Chapter 5 Knowledge Representation 知識表示法

Expert Systems sstseng 1

Chapter 　 5

Knowledge Representation

知識表示法


•　 Knowledge （知識）＋ Inference （推論）＝ Expert Systems （專家系統）•　 Affect the development, efficiency, speed, and maintenance of 　　　 expert systems•　 epistemology: concerned with the nature, structure, and origin of knowledge•　 a priori comes from the Latin and means “That which precedes”

Philosophic Theories

ARISTOTLE PLATO LOCKE MILL

A Priori Knowledge

e.g. all triangles have 180 degrees

(considered to be universally true)

A posteriori Knowledge

e.g. the light is green

•　 a posteriori knowledge can be verified using 　 sense experience

5.1 The meaning of Knowledge5.1 The meaning of Knowledge （知識）（知識）

Epistemology( 認知論 )


•　 Procedural Knowledge （程序性知識）　　 How to do something

•　 Declarative Knowledge （陳述性知識）　　 The truth of something

　　“ Don’t put your fingers in a pot of boiling water”

•　 Tacit Knowledge （隱含知識）　 (Unconscious Knowledge)

　　 Cannot be expressed explicitly

－ An example is how to move your hand

－ Walking or riding a bicycle

－ ANS is related to tacit knowledge

Classifications of knowledgeClassifications of knowledge （知識）（知識）


Analogy to Wirth’s classic expression

• Algorithms + data structures = programs

• Knowledge + Inference = expert systems


LevelsLevels

MetaKnowledge

Knowledge

Information

Data

Noise

(rules about rules)

(rules+facts)

(facts)


The sequence of 12 numbers ： 137178007124

Without knowledge. This entire sequence may appear to be

noise.

Rule 1 ： IF Rain THEN Bring Raincoat

Rule 2 ： IF Rain THEN Bring Umbrella

Meta Rule 1 ： Try Rule 2 First

Meta Rule 2 ： IF Ride a motorcycle THEN

　　　　　　 Try Rule 1 First

Meta knowledge is knowledge about knowledge and expertise.

－ would specify which knowledge base was applicable.


•　 Backus - Naur form

•　 Ontology （本體論）•　 Semantic Network （語意網路）•　 Frames-based Knowledge （框架式知識）•　 Case-based Knowledge （案例式知識）•　 Rule-based Knowledge （規則式知識）•　 Knowledge Object （知識物件）•　 Logic （邏輯）

RepresentationRepresentation （表示法）（表示法）


•　 This notation is a meta language for defining the 　

　 syntax of a language

•　 Define the syntax of a language

e.g.

<sentence>:: ＝ <subject><verb><end-mark>

<subject>:: ＝ I ｜ You ｜ We

<verb> :: ＝ left ｜ came

<end-mark> :: ＝ . ｜ ? ｜！

•　 Parse Tree (derivation tree) sentence

subject verb end-mark

You came ?

5.2 Backus - Naur form ( BNF )5.2 Backus - Naur form ( BNF )


5.3 5.3 OntologyOntology（本體論）（本體論）

• Ontology一詞在 90年代就開始被使用在人工智慧領域，描述知識的知識構成要素之間的關係。

• Ontology的研究大致上可略為分為兩個方向：– 針對特定的問題領域建立大量的 Ontology

• 例如：建立某些領域詞彙的 Ontology– 研究 Ontology的建構方法與表示方法

•例如：利用 XML （可延伸標記語言）或是 RDF （資源描述格式）


• Ontology 的發展主要是用來使知識分享和再用更為容易。

• 不同的研究對於 Ontology 的表示與描述有不同的方法，目前還未看到較一般化、通用的表示法。

• 範例：使用 RDF 來描述適性化教材的 Ontology

sw:教學策略

sw:評估策略

rdf:type

sw:Ontology

rdfs:Class

rdf:type

sw:學習概念

rdfs:Resourcerdfs:subClassOfrdfs:Property

rdfs:domain

rdf:typerdfs:rangerdfs:subClassOf

rdfs:subClassOf rdf:type

rdfs:domain

rdfs:range

rdf:Literal

rdfs:domain

sw:後繼者

rdf:type


•　 A classic AI representation technique used for 　 propositional information is sometimes called 　 Propositional Net•　 A proposition( 命題 ) is a statement that is either true or false•　 A directed graph （有向圖形）

•　 Node （點） : 知識的組成元素或是種類•　 Arc （有向線段） : 知識組成元素間的關

•　「 is a 」•　「 a kind of 」

5.4 Semantic 5.4 Semantic NetworkNetwork （語意網路）（語意網路） (Quill(Quillian 67 & 68)ian 67 & 68)


General NetGeneral Net

Los Angeles

San Francisco Chicago New York

Indianapolis

Houston


John

Ann

Mother-of

Susan

Mother-of father-of

Tom

father-of

David

sister-of

wife-of

husband-of

Carol

husband-of

wife-of

Father-of

Mother-of

wife-of

husband-of

A Semantic NetA Semantic Net （語意網路）（語意網路）

Mark


•　「 is a 」 :在 Tail （有向線段尾段）所表示的知識物件

屬於 Head （有向線段頭段）的知識類別中的一個例子。

•　「 a kind of 」 (AKO) :在 Tail （有向線段尾段）的知識類別屬 Head（有向線段頭段）所表示的知識類別。

•　 Superclass （父類別） and Subclass （子類別）•　 Attribute, Value, Property

•　 Inheritance （繼承）

「「 is ais a 」」 and and 「「 a kind ofa kind of 」」


動物鴿子鳥

飛

is a

has-property

AKO

A Semantic Network with 「 is a 」 and 「 a kind of 」 (AKO) Links


aircraft

roundPropeller

drivenjetballoon

ConcordeDC-9DC-3specialblimpellipsoidal

AirForce 1

Spirit of St. Louis

GoodyearBlimp

is a is a is a

AKOAKO AKO AKOAKO

has-shape

has-shape

AKO

AKO AKOAKO

A Semantic Network with 「 is a 」 and 「 a kind of 」 (AKO) Links


5.5 PROLOG and Semantic Nets5.5 PROLOG and Semantic Nets （語意網路）（語意網路）• Essentials( 本質、要素 ) of PROLOG

Each of the statements above is a PROLOG predicate( 述部 ) ex

pression, or simply a predicate.

　 Color(red). 　　　　　　　　 ; red is a color

　 father_of(Tom,John). 　　　　 ; Tom is the father of John

　 mother_of(Susan,John). 　　　 ; Susan is the mother of John

　 parents(Tom,Susan,John). 　　 ; Tom and Susan are

　　　　　　　　　　　　　　 parents of John


Predicates can also be expressed with relations such as the

IS-A and HAS-A.

　 is_a (red,color).

　 has_a (John,father).

　 has_a (John,mother).

　 has_a (John,parents).

Some additional predicates

　 is_a (Tom,father).

　 is_a (Susan,mother).

　 is_a (Tom,parent).

　 is_a (Susan,parent).


Programs in PROLOG consist of facts and rules in the general form of goals.

　　　 p:-p1,p2…pn.

In which p is the rule’s head and the pi are the subgoals.

The symbol,:-, is interpreted as an IF.

parent (x,y) : - father (x,y).

parent (x,y) : - mother(x,y).

grandparent(x,y) :- parent (x,z) ,parent(z,y).

and an ancestor can be defined as:

　 (1) ancestor(x,y) :- parent(x,y).

　 (2) ancestor(x,y) :- ancestor(x,z),ancestor(z,y).


Predicate Database(Rules and Facts)

Interpreter

User

Queries Answers

General Organization of a PROLOG SystemGeneral Organization of a PROLOG System


　 (3) parent (Ann,Mary).

　 (4) parent (Ann,Susan).

　 (5) parent (Mary,Bob).

　 (6) parent (Susan,John).

As another example, suppose the query is

:-ancestor(Ann,John).

The first ancestor rule(1) matches and X is set to Ann and

Y is set to John. PROLOG now tries to match the body

of (1), parent (Ann,John) with every parent statement.


(1) is not true, the head cannot be true.

　 Because(1) cannot be true, PROLOG then tries the

　 second ancestor statement

(2) X is set to Ann and Y is set to John.

Control structure of PROLOG is of the Markov algorithm

type, in which searching for pattern matching is normally

determined by the order in which the Horn clauses are

entered.


5.6 Schema (plural schemas or schematas)5.6 Schema (plural schemas or schematas)

• A semantic net （語意網路） is an example of

a shallow knowledge （淺層知識） structure.

• A general term to describe a complex knowledg

e structure

• Focus on only relevant( 有意義的 ) knowledge

• For examples ： FRAME,SCRIPT


5.7 Frames-based Knowledge5.7 Frames-based Knowledge （框架式知（框架式知識）識） (Minsky 75)(Minsky 75)

• Suitable for related knowledge about a narrow subject with much default knowledge

• script － a time-ordered sequence of frames• Slot( 槽 ) ： Attribute( 屬性 )　 Slot 值： Value • Example a car frame

Slots Slots 值 manufacturer General Motors model Chevrolet Cqprice year 1979 transmission automatic engine gasoline tires 4 color blue


Slot Slot 值值• Some frame-based tools (KEE) allow a

wide range of items to be stored in slots

• an assigned value .a default value

• Rules .graphics

• Comments .debugging information

• questions for users .function

• procedural attachment .to other frame


Procedural AttachmentProcedural Attachment

• If – needed, if-added, if-removed

• Examples ： Human Property

Slots Slots 值

name property

specialization_of a_kind_of object

types (car, boat, house) if-added：Procedure ADD_PROPERTY

owner default：government if-needed：Procedure FIND_OWNER

location (home, work, mobile)

status (missing, poor, good)

under_warranty (yes, no)


HierarchyHierarchySlots Slots 值

name car specialization_of a-kind-of property types (sedan,sport,convertible) manufacturer (GM,Ford,Chrysler)

location mobile wheels 4 transmission (manual, automatic) engine (gasoline, diesel)

Slots Slots 值

name John's car specialization_of is_a car

manufacturer GM owner John Doe transmission automatic engine gasoline status good under_warranty yes

un


• FRAMESSchool meeting

Time Wed. 14:00Place Meeting Room#1

Topic School Stuffs

Chair Principal

NO. Meeting #912Place Meeting Room#2

Topic

Paticipant …….

TimePlaceTopicChairParticipant ……

TimePlace C.J.HallTopic PrizeChairParticipant ……

TimePlaceTopicChairParticipant ……

Monthly Meeting Weekly Meeting Occasional Meeting

IF-ADDED:informthe participantsIF-REMOVED: informthe participants

IF-ADDED:informthe participantsIF-REMOVED: informthe participants

IF-ADDED:informthe personIF-REMOVED:inform the personIF-CHANGED:...

IF-ADDED:informthe personIF-REMOVED:inform the personIF-CHANGED:...

IS A

A KIND OF


Difficulties with FRAMESDifficulties with FRAMES （框架）（框架） • Stereotype is that it have well defined features so that

many of its slots have default values

name 　　　　　　　　　　　　 elephant

specialization of 　　　　　　　 a-kind-of mammal

color 　　　　　　　　　　　　　 gray

legs 　　　　　　　　　　　　　　　 4

trunk 　　　　　　　　　　　　 a cylinder

Three-legged, two-legged

• Most frame （框架） systems do not?

• Provide a way of defining unalterable slots

• Nothing is really certain is such a unrestrained system


Shopping Script：C(customer),S(salesperson)

M(merchandise),D(dollars)

L(a store)1.Centers L

2.C begins looking around

3. C looks for a specific M

5. C asks S for help

4. C looks for any interesting M

6.

7.C finds M’

9. C leaves L 10.C buys M’

13.C leaves L

11.C leaves L 12. goto step 2

14.C takes M’

8. C fails to find M


Mary went shopping for a new coat. She

found a new one. She really liked When

she got it home, and discovered that it

went perfectly with her favorite dress .

Question ： Did Mary buy anything?

Did Mary buy anything?


5.8 5.8 Case-based KnowledgeCase-based Knowledge （案例式知（案例式知識）識）

• 通常是用來描述屬於經驗的知識• 從過去的經驗中，判定是何種相似的 case （案

例），並且依據過去解決此問題的方法，來解決此次問題

• Case （案例） :• 案例名稱• 屬性• 屬性值

案例名稱

屬性 1 屬性值

屬性 2 屬性值

…… ……

屬性 N 屬性值


利用利用 Case-based KnowledgeCase-based Knowledge （案例式知（案例式知識）建構識）建構 Expert SystemExpert System （專家系統）（專家系統）

• Case Retrieve （案例擷取）

• Case Reuse （案例再用）

• Case Revise （案例修正）

• Case Retain （案例更新）


案例擷取

案例庫案例再用

案例修正

案例更新

新案例

案例推論循環


5.9 5.9 Rule-based KnowledgeRule-based Knowledge （規則式知（規則式知識）識）

• 知識領域具備需要推論的特性– 例如：醫生依據其所學的醫學知識及病人所呈現的

症狀去判別所罹患的疾病• 最基本的 Rules（規則）形式

如果「狀態」則「結論」IF (condition) THEN (conclusion)

• Inference Chaining （推論鏈）– Forward Inference （前向推論）– Backward Inference （後向推論）


5.10 5.10 Knowledge ObjectKnowledge Object （知識物件）（知識物件）

• Object Oriented （物件導向）– Class （類別） and Object （物件）– Super-class （父類別） and Sub-class （子類別）– Inheritance （繼承）、 Encapsulation （封裝）、

Polymorphism （多型）• Knowledge Object （知識物件）

– Object-Attribute-Value Triples ( OAV )（物件 - 屬性 - 屬性值法）

– 物件導向規則庫管理系統– Knowledge Object Model （知識物件模型）


Object-Attribute-Value Triples ( OAV )Object-Attribute-Value Triples ( OAV )（物件（物件 -- 屬性屬性 -- 屬性值法）屬性值法）

• OAV can be used to characterizes all the knowledge（知識） in a semantic net （語意網路） and was used in MYCIN for diagnosing infections diseases

Object Attribute Value

appleappleapplegrapesgrapesgrapes

colortypequantitycolortypequantity

redmcintosh100redseedless500

• Especially useful for representing facts （事實）• for only a single object ：

only attribute-value pairs (AV)


Object-Attribute-Value TriplesObject-Attribute-Value Triples （物件（物件 -- 屬性屬性 -- 屬性值屬性值法）法）

Wheel: 4Function:run

Door:3...

Door:4...

Carry:peoplesize:small

Carry:goodssize:big

price:$$$ price:$$$ ‧‧‧‧‧‧ ‧‧‧‧‧‧

year:1988owner:gjh

year:1992owner:crt

AKO

is a is a

AKO AKO

AKO

AKOAKO

ValueObject

Attribute

Car

price:$$$price:$$$

R9Civic


LimitationsLimitations

• Lack of standard names for links and nodes （點）

• Combinatorial explosion of searching nodes （點）

• Logically inadequate

　　　 no “for all”, “there exist”...

• Heuristically inadequate

　　　 no effective search heuristics


物件導向規則庫管理系統物件導向規則庫管理系統• 將規則集合與物件導向概念結合

data setrole set

inference1

Rule-Class Class

role1

role2

data_member1

data_member2

method1

statement11

OO-RM Concepts OO Concepts

statement21

method2

statement12

statement22......

......

rule1

rule2...

inference2

rule1

rule2...

• Rule Class （規則類別） and Rule Object（規則物件）


5.11 Logic5.11 Logic （邏輯）（邏輯）•A description team for logic programming and expert systems is automated reasoning systems

• Syllogism （三段論） : The oldest and one of the simplest types of formal logic

premise: all men are mortalpremise: Socrates is a manConclusion: Socrates is mortal

• Propositional Logic （命題邏輯）－ a symbolic logic for manipulating propositions•First － Order Predicate Logic （第一層敘述邏輯）•Fuzzy Logic （模糊邏輯）


• Proposition

A sentence whose truth value can be determined

　 e.g. it is raining

　　　 Feather ( Albatrass)

• Compound Statement

　　　

　 e.g.

　　 If it is raining then carry an umbrella

Propositional LogicPropositional Logic （命題邏輯）（命題邏輯）


• Tautology

　 A compound statement that is always true

　 e.g. P ~p

• Contradiction

　 A compound statement that is always false

　 e.g. P ~p

• Contingent Statement

　 neither tautology nor contradiction

　 e.g. P


5.12 First - Order Predicate Logic5.12 First - Order Predicate Logic （第一層（第一層敘述邏輯）敘述邏輯）

• Propositional logic （命題邏輯） is a subset of predicate logic （敘述邏輯）

• The basis of logic programming languages

　　　　 e.g. Prolog

• Addition 　 : 　　　 Variable

• universal quantifier: For all

• existential quantifier: There exist 　　　　 e.g.

　　 ( 　 x) (x is a triangle x is a polygon)


Limitations of Predicate LogicLimitations of Predicate Logic （敘述邏輯）（敘述邏輯）

• The following statement can’t be expressed in p

redicate logic （敘述邏輯） :

• Most of the class received As

• To implement Most, a logic must provide some

predicates for counting, e.g. fuzzy logic （模糊邏輯） .


知識表示法知識表示法• 邏輯（ Logic ）

– 　語言正規而簡單（ formal syntax ）– 　嚴密的理論– 　完整的推理法則（ rules of inference ）– 　可證性– 　彈性大

• 模組性高（ modularity ）• 不容易表示有處理（ processing ）和控制（ control ）的

　知識


• 缺乏結構性• 有時不太自然• 解釋不易

　採用解析原則（ resolution principles ）的邏輯

　系統解不易

　事實量大時，法則的選取（ rule selection ）會

　有組合膨脹（ combinatorial explosion ）的現象


Exercise

• 1. Draw an action frame system explaining what to do in case of hardware failure for your computer system. Consider disk crash , power supply , CPU, and memory problems.

• 2. Determine whether the following are valid or invalid arguments.– A) pq, ~qr, r; ∴ p

– B)~pq, p(r s),s q; q ∴ r– C) p (q r), q; p∴ r


專題進度規劃專題進度規劃

• 10/18 交分組名單（每組最多四人）• 11/01 交專題題目與初步構想書• 11/29 交專題計劃書• 12/20~1/10 上台 presentation （每組十

五分鐘）• 01/17 系統 Demo & 交期末專題報告


誰殺了仙道？ (1)

• 神奈川縣高中籃球決賽前夕，陵南高中籃球隊中的明星選手——仙道彰被殺死於自家住處。警方稍後拘捕了五名嫌犯。他們是湘北高中籃球隊的櫻木花道、三井壽、流川楓、赤木剛憲、宮城良田。在警方的盤問中，他們各人都要回答四個問題。但是由安西教練側面瞭解，各嫌犯所答的四個問題中有三個答案是真話，另一個答案是假話。而且兇手就是五人其中之一。以下是五人的供詞：



• 櫻木花道： – （ a ）我沒有殺死仙道。 – （ b ）我從未有手槍。 – （ c ）流川楓討厭我。 – （ d ）當天下午我在練球。



• 三井壽： – （ a ）我沒有殺死仙道。 – （ b ）流川楓在今年內從未到過仙道家。 – （ c ）我和赤木不熟。 – （ d ）當天下午，我和櫻木在練球。



• 流川楓： – （ a ）我沒有殺死仙道。 – （ b ）我今年內從未到過仙道家。 – （ c ）我不討厭櫻木。 – （ d ）如果赤木說我是兇手，這是謊言。



• 赤木剛憲： – （ a ）仙道被殺時，我在家中。 – （ b ）我從未殺過人。 – （ c ）流川楓是兇手。 – （ d ）我和三井是好朋友。



• 宮城良田： – （ a ）如果櫻木說他從未有手槍，這是謊言。

– （ b ）仙道在決賽前夕被殺的。 – （ c ）命案發生時，赤木在家中。 – （ d ）我們其中一人是兇手。

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Chapter 5 Knowledge Representation 知識表示法