Chapter 3: Representing Knowledge in Computer

Chapter 3: Representing Knowledge in Computer Introduction (Representing knowledge, Metrics for assessing knowledge representation schemes), Logic representation, Inference rules, Semantics networks, Frames and Scripts, Decision trees.

Chapter 3

Representing Knowledge

in Computer

K216 C: Studies on Intelligence School of Knowledge Science JAIST

TuBao Ho

 declarative knowledge is knowledge about

things

 location of JAIST, its transport links

 “JAIST is in Tatsunokuchi”, “Hokuriku Railroad Ishikawa

line goes from Nomachi to Tsurugi”

 procedural knowledge is knowledge about

how to do things

 how to get to JAIST

 “Take the Hokuriku Railroad, Ishikawa line to go to

Tsurugi”, “Get on the JAIST shuttle”

particular subject

Example: “JAIST shuttle goes from Tsurugi to JAIST”

that applies throughout our experience

Example: “shuttle bus is a means of transport”

that is possessed by every schoolchild It is evident for human but not for machine

 In order to make use of knowledge in AI and

intelligent systems we need to get it from the source

(knowledge acquisition) and represent it in a form

usable by the machine

 Human knowledge is usually expressed through

machine

 The representation of knowledge in computer must

therefore be both appropriate for the computer to use and allow easy and accurate encoding from the source

The “15 game”: two people A and B take turns

selecting numbers from 1 to 9 without replacement

The person who first has exactly three numbers in his

collection that add up to 15 wins the game

 A 5 9 4 6 win!! (A selects 6 and wins with

Example of representing knowledge

Example of representing knowledge

 A choosing 5 is equivalent to

putting A’s marker in the

tick-tack-toe board Use tick-tick-tack-toe

representation for the “15 game”

A

A BB

B A A

A BB

A

31

45

9

2

6

Aspects of representation languages

1 The syntax describes the possible configurations that

can constitute sentences

 External representation : how sentences are represented on

the printed page

 Internal representation : the real representation inside the

computer

2 The semantics determines the fact in the world to

which the sentences refer Without semantics, a

sentence is just an arrangement of electrons or a

collection of marks on a page

Metrics for assessing knowledge representation schemes

Propositional logic

 A proposition is a statement that can

have one of two values: true or false

( known as truth values )

Example: “It is raining” and “I am

hungry” are propositions whose values

depend on the situation at the time

 Propositions P and Q can be combined

using operators such as and  (PQ)

 simple syntax : proposition symbols such as P and

 the logical connectives  ,  ,  ,  ,  , and ()

 sentences are made by symbols using rules:

- Propositional symbol such as P or Q is a sentence by itself

- Wrapping parentheses around a sentence yields a sentence, e.g.,

(PQ)

- A sentence can be formed by combining simpler sentences with

one of the five logical connectives

Propositional logic

 (and): A sentence using , such as P  (Q  R), is called a

conjunction (logic); its parts are the conjuncts

 (or): A sentence using , such as A  (P  Q), is a

disjunction of the disjuncts A and (P  Q)

 (implies): A sentence such as (P  Q)  R is called an

implication Its premise or antecedent is P  Q, and its

conclusion or consequent is R Implications are also known as

rules or if-then statements

 (equivalent): The sentence (P  Q)  (Q  P) is an equivalence

 (not): A sentence such as P is called the negation of P;

 is the only connective that operates on a single sentence.

Propositional logic

Straightforward semantics: we define it by specifying the interpretation of the proposition symbols and

constants, and specifying the meanings of the logical connectives

Predicate logic

 The propositional logic has limitations in its expressive

power and is expanded to the predicate logic by

introducing terms, functions, predicates, and quantifiers

 A “predicate” denotes a relationship between objects

- Red(x) , a unary relation, is a predicate expression that asserts

that x is red

- Father(Ichiro, Taro) asserts that Ichiro is the father of Taro

 A predicate can take on a value of true or false when its variables have assumed specific values

Predicate logic

 Parametrized propositions give us predicate logic

father(Ichiro, Taro), father(Ichiro, Jiro)

father is the predicate, Ichiro, Taro and Jiro are

 The universal quantifier (  ), e.g.,  x, is the

notation that indicates “for all x”

 The existential quantifier , “there exists” is

 These quantifiers can be combined in the same expression

“Everyone has a mother” can be expressed as (x)(y)[(Human(x)  Mother(y, x)]

 (x)Q(x) expresses the fact that something has a certain property without saying which thing has that property

 (x)[P(x)  Q(x)] expresses the fact that everything in a certain class has a certain property without saying what everything in that class is

Predicate logic

Semantics in logic representation

are merely symbols that are to be manipulated

The system sees no difference between P(x) and

provided by the user mapping the variables and functions to things in the problem domain

between logical symbols and the problem domain

logical system.

Assessing logic representation

relationships between facts and assertions about facts

It is relatively understandable

amenable to computation through PROLOG

representation scheme relatively efficient, although

computational efficiency depends to a degree on the

interpreter being used and the programmer

Outline of chapter 3

 Inference rules

Representing knowledge by rules

 Inference rules (production rules)

A  B （if A then B）

 if (Primary Exam>700) (live in Kansai)(good at

math)

then (take the entrance exam at the School of

Knowledge Science of JAIST)

 if (feel tired)  (has fever)  (sneeze)

Representing knowledge by rules

Given a true fact “Wind blows”, and the rule

if wind blows then the hooper makes money,

We have a total match of the form

A = true

if A then B

and we can conclude B = true To check whether a condition part

matches a fact or an expression is called pattern-matching

if height of X > height of Y

then X is taller than Y

height of Ichiro = 1.70m

height of Jiro = 1.75m, X = Jiro, Y = Ichiro

We get the result “Jiro is taller than Ichiro”

Using logical expressions

The condition part of a production rule can contain the

usual logical expressions The following is a sample

condition:

Ex if the season is june  isobarometric line runs

east to west

then isobarometric line is the line of rainy season

Ex if the line of rainy season is at the south shore of

Japan  cloud is growing at the south shore of Japan

then the south shore will have heavy rain

 should not write rules that are inconsistent Rules in

which the condition parts are the same should have the same action parts

if A then B and if A then B

 should not write a production rule that causes a loop

Assessing inference rules

procedural knowledge They are ideal in situations

where knowledge changes over time and where the

final and initial states differ from user to user (or

subject to subject)

procedural problems, and their flexibility makes it

transferable between domains

Semantics networks

itself; it is also the relationships that exist among facts

that objects or concepts can be joined by some relationship Semantic networks

Relationship among concepts

x1 x2

pred

xn

R

x1 x2

The basic unit of a semantic network, as shown in Figure (a),

corresponds to R(x,y) in predicate logic A relation, R(xl, x2, …, xn),

with n arguments when expressed in logic, is hard to express in a

semantic network But it might look like Figure (b).

 A common relation that joins two concepts in a

semantic network is the more General/less General

Taro  human being  animal

 Other relations besides isa links are:

has X has Y (Y is a partial concept of X)

Relationship among concepts

black hair has

is isa

23 year old Taro student

is studies with

at tall friend knowledge science school

Taro is a student.

Taro is 23 years old

Taro is tall

Taro has black hair.

Taro studies with a

friend at the school

of knowledge science

ISA(Taro, student)

IS(Taro, 23 years old)

IS(Taro, tall)

HAS(Taro, black hair)

STUDY(Taro, friend, school of Knowledge Science)

Relationship among concepts

Property inheritance

animal

isa isa invertebrate animal mollusk

do isa

move arthropod ~fly isa wing do isa

has has penguin insect isa isa isa vertebrate animal bird dove

has has do color

isa fly white and neck bone black

mammal carnivorous tiger isa animal isa

Bird

Some labels are isa

Labels on the other arcs

represent other properties

 The principle of property inheritance says that objects belonging

to more specific concepts inherit all the properties of objects

belonging to a more general concept (default value) The isa arc

satisfies the transitive law and we can prove “ A isa C ” from “ A

isa B ” and “ B isa C ”

 A penguin is a bird and a bird has a property that it can fly

However, a penguin can not fly, and we must clearly indicate

that fact, that means we need to modify the default value (a

penguin “does not fly”)

 Once we organize knowledge, it is easy to answer many

questions

- Does a bird fly?

- What properties does a bird have?

- Does a dove have a neck?

Property inheritance

Property inheritance

 there are two Taros and one is a teacher and the other is a student?

 imagining that “Taro” is a label and using two nodes (token), <taro-1> and <taro- 2>, both of which are joined to the label “Taro”

Case frames

Consider knowledge relates to movement and change

(persisting over time and space and relates many objects):

time (when), location (where), agent (who),

object (what), tool (how), purpose (why), method (how)

study

agent time (who) EVENT (when)

object location (what) (where) tool method

purpose (how) (how) (why)

A semantic network using a token expression:

“Taro studied English in his room on April

Semantics networks

mechanism for representing general and specific

knowledge The representation is a model of human

memory, and it is therefore relatively understandable

inheritance

and help maintain consistency in the knowledge base

through the network, so the relationships and

inference are explicit in the network links

 Proposed by M Minsky: when we look at, listen

to, or think about something, we do so within a

there is often a frame (its internal structure)

element of the idea

Frames

name: instructor

specialization of: teacher

name: unit(last name, first

specialization of : young person

name: unit(last name, first name)

subject: range(information

science, computer, …)

date entered: unit(year, month)

Connection between frames

teach frame young people student frame

frame

instructure frame ADDRESS

SALARY

name: SALARY

monthly salary: unit(dollars)

annual salary: unit(dollars)

average monthly salary: unit(dollars),

compute(AVE-M)

tax amount: unit(dollars), compute(TAX)

the system will do the calculation at the

frames called AVE-M and TAX and return the results

 expressiveness : they allow representation of

structured knowledge and procedural knowledge

 effectiveness : actions or operations can be

associated with a slot and performed

 efficiency : they allow more complex knowledge

to be captured efficiently

 explicitness: the additional structure makes the relative importance of particular objects and

concepts explicit

location: bed room action: make bed open the window

go to the door open the door and get out

1 get out of the bed

go to the Bathroom France

2 wash one’s face

3 eat breakfast

bath room

location: bath room action: enter the bath room use the tooth brush wash one’s face comb one’s hair get out of the bath room

location: kitchen action:

folk blankets

unlock the window key hold the window handle pull the handle

walk

hold the door knob turn the knob push the door open the door,

turn on the tap,

wipe your face by hand shave

dry your face

washstand mirror light

tap sink tooth cleaning set shaving

Decision Trees

Decision Tree is a classifier in the form of a tree structure that is either:

A decision tree can be used to classify an instance by

starting at the root of the tree and moving through it

until a leaf is met

 a leaf, indicating a class of instances, or

 a decision node that specifies some test to be

carried out on a single attribute value, with one

branch and subtree for each possible outcome of

the test

Data of London Stock Market

Major factors affecting the stock market:

- What it did yesterday - Bank interest rate

- What the New York market - Unemployment rate

is doing today - England is losing

Instance No ( previous days ) 1 2 3 4 5 6

? 7

The London market

will rise today

Mercedes Benz

Goes to

Married

to

Example of Frames

Automobile Frame

Class of: Transportation

Name of manufacturer: Audi

Origin of manufacturer: Germany

Model: 5000 Turbo

Type of car: Sedan

Weight (kg): 1500

Wheelbase (inches): 105.8

Number of door: 4 (default)

Transmission: 3-speed automatic

Number of wheels: 4 (default)

Engine: (Reference Engine Frame)

- Type: In-line, overhead cam

Horsepower: 140 hp Torque: 160 ft/LB

Name Machine Unit cap.

Measured

… Is-a Total capacity N X

…

Capacity Mach Prod Cap

Demon: Active rule # 36

Name Product Capacity required

for a unit product Danish 10

Mixer cookie

Frame C

In relationships