Tuna)

F. (x) Cat(x) => Animal(x)Q. Kills(Curiosity, Tuna)

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• Convert to clause form

A1. (Dog(D)) /* D is a skolem constant */

A2. (Owns(Jack,D))

B. (~Dog(y), ~Owns(x, y), AnimalLover(x))

C. (~AnimalLover(x), ~Animal(y), ~Kills(x,y))

D. (Kills(Jack,Tuna), Kills(Curiosity,Tuna))

E. Cat(Tuna)

F. (~Cat(x), Animal(x))

• Add the negation of query:

Q: (~Kills(Curiosity, Tuna))

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• The resolution refutation proofR1: Q, D, {}, (Kills(Jack, Tuna))

R2: R1, C, {x/Jack, y/Tuna},

(~AnimalLover(Jack), ~Animal(Tuna))

R3: R2, B, {x/Jack}, (~Dog(y), ~Owns(Jack, y),

~Animal(Tuna))

R4: R3, A1, {y/D}, (~Owns(Jack, D),

~Animal(Tuna))

R5: R4, A2, {}, (~Animal(Tuna))

R6: R5, F, {x/Tuna}, (~Cat(Tuna))

R7: R6, E, {} ()

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Proof by contradiction

cat(Tuna) cat(x) animal(x) kills(Jack, Tuna)kills(Curiosity, Tuna)

kills(Curiosity, Tuna)

animal(Tuna)

kills(Jack, Tuna)

aniaml(y)kills(x,y) loves(z,x)

kills(x,Tuna)loves(z,x)

loves(z,Jack)

loves(x,F(x)) loves(G(x), x)

aniaml(x)loves(Jack,x)

aniaml(F(Jack)) loves(G(Jack), Jack)

animal(F(x)) loves(G(x), x)

loves(G(Jack), Jack)

loves(z, Jack)

{ }

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Horn Clauses

• A Horn clause is a clause with at most one positive literal:

(~P1(x), ~P2(x), ..., ~Pn(x) v Q(x)), equivalent to

x P1(x) ^ P2(x) ... ^ Pn(x) => Q(x) or

Q(x)

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Procedural Representation

• This is the rule-based representation of

knowledge

• In this approach knowledge is represented

in the form of

IF

THEN

ELSE

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Examples– rule-based representation

• IF you follow lectures and do assignment

THEN you will pass the examination.

• IF you pass the exam THEN you will find a

job ELSE you should change the career

path

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Production Systems

• Expert systems that use rule-based KR

are called production systems

• Rules-based KR is the most widely use

KR technique for Expert systems

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Inference in rule-based representation

• Backward chaining

– Begins with a hypothesis, matches with the

head of a rule and tries to satisfy its body by

matching with head of another rule

– By default Prolog operates in this manner

• Forward chaining

– Begins with facts, and tries to derive moving

towards conclusion.

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Example – Rule-based KB

kitchen

br hall

leak_in_bathroom :- hall_wet, kitechn_dry

problem_in-kitechen :- hall_wer,bathroom_dry

no_water_fron_out_side :- window_closed

; no_rain

leak_in_kichen :- problem_in_kitchen,

no_water_from out_side

Some Observations as facts

hall_wet.

bathroom_dry.

window_closed.

Query ?- leak_in_kitchen.

yes

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Inference network

kitechn_dry

leak_in_bathroom

hall_wet

problem_in_kitchen

bathroom_dry

leak_in_kitchen

window_closed

no_water_from_outside

no_rain

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Backward chaining example

• Begin with the hypothesis say, leak_in_kitchen

• Moving backward, to confirm this we need problem_in_kitchen and

no_water_from_outside to be true

• The former is confirmed with hall_wet and bathroom_dry

• Latter is confirmed, say by knowing window_is_closed

• Thus our hypothesis is proved.

• Note: BC begins with the goal in mind. So, good for problems when

the goal is known.

• E.g. diagnosis

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Forward chaining example

• Start with some known facts (but not from a hypothesis)

• For example, having noticed the hall_wet and bathroom_dry concludes that problem_in_kitchen

• Having noticed, window_closed the concludes no_water_from_outside

• From the above two, we conclude leak_in_kitchen

• Note: if we begin with facts, kitchen_dry and hall_wet we get unnecessary conclusion, leak_in_bath_room

• As such FC can go ahead with unnecessary derivations, without an idea about a goal

• Good for configuration, planning, design problems

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Advantages of rules

• Easy to implement

• Easy to drive process reasoning

• Easy to modify and maintain

• Can extend incorporating concepts such

as uncertainty

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Network Representation

• A graphical representation of knowledge

• It comprises of nodes and links

• The nodes represent objects/entities, while

links represent relationships

• Semantic Network is the well-known

network representation of knowledge

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Example 1 - Semantic networks

buddithaAI

teaches

lecturer

Is_a

Human

being

Is_a

writing

enjoys

needs

food

Semantic net represents inheritance

For example, ‘budditha is_a lecturer, lecturer is_a

human being, human being needs food infer that

Budditha needs food

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Example 2 – Semantic network

Ostrich

bird

cannot flyhas_feature

can fly

has_feature

is_a

animal

subset

Can move

has_feature

Due to inheritance from superior

nodes we can conclude that

(i) Ostrich can move

(ii) Ostrich can fly

However, local assigned attribute can override inherited attributes

Therefore, we can conclude that Ostrich cannot fly

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Comments on Semantic networks

• Easy to understand

• Large domains may need very complex

semantic networks

• Cannot represent negations, disjunction,

variables and quantifiers

• Yet, we can include logic and rules with

semantic networks to overcome the above

issue

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Structured Representation

• There are two major types of structured

representations of knowledge

– Frames

– Scripts

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Frames

• A frame is a collective description

• As such, frames are more comprehensive

than nodes in a semantics network

• The concept of frames has been influential

to develop the modern object-oriented

representation too

• A frame comprises of its name, slots

(attribute) and filers (values)

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Example - FrameConsider the following frame describing about a car

Vehicle: car

Make: Toyota

Model: 1002

Fuel: diesel

Name of the frame

slots

value

Note: we can define new frames by referring to values of slots of a given frame

For example, we define new frame as vehicle:Toyota and link the new

frame with the above frame through the slot called ‘Make’

So we can have a network of frames

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Comments on Frames

• Frames are more comprehensive than

semantics networks

• Frames can also be manipulated through

concepts such as inheritance

• However, Frames can represent only the

Static descriptions, but not dynamic

scenarios.

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Scripts

• Scripts can represent dynamic scenarios

• Its inspired by the concept of script in film

and drama

• As such scripts are modeled in terms of

props, actors, acts, scene, etc.

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Components of a script

• Entry conditions– Assumption about the world for a script to begin (e.g. fight)

• Results– Condition to meet once the script terminate

• Props– Things that are involved in the scene (tables, etc.)

• Roles– People and actions

• Scenes– Temporal sequence of the sub-event in a script

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Ontology

• Ontology has many definitions

• It’s a specification something showing related

entities

• It’s about categories of objects

• More comprehensive than objects in isolation

• Next paradigm for KR and computing

• Many tools are available for ontological

modelling (OntoWeb)

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Ontology: Origins and History

Ontology in Philosophy

A philosophical discipline - a branch of philosophy that deals with the nature and the organisation of reality

Science of Being (Aristotle, Metaphysics, IV, 1) Tries to answer the questions:

What characterizes being?Eventually, what is being?

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Ontology in Linguistics

ReferentFormStands for

Relates toactivates

Concept

[Ogden, Richards, 1923]

“Tank“ ?

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Ontology Definition

Formal, explicit specification of a shared conceptualization

commonly accepted

understanding

conceptual model

of a domain

(ontological theory)

unambiguous

terminology definitions

machine-readability

with computational

semantics

[Gruber93]

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Ontology in Computer Science

• An ontology is an engineering artifact:

– It is constituted by a specific vocabulary used to describe a certain reality, plus

– a set of explicit assumptions regarding the intended meaning of the vocabulary.

• Thus, an ontology describes a formal specification of a certain domain:

– Shared understanding of a domain of interest

– Formal and machine manipulable model of a domain of interest

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Structure of an Ontology

Ontologies typically have two distinct components:

Names for important concepts in the domain– Elephant is a concept whose members are a kind of animal

– Herbivore is a concept whose members are exactly those animals who eat only plants or parts of plants

– Adult_Elephant is a concept whose members are exactly those elephants whose age is greater than 20 years

• Background knowledge/constraints on the domain– Adult_Elephants weigh at least 2,000 kg

– All Elephants are either African_Elephants or Indian_Elephants

– No individual can be both a Herbivore and a Carnivore

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Ontology Example

Concept conceptual entity of the domain

Attributeproperty of a concept

Relation relationship between concepts or properties

Axiom coherent description between Concepts / Properties / Relations via logical expressions

Person

Student Professor

Lecture

isA – hierarchy (taxonomy)

name email

studentnr.

researchfield

topiclecture

nr.

attendsholds

holds(Professor, Lecture) Lecture.topic Professor.researchField

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Ontology Elements

• Concepts (classes) + their hierarchy

• Concept properties (slots/attributes)

• Property restrictions (type, cardinality,

domain)

• Relations between concepts (disjoint,

equality)

• Instances

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How to build an ontology?

• Steps:

– determine domain and scope

– enumerate important terms

– define classes and class hierarchies

– define slots

– define slot restrictions (cardinality, value-type

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Step 1: Determine Domain and Scope

Domain: geography

Application: route planning agent

Possible questions:Distance between two cities?

What sort of connections exist between two cities?In which country is a city?How many borders are crossed?

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Step 2: Enumerate Important Terms

country

city capital

border

connection

Connection_on_land

Connection_in_air

Connection_on_water

road

railway

currency

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Step 3: Define Classes and Class Hierarchy

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Step 4: Define Slots of Classes

Geographic_entity

Country CityHas_capital

Capital_ofBorders_with

ConnectionStart_point

End_point

Capital_city

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Step 5: Define slot constraints

• Slot-cardinality

– Ex: Borders_with multiple, Start_point single

• Slot-value type

– Ex: Borders_with- Country

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Many languages use “object oriented”

model based on:

• Objects/Instances/Individuals– Elements of the domain of discourse

– Equivalent to constants in FOL

• Types/Classes/Concepts– Sets of objects sharing certain characteristics

– Equivalent to unary predicates in FOL

• Relations/Properties/Roles– Sets of pairs (tuples) of objects

– Equivalent to binary predicates in FOL

• Such languages are/can be:– Well understood

– Formally specified

– (Relatively) easy to use

– Amenable to machine processing

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Ontology-development tools

• Protégé

• OntoEdit

• OilEd

• Chimaera

• …

Activity

• Create a simple ontology using protege

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Thank you

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Knowledge Representation - Budditha Hettige...2019/11/02 · – Frames – Scripts – Ontology 3...

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