Transcript Knowledge Representation Methods(1/2)

KNOWLEDGE
REPRESENTATION
최윤정
Knowledge Representation Methods
2

Declarative Methods
--knowledge is knowing WHAT

Procedural Methods
--knowledge is knowing HOW
Logical Approach





Predicate Calculus
Nonstandard Logics
Fuzzy Logic
Non-Logical Approach



Semantic Net
Frame (procedural features)
Conceptual Dependency


PLANNER, CONNIVER
Rule-based systems
Semantic Net(1/3) (Quillian(1968)
Psychological Model)
3

Basic Constructs
Node-Object, Concept
 Links-Relation

Tweety
Wings
isa
Robin
Wings
isa
Bird
has-part
Wings
property inheritance
-Property Inheritance is the main inference mechanism!
Semantic Net(2/3)
4
Example
Furniture
store
Sold-by
Furniture
isa
Chair
has-part
Seat
isa
Park
My-Chair
owner
isa
Person
cover
Leather
Color
Black
Semantic Net(3/3)
5

Internal Representation(LISP)

My-Chair:
((ISA CHAIR)(COLOR BLACK)
(OWNER PARK)(COVER LEATHER))

Chair:
((ISA FURNITURE)(HASPART SEAT))
(get `My-CHAIR `COLOR)= `BLACK
Action and Event(1/2)
6

“John gave the book to Mary.”
Event
John
agent
isa
EV-1
object
BK-1
beneficiary
Mary
time
action
Give
Past
isa
Book
Action and Event(2/2)
7

“John is taller than Bill.”
John
Is-taller
Bill
Bill
John
height
height
H1
isa
Number
greater-than
isa
H2
Reasoning with Semantic Nets(1/2)
8

Spreading Activation
“What is the relation between John and Mary?”
John
?
Mary
Reasoning with Semantic Nets(2/2)
9

Matching
Fact
Goal Net
isa
Tweety
Tweety
isa
isa
Robin
?
Direct Match vs. Semantic Match
 What is Tweety?
isa
Bird
Problems of Semantic Net(1/2)
10
1. Different people use different nets to represent the
same thing.
John
married
Mary
Event
isa
Marriage
isa
male
John
M1
female
Mary
Problems of Semantic Net(2/2)
11
2. Same Net interpreted differently by different person.
Jack
Tom
Father-of
3. Quantification
Dealing with Exceptions(1/2)
12
Fly
CAN
Exception
node
Bird
ISA
Ostrich
ISA
Henry
Dealing with Exceptions(2/2)
13

Inferential Distance(Touretzky)
Grey
COLOR
Elephant
ISA
Royal Elephant
ISA
Circus Elephant
ISA
Clyde
isa
Frame (1/2)
-Minsky
14

Slot-Filler Concept
: Typical Expected Situation

[frame: Sedan
ISA: Vehicle
Slots: (number-of-wheel 4)]


[frame: Vehicle
ISA: Object
Slots: (Weight (a wt-measure))
(color (a color(default black)))
(number-of-wheel (a integer))]
[frame: Trailer-Truck
ISA: Vehicle
Slots: (trailer-size (a length-measure))
(weight (default 8))
(number-of-wheel (default 18))]

[frame: My-truck
instance-of: Trailer-Truck
Slots: (trailer-size = 12)
(color red)]
Frame(2/2)
weight=
color= black
wheel=
15
Object
ISA
Vehicle
ISA
weight=8
trailer-size=
wheel=18
Color=black
Trailer-truck
ISA
My-Truck
Weight=8
Trailer-size=12
Wheel=18
Color=red
Procedural Attachment(1/2)
-Procedural knowledge is attached to slots
16
If-Added: Triggered to fill in
If-Needed: Triggered when filled in
If-Modified: Triggered when changed
Employee:
ISA: Person
Sex: (M, F)
Birthday: Date
Age: integer
If-Needed: CALC-AGE
Skill: code
If-Added: ADD-TO-SKILL-FILE
Procedural Attachment(2/2)
17
Proc CALC-AGE;
x:= get-current-year;
y:= get-birth-year;
age:= x-y
end;
Proc ADD-TO-FILE;
c:= get-code;
open-file(skill);
put-file(c, skill)
end;
LOGICAL PRELIMINARIES
18

LOGIC-

LOGIC AS LANGUAGE


ARTIFICIAL LANGUAGE TALKING ABOUT “TRUTH”
SYNTAX(GRAMMAR)
-Symbol
-WFF(Well Formed Formula)
-Deductive Closure
-Proof Theory
SEMANTICS
-Meaning
-Model
-Validity, Consistency
-Model Theory

LOGIC AS A PROGRAMMING LANGUAGE

SYNTAX

SEMANTICS
LOGIC
- LANGUAGE and its MEANING
19
LOGIC
LANGUAGE
MODEL
PROPOSITIONAL
LOGIC
P, Q, P->Q
(P->((-Q->R) ∨P))
Truth Assignment
PREDICATE
CALCULUS
Variables x,y
Functions f, g
Predicates P,Q
Quantifiers ∀,∃
First Order Structure
<D,C,F,P>
MODAL LOGIC
ᄆP, ◇P
Kripke Structure
<W, R, V>
Possible World
Semantics
PROPOSITIONAL LOGIC (1/2)
20

(P∧Q)R
P
Q
R
P∧Q
F
F
F
F
T
T
T
T
F
F
T
T
F
F
T
T
F
T
F
T
F
T
F
T
F
F
F
F
F
F
T
T
(P∧Q)->R
T
T
T
T
T
T
[F]
T
Falsifying Model
PROPOSITIONAL LOGIC (2/2)
21




((PQ)∧~Q)~P
P
Q
F
F
T
T
F
T
F
T
VALID
INCONSISTENT
CONSISTENT
P->Q
T
T
F
T
(P->Q)∧~Q
((P->Q) ∧~Q)->~P
T
F
F
F
TRUE in Every Model(Tautology)
FALSE in Every Model
TRUE in at least ONE Model
VALID

INVALID
INCONSISTENT  CONSISTENT
(Unsatisfiable)
(Satisfiable)
T
T
T
T
FORMAL SYSTEM
22
Well Formed Formula
AXIOM
+
INFERENCE RULES
PROOF THEORY
Language
THEOREM
├ A
VALID
╞ A
MODEL THEORY
THEOREM
VALID
SOUNDNESS (→)
COMPLETENESS (←)
Types of Logical Reasoning
23

Deduction
Given A, AB infer B

Induction
Given A, B find the rule AB

Abduction (Not logically valid!)
Given AB, B infer A

Refutation Proof
Proof by Cases
24

Is there a Red Box right next to a Non-Red Box?
?
Refutation Proof
25

A, AB
want to prove B
Assume ¬B and find a contradiction
Most Common Method using Computer
- Resolution, Tableau Method etc.
PROVING VALIDITY in
PROPOSITIONAL LOGIC
26




1. TRUTH TABLE
2. TABLEAU METHOD
3. SEQUENT CALCULUS
4. RESOLUTON
TABLEAU METHOD
27

Refutation Method
(Assuming FALSE and draw CONTRADICTION)
Q) ∧ -Q )
(( P
-P
F
T
T
F
T
T
T
F
CONTRADICTION
RESOLUTION (Robinson)
28

A  B, B  C, A
C?
-A ∨ B
-B ∨ C
-A ∨ C
C
A
-C
Example 1 (1/2)
29
“Head I win, Tail you lose.”
Prove I win.
H: head
T: tail
W: I win
L: You lose
(Hidden information)
H∨T
WL
L W
HW
T L
Example 1 (2/2)
30
-H∨W
-T∨L
H∨T
-W∨L
-L∨W
-W
~L
~T
H
W
Example: Lion Sleeps Tonight
31





Lion always sleeps except when he is hunting.
Lion cannot sleep when he is hungry.
When he is tired he cannot hunt.
Lion is tired when he does not sleep.
Prove Lion is not hungry.
Resolution Strategies (1/4)
32

1. UNIT RESOLUTION (Wos)
 Not
complete
 UNIT
PREFERENCE RESOLUTION
 Unit clause always reduces the size!
P∨Q
P ∨ -Q
-P ∨ Q
-P ∨ -Q
P
Q
-Q
Resolution Strategies (2/4)
33

2. INPUT RESOLUTION
 Not
complete
 INPUT
P∨Q
CLAUSES HAVE MEANINGFUL INFORMATION
P ∨ -Q
-P ∨ Q
-P ∨ -Q
P
Q
-Q
INPUT
CLAUSES
Resolution Strategies (3/4)
34

3. LINEAR RESOLUTION(Loveland)
 Chain
of Reasoning
 Depth
First
 COMPLETE
P∨Q
P ∨ -Q
-P ∨ Q
-P ∨ -Q
P
Q
-P
Resolution Strategies (4/4)
35

4. LOCK RESOLUTION(BOYER)

COMPLETE

Index every literal (Lock) : consider smallest
P1 Q2
P3 -Q4
-P6 Q5
-P8 -Q7
-P6
Q2
-Q4
Predicate Calculus
36





Variable : object
x, y, z, ..
Constant : a, b, c, tom, 1, 2, ..
Function : f, g, h, father(tom),…
Predicate : P, Q, R
Quantifier : ∀, ∃
Well Formed Formula
37
Term
constant, variable, f(t1, .. tn): ti term
 Atom
P(t1,..tn)
 Formula(wff)
1. atom
2. F∨G, -F, FG
3. (∀x)F, (∃x)F

Nested Quantifiers
38

Describe each statement
∀x ∀y Love(x, y)
∀x ∃y Love(x, y)
∃x ∀y Love(x, y)
∃x ∃y Love(x, y)
∀x ∃y Love(y, x)
∃x ∀y Love(y, x)
Negation of these?
Symbolize the Statement
39








Every rational number is a real number.
There exists a number that is prime.
For every number x, there exists a number y such that x<y.
Not every real number is a rational number.
Everybody has somebody who loves him.
There is someone whom everybody loves.
Mimi loves only those who is younger than her.
Everyone who eats BigMac listens Jazz music.
Clausal Form Conversion
40







1. Eliminate 
2. Reduce the scope of ~
3. Rename the variables
4. Move quantifiers to the left
(prenex normal form)
5. Eliminate ∃ : Skolemize
6. Eliminate ∀
7. Conjunctive Normal Form
Reducing the Scope of ~
41

~ (p ∧ q) = ~p ∨ ~q
~ (p ∨ q) = ~p ∧ ~q

~ Q1Q2..Qn P(x,y,..)
= Q’1Q’2..Q’n ~P(x,y,..)
where Q’ = ∃ if Q=∀
∀ if Q= ∃
Prenex Normal Form
42

Prenex normal form:
Q1Q2..Qn P(x,y,..) where Q i = ∀, ∃

∀x (P(x) ∨ ∀y (Q(y)))
= ∀x ∀y (P(x) ∨ Q(y))

∀x (P(x) ∨ ∃y (Q(x, y)))
= ∀x ∃y (P(x) ∨ Q(x, y))
Skolem Function
43

Eliminating ∃’s
∃x P(x)  P(sk1) : sk1 is skolem constant
∃x ∀y P(x,y)  ∀y P(sk1, y)
∀y ∃x P(x,y)  ∀y P(sk1(y),y)
∀x ∃y ∀z ∃w P(x,y,z,w) 
∀x ∀z P(x,sk1(x),z,sk2(x,z))
Example : Clausal Form
44

∀x((∀y P(x,y)  ~∀y(Q(x,y)  R(x,y)))
∀x( ~∀y P(x,y) ∨ ~∀y (~Q(x,y) ∨ R(x,y))) … (1)
∀x( ∃y ~P(x,y) ∨ ∃y (Q(x,y) ∧~R(x,y))) … (2)
∀x( ∃y ~P(x,y) ∨ ∃z (Q(x,z) ∧~R(x,z)))
… (3)
∀x∃y∃z (~P(x,y) ∨((Q(x,z) ∧~R(x,z)))
… (4)
∀x(~P(x,s1(x))∨((Q(x,s2(x))∧~R(x,s2(x)))) … (5)
~P(x,s1(x))∨((Q(x,s2(x))∧~R(x,s2(x)))
… (6)
(~P(x,s1(x))∨Q(x,s2(x)))∧(~P(x,s1(x))∨~R(x,s2(x)))
Matching
45
Rule : Mother(x, y)  Like(x, y)
“Every Mother Like their Son”
 Fact
Like(Joe, Jack), Like(Kim, Mary)
Mother(Judy, Jack), Mother(Mary, Jay)
 Query
Like(Judy Jack)?
Like(Mary, ?)

Unification(2-way Matching)
46
Find a substitution σ(unifier) which makes two clause
equal
 Essential step for Resolution of Predicate Calculus
 Usually unification tries to find a
most general unifier

Most General Unifier (mgu)
47

Substitution : σ
C = Like(x, father(x))
σ = {jack/x}
C • σ = Like(Jack, father(Jack))

C, D are unifiable iff there is σ s.t.
C • σ = D • σ (σ is called unifier)

Mgu  least specific unifier
Like(x, y), Like(Jack, y)
σ1={Jack/x}, σ2={Jack/x, Mary/y}
Unification - Examples
48
Like(x, y) Like(joe, father(joe))
Like(jack, y) Like(x, father(x))
Like(x, father(x)) Like(joe, y)
Like(x, father(joe)) Like(jack, father(y))
Like(x, father(x)) Like(jack, father(joe))
Like(x, father(x)) Like(father(y),z)
Like(x, x) Like(father(z), z) ?
Factoring
49
If 2 literals in a clause C have mgu σ
then C • σ is called a factor of C
 If C = P(x) ∨ P(f(y)) ∨ ~Q(x)
Then σ = {f(y)/x}
P(f(y))∨P(f(y))∨~Q(f(y))
P(f(y))∨~Q(f(y)) : factor of C

Subsumption
50





Clause C subsumes D iff
∀C  D
(A ∧ B) subsumes A
A subsumes A ∨ B
Subsumed clause can be deleted
C=P(x) D=P(a)  delete P(a)
Note: factoring – within a clause
subsumption – between two clauses
Example
51
1. All EWU students are pretty.
2. Kim only likes an intelligent girl.
3. Pretty girls do not read books.
4. Intelligent girls are either good reader or music lovers.
5. Kim likes Mimi who attends to EWU.
* Prove that Mimi is a music lover
E(x): EWU students
B(x): Book reader
Like(x, y): x likes y
P(x): Pretty
M(x): Music lover
I(x): intelligent
Example - Skolemize
52
Customer officials search everyone who entered the country
who is not a VIP
 Some of the drug dealers entered the country and they were
only searched by drug dealers.
 No drug dealer was a VIP
 Conclusion: Some of the officials were drug dealers.
 E(x) : x entered the country V(x): VIP
C(x) : custom official D(x): drug dealer
S(x,y): x searched y

Types of Question - Resolution
53
Type1: Yes/No Question
“Is Mimi a Music Lover?”
 Type2: Short Answer
“Who is a Music Lover?”
Use special predicate: Ans(x)
 Type3: How to type Question

Type2 Question
54



Every Pompeian died in 79.
Marcus was a Pompeian.
When was Marcus died?
~Died(marcus, x) ∨ Ans(x)
Type3:Monkey Banana Problem
55
P(x, y, z, s) : x: monkey y: banana
z: chair s: state
R(s) : monkey reachable to banana at s
 Functions
walk(l1, l2, s) : at state s, monkey walk
from l1 to l2
carry(l1, l2, s) : carry chair from l1 to l2
climb(s) : at s, monkey climb to the chair

Monkey – continue
56
P(x,y,z,s)  P(z,y,z, walk(x,z,s))
P(x,y,x,s)  P(y,y,y, carry(x,y,s))
P(kit,kit,kit,s)  R(climb(s))
P(liv, kit, din, s1)
R(x)  Ans(x)
----Ans(climb(carry(din,kit,(walk(liv,din,s1)))))
Merit of using Logic as KR
57



Flexible (Rich) Representation
Natural Language > Logic Formula
Note: flexibility is also a weak point of logic
Powerful Inference Mechanism
Resolution, Graphical methods
Theoretical Background  Solid
Weak Points of Logic a KR
58


Too Rigid (Not Flexible)
- no contradiction
- no exception
- no change
Complexity
- NP-complete
Horn-clause (restricted form)
Spin-off Products of Logic
59



Prolog Language
- Specification Language
- Horn clause
Knowledge-base Systems
- Rules & Inference Engine
New Breed of Logics
Real World vs Logic World
60
Dynamic - Static
- keeps on changing
 Incomplete Knowledge
- implicit vs explicit
Default Rules, Closed World Assumption
 Belief vs Truth
 Non-monotonic vs Monotonic
 Uncertainty – Statistical Reasoning

TMS (1/2)
61





Truth Maintenance System - Doyle
Intended to Model Belief Changes
Information is linked together by its justifications
Dependency-directed backtracking
Basic Data Structure


Node: belief
Justification: reason to believe

http://www.aistudy.com/problem/exercise/%EC%A7%84%EB%
A6%AC%EA%B0%92%20%EC%9C%A0%EC%A7%80%20%E
C%8B%9C%EC%8A%A4%ED%85%9C.htm

http://www.aistudy.com/ai/logic_rich.htm
TMS (2/2)
62

2 states of node
– current belief
 OUT – not believed (cf. believed to be not true)
 IN



A node is assigned a justification set
A node is IN iff there is at least one valid
justification
A node is OUT iff there is no valid justification
SL justification (1/3)
63

(SL (list of IN-nodes)(list of OUT-nodes))
 SL-justification
is valid if all the nodes in the IN-node list
are currently IN, and those in the OUT-node list are
OUT.


Statement-1: (SL (x)(y))
Meaning:
 If
x is believed and y is not believed, the statement-1 is
believed.
SL justification (2/3)
64

Special nodes:
– nodes with (SL ()()) always IN
 Assumption – nodes with nonempty OUT-list which is
currently IN. (Default Rule)
 eg. 1. There is other schedule
2. I will be at the party. (SL ()(1))
 Premise
“Unless there is other schedule, I will be at a party.”
SL justification (3/3)
65



1. X : (SL (2)()) : If Y Then X
2. Y
(normal rule)
1. X : (SL ()(2)) : X unless Y
2. Y
(strong default rule – CWA)
1. X: (SL (2)(3)) : If Y Then X Unless Z
2. Y
3. Z
(default rule)
Example 1- Dream
66
If I win Lotto, I’ll be Rich unless it is a Dream.
1. Rich : (SL (2)(3))
2. Lotto Win!
3. Dream
I win Lotto!!!
1. Rich : (SL (2)(3))
2. Lotto Win! ------------- (SL ()())
3. Dream
I pinched myself, and woke up..
1. Rich : (SL (2)(3))
2. Lotto Win! (SL()())
3. Dream -----------------(SL ()())
Example 2
67
1. It is winter
2. It is cold
3. It is warm
4. It is summer
OUT
(SL(1)(3))
(SL(4)(2))
(SL()(1))
OUT
IN
IN
(SL()())
(SL(1)(3))
(SL(4)(2))
(SL()(1))
IN
?
?
?
(SL()())
(SL(1)(3))
(SL(4)(2)) (SL()())
(SL()(1))
IN
?
IN
?
It is winter.
1. It is winter
2. It is cold
3. It is warm
4. It is summer
It is warm outside.
1. It is winter
2. It is cold
3. It is warm
4. It is summer
Example 3 (1/5)
68

This is how Mimi likes to see as her marriage partner.

Not OK unless she really likes him.

She likes a rich man as long as he doesn’t have a problem.

She likes a man if he is healthy and kind as long as he does not have a
problem and is not the eldest son.

A man is problematic if he is older than 35 unless he is exceptional.

Married man is problematic

Love is an exception.
Example 3(2/5)
69

Nodes:
1. Not OK
(SL()(2))
2. She likes him
(SL(3)(4)) (SL(5,6)(4,7))
3. He is rich
4. He has a problem (SL(8)(9)) (SL(10)())
5. He is healthy
6. Kind
7. The eldest son
8. Older than 35
9. Exception
(SL(11)())
10. Married
11. Love
OUT IN
OUT
OUT
OUT
OUT
OUT
OUT
OUT
OUT
OUT
OUT
Example 3(3/5)
70

Currnet belief:
He is healthy and kind
She likes him --- OK
He looks healthy and kind
1. Not OK
(SL()(2))
2. She likes him
(SL(3)(4)) (SL(5,6)(4,7))
3. He is rich
4. He has a problem (SL(8)(9)) (SL(10)())
5. He is healthy
(SL()())
6. Kind
(SL()())
7. The eldest son
8. Older than 35
9. Exception
(SL(11)())
10. Married
11. Love
IN -- OUT
OUT -- IN
OUT
OUT
IN
IN
OUT
OUT
OUT
OUT
OUT
Example 3(4/5)
71

His age is 38!
1. Not OK
(SL()(2))
2. She likes him
(SL(3)(4)) (SL(5,6)(4,7))
3. He is rich
4. He has a problem (SL(8)(9)) (SL(10)())
5. He is healthy
6. Kind
7. The eldest son
8. Older than 35
(SL()())
9. Exception
(SL(11)())
10. Married
11. Love
OUT -- IN
IN -- OUT
OUT
OUT -- IN
IN
IN
OUT
IN
OUT
OUT
OUT
Example 3(5/5)
-- So they married, and
happily there after …
72

Mimi finds herself that she is in love with him.
1. Not OK
(SL ()(2))
2. She likes him
(SL(3)(4)) (SL(5,6)(4,7))
3. He is rich
4. He has a problem (SL(8)(9)) (SL(10)())
5. He is healthy
6. Kind
7. The eldest son
8. Older than 35
(SL()())
9. Exception
(SL(11)())
10. Married
11. Love
(SL()())
IN -- OUT
OUT -- IN
OUT
IN -- OUT
IN
IN
OUT
IN
OUT -- IN
OUT
IN
Cyc : KB for Commonsense
73




Lenat,D (MCC)
Limitation of Logic
Predicate Symbol – No Semantics
Need More Background Knowledge
Build a Huge Knowledgebase to cover human
everyday commonsense
Enough to Understand –
Newspaper Article or Encyclopedia
Cyc: Structure
74
Cyc KB – Knowledgebase
 CycL – Representation Language
 Environment (UE, MUE)
Interface Editing/Browsing
UE: Spread Sheet Type
MUE: Museum Type (Graphic)
(Note: Cyc Needs Lot of Update/Expansion)

CycL : Cyc Language
75


CycL is Frame-Based
Slot-Value
Texas
capital: (Austin)
residents: (Fred Tom Park)
stateOf: (UnitedStatesOfAmerica)
CycL (2)
76
Constraint Language (on Top of Frame)
 Predicate Calculus Type
(#%ForAll x #%Number
(#%LogImplication
(#%GreaterThan x 1)
(#%GreaterThan (#%NumOfDiv x) 1)))

Constraint Language
77
First Order Logic
 ‘All of Fred’s Friends are artists’
(#%ForAll x(#%Fred #%friends)
(#%allInstanceOF x #%Artist))

‘Some of Fred’s Friends are artists’
(#%ThereExists x(#%Fred #%friends)
(#%allInstanceOF x #%Artist))
Frame Types of Cyc
78




Normal
Texas, Fred, Red, Walking.. Etc.
SlotUnit
Frames to Define Slots
SeeUnit
Meta-level Info for certain slot of a unit
SlotEntryDetail
SeeUnit for a member of slot entry
(eg. Park of resident slot of Texas frame)
Slot Unit
79
Slot Frame is a Frame about a Slot
 Define, Constraints, Interrelationships
among Slots
Residents
instanceOf: (Slot)
inverse: (residentOf)
entryIsA: (Person)
…..

SeeUnit
80
Metalevel Information for particular slot for particular unit
(footnote)
 Texas
capital: (Austin)
*residents: (Tom Jack Park..)
…
SeeUnitFor-residents.Texas
instanceOf: (SeeUnit)
modifiesUnit: (Texas)
*rateOfChange: ..

SlotEntry-Details
81
Similar to SeeUnit except it talks about single entry of a slot
 Texas
capital: (Austin)
residents: (Tom Jack *Park..)
…
SeeUnitFor-Park∈residents.Texas
instanceOf: (SlotEntryDetailTypeofSeeUnit)
modifiesUnit: (Texas)
modifiesSlot: (residents)
modifiesEntry: (Park)
…

Inference in CycL
82








What Does Cyc “Do”?
More than 20 Special Purpose Inference Schemes
Inheritance
Automatic Classification
Constraint Maintenance
TMS
Guessing by Closed World Assumption
Analogy Reasoning
Meta-Level Inference
83
Inference Schemes are Divided into Several Levels
 Simple and Fast Schemes are Used before more Slow
and Complex Ones
 Level1: Simply Access the Data Structure
Level2: Inheritance
Level3: Subsumption, Classification
Level4: Constraint
….
Level n : Analogy, Guess, etc.

Cyc Review
84
First Attempt for Global Ontology
 Frame-based
 Mixture of Inference
 Reference:
‘Building Large Knowledge-Based Systems’ by Lenat
& Guha
