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From Search Engines to Question-Answering

SystemsThe Problems of Relevance and World

Knowledge Lotfi A. Zadeh Computer Science

Division Department of EECSUC

Berkeley February 11, 2005 BEARS 2005, UC

Berkeley URL http//www-bisc.cs.berkeley.edu URL

http//zadeh.cs.berkeley.edu/ Email

Zadeh_at_cs.berkeley.edu

BACKDROP

WEB INTELLIGENCE (WIQ)

- Principal objectives
- Improvement of quality of search
- Improvement in assessment of relevance
- Upgrading a search engine to a question-answering

system

KEY ISSUEDEDUCTION CAPABILITY

- Existing search engines, with Google at the top,

have many remarkable capabilities. Furthermore,

constant progress is being made in improving

their performance. But what should be realized is

that existing search engines do not have an

important capabilitydeduction capabilitythe

capability to synthesize an answer to a query by

drawing on bodies of information which reside in

various parts of the knowledge base. - example of incapability
- query What is the distance between the largest

city in Spain and the largest city in

Portugal? - query What is the combined population of the

three largest cities in Japan?

CONTINUED

- By definition, a question-answering system is a

system which has deduction capability. Can a

search engine be upgraded to a question-answering

system through the use of existing toolstools

which are based on bivalent logic and

bivalent-logic-based probability theory? A view

which is articulated in the following is that the

answer is No. - To upgrade a search engine to a

question-answering system new tools are needed

HISTORICAL NOTE

- 1970-1980 was a period of intense interest in

question-answering and expert systems - There was no discussion of search engines
- Example L.S. Coles, Techniques for Information

Retrieval Using an Inferential Question-Answering

System with Natural Language Input, SRI Report,

1972 - Example PHLIQA, Philips 1972-1979
- Today, search engines are a reality and occupy

the center of the stage - Question-answering systems are a goal rather than

reality. This goal is not achievable through the

use of existing bivalent-logic-based approaches.

The major obstacles are world knowledge

assessment of semantic relevance. Neither world

knowledge nor semantic relevance can be dealt

with effectively through the use of existing

tools.

DIGRESSIONQUALITATIVE COMPLEXITY SCALE TASKS,

PROBLEMS AND CONCEPTS

hard

intractable

new tools are needed

question-answering system

instances of tasks

achievable with prolongation of existing tools

achievable with existing tools

easy

tractable

EXAMPLES

summarization

automation of driving a car

book

Istanbul

Rome

Washington

Princeton

limit of what is achievable with current

technology

current performance

freeway, light traffic

stereotypical document

freeway, no traffic

MAJOR OBSTACLES

- World knowledge
- Semantic relevance
- World knowledge is the knowledge which humans

acquire through experience, education and

communication - World knowledge plays an essential role in

search, assessment of relevance, deduction and

summarization - Much of world knowledge is perception-based
- Perception-based information is intrinsically

imprecise

WORLD KNOWLEDGE

- Few professors are rich
- Almost all professors have the PhD degree
- It is not likely to rain in San Francisco in

midsummer - Swedes are tall
- Usually Robert returns from work at about 6 pm
- There are no mountains in Holland
- Usually Princeton means Princeton University
- Check out time is 1pm

RELEVANCE

- A major obstacle to upgrading is the concept of

relevance. There is an extensive literature on

relevance, and every search engine deals with

relevance in its own way, some at a high level of

sophistication. But what is quite obvious is that

the problem of assessment of relevance is very

complex and far from solution - What is relevance? There is no definition in the

literature - Relevance is not bivalent
- Relevance is a matter of degree, i.e., is a fuzzy

concept - Fuzziness of relevance is the reason why there is

no definition of relevance in the literature

q How old is Vera p1 Vera has a son who is in

mid- twenties p2 Vera has a daughter who

is in mid-thirties w child-bearing

age is about sixteen to about forty two

t summarization p1 knowledge

representation p2 passing w world knowledge

q How old is Vera p1 Vera has a son who is in

mid- twenties p2 Vera has a daughter who

is in mid-thirties w child-bearing

age is about sixteen to about forty two

page ranking algorithms word counts keywords

ASSESSMENT OF RELEVANCE

topic relevance

summarization

knowledge representation

A

B

0.7

?

? aggregated relevance of knowledge

representation to summarization typical

value of ? likely to be high (bimodal)

ABANDONMENT OF BIVALENCETHE NEED FOR NEW TOOLS

- Abandonment of bivalence entails an abandonment

of the traditional view that information and

uncertainty are statistical in nature - Instead, a much more general view which is

adopted is that information and uncertainty are

representable as generalized constraints - The concept of a generalized constraint is the

centerpiece of the new toolsthe tools that are

needed to upgrade a search engine to a

question-answering system

NEW TOOLS

computing with numbers

computing with words

CW

CN

PNL

IA

precisiated natural language

computing with intervals

GTU

CTP

THD

PFT

PT

CTP computational theory of

perceptions PFT protoform theory PTp

perception-based probability theory THD

theory of hierarchical definability GTU

Generalized Theory of uncertainty

PTp

probability theory

THE CONCEPT OF A GENERALIZED CONSTRAINT

- The concept of a generalized constraint is the

centerpiece of new tools - The concept of a generalized constraint serves as

a bridge from natural languages to systems

analysis

GENERALIZED CONSTRAINT (Zadeh 1986)

- Bivalent constraint (hard, inelastic,

categorical)

X ? C

constraining bivalent relation

- Generalized constraint

X isr R

constraining non-bivalent (fuzzy) relation

index of modality (defines semantics)

constrained variable

r ? ? ? ? blank p v u rs

fg ps

bivalent

non-bivalent (fuzzy)

CONTINUED

- constrained variable
- X is an n-ary variable, X (X1, , Xn)
- X is a proposition, e.g., Leslie is tall
- X is a function of another variable Xf(Y)
- X is conditioned on another variable, X/Y
- X has a structure, e.g., X Location

(Residence(Carol)) - X is a generalized constraint, X Y isr R
- X is a group variable. In this case, there is a

group, GA (Name1, , Namen), with each member

of the group, Namei, i 1, , n, associated with

an attribute-value, Ai. Ai may be vector-valued.

Symbolically - GA (Name1/A1Namen/An)
- Basically, X is a relation

SIMPLE EXAMPLES

- Check-out time is 1 pm, is an instance of a

generalized constraint on check-out time - Speed limit is 100km/h is an instance of a

generalized constraint on speed - Vera is a divorcee with two young children, is

an instance of a generalized constraint on Veras

age

GENERALIZED CONSTRAINTMODALITY r

X isr R

r equality constraint XR is abbreviation of

X isR r inequality constraint X

R r? subsethood constraint X ? R r

blank possibilistic constraint X is R R is the

possibility distribution of X r v veristic

constraint X isv R R is the verity distributio

n of X r p probabilistic constraint X isp R R

is the probability distribution of X

CONTINUED

r rs random set constraint X isrs R R is the

set- valued probability distribution of X r

fg fuzzy graph constraint X isfg R X is a

function and R is its fuzzy graph r u usuality

constraint X isu R means usually (X is R) r

g group constraint X isg R means that R

constrains the attribute-values of the group

GENERALIZED CONSTRAINTSEMANTICS

A generalized constraint, GC, is associated with

a test-score function, ts(u), which associates

with each object, u, to which the constraint is

applicable, the degree to which u satisfies the

constraint. Usually, ts(u) is a point in the unit

interval. However, if necessary, it may be an

element of a semi-ring, a lattice, or more

generally, a partially ordered set, or a bimodal

distribution. example possibilistic constraint,

X is R X is R Poss(Xu) µR(u) ts(u) µR(u)

CONSTRAINT QUALIFICATION

- p isr R means r-value of p is R
- in particular
- p isp R Prob(p) is R (probability

qualification) - p isv R Tr(p) is R (truth (verity)

qualification) - p is R Poss(p) is R (possibility

qualification) - examples
- (X is small) isp likely ProbX is small

is likely - (X is small) isv very true VerX is small

is very true - (X isu R) ProbX is R is usually

GENERALIZED CONSTRAINT LANGUAGE (GCL)

- GCL is an abstract language
- GCL is generated by combination, qualification

and propagation of generalized constraints - examples of elements of GCL
- (X isp R) and (X,Y) is S)
- (X isr R) is unlikely) and (X iss S) is likely
- If X is A then Y is B
- the language of fuzzy if-then rules is a

sublanguage of GCL - deduction generalized constraint propagation

EXAMPLE OF DEDUCTION

- compositional rule of inference in FL
- X is A
- (X,Y) is B
- Y is AB

- min (t-norm)
- max (t-conorm)

THE CONCEPT OF PRECISIATION

PRECISIATION TRANSLATION INTO GCL

NL

GCL

p

p

precisiation

GC-form GC(p)

translation

- annotation
- p X/A isr R/B GC-form of p
- example
- p Carol lives in a small city near San

Francisco - X/Location(Residence(Carol)) is R/NEARCity ?

SMALLCity

PRECISIATION

s-precisiation

g-precisiation

- conventional (degranulation)
- a a
- approximately a

GCL-based (granulation)

precisiation

a

precisiation

X isr R

p

proposition

GC-form

common practice in probability theory

- cg-precisiation crisp granular precisiation

PRECISIATION OF approximately a, a

?

1

singleton

s-precisiation

0

x

a

?

1

interval

0

cg-precisiation

a

x

p

probability distribution

0

g-precisiation

a

x

?

possibility distribution

0

a

x

?

1

fuzzy graph

0

20

25

x

CONTINUED

p

bimodal distribution

g-precisiation

0

x

- GCL-based (maximal generality)

g-precisiation

a

X isr R

GC-form

COMPUTATIONAL THEORY OF PERCEPTIONS (CTP)

KEY IDEAS

- Perceptions play a key role in human cognition
- Humans have a remarkable capability to perform a

wide variety of physical and mental tasks using

perceptions, without any measurements and any

computations. CTP is aimed at automation of this

capability - In CTP, perceptions are dealt with not directly

but through their descriptions in a natural

language - Note A natural language is a system for

describing perceptions - Perceptions are intrinsically imprecise

BASIC FACET OF HUMAN COGNITION

X attribute

perception of X

perception

singleton a

a (granule)

approximately a

domain of X

- perceptions are intrinsically imprecise
- principal reasons
- Bounded ability of sensory organs, and ultimately

the brain, to resolve detail and store

information - Incompleteness of information

THE BALLS-IN-BOX PROBLEM

- Version 1. Measurement-based
- A flat box contains a layer of black and white

balls. You can see the balls and are allowed as

much time as you need to count them - q1 What is the number of white balls?
- q2 What is the probability that a ball drawn at

random is white? - q1 and q2 remain the same in the next version

CONTINUED

- Version 2. Perception-based
- You are allowed n seconds to look at the box. n

seconds is not enough to allow you to count the

balls - You describe your perceptions in a natural

language - p1 there are about 20 balls
- p2 most are black
- p3 there are several times as many black balls

as white balls - PTs solution?

CONTINUED

- Version 3. Measurement-based
- The balls have the same color but different

sizes - You are allowed as much time as you need to

count the balls - q1 How many balls are large?
- q2 What is the probability that a ball drawn at

random is large - PTs solution?

CONTINUED

- Version 4. Perception-based
- You are allowed n seconds to look at the box. n

seconds is not enough to allow you to count the

balls - Your perceptions are
- p1 there are about 20 balls
- p2 most are small
- p3 there are several times as many small balls

as large balls - q1 how many are large?
- q2 what is the probability that a ball drawn at

random is large?

CONTINUED

- Version 5. Perception-based
- My perceptions are
- p1 there are about 20 balls
- p2 most are large
- p3 if a ball is large then it is likely to be

heavy - q1 how many are heavy?
- q2 what is the probability that a ball drawn

at random is not heavy?

A SERIOUS LIMITATION OF PT

- Version 4 points to a serious short coming of

PT - In PT there is no concept of cardinality of a

fuzzy set - How many large balls are in the box?

0.6

0.8

0.4

0.9

0.9

0.5

- There is no underlying randomness

MEASUREMENT-BASED

PERCEPTION-BASED

version 2

- a box contains 20 black and white balls
- over seventy percent are black
- there are three times as many black balls as

white balls - what is the number of white balls?
- what is the probability that a ball picked at

random is white?

- a box contains about 20 black and white balls
- most are black
- there are several times as many black balls as

white balls - what is the number of white balls
- what is the probability that a ball drawn at

random is white?

COMPUTATION (version 2)

- measurement-based
- X number of black balls
- Y2 number of white balls
- X ? 0.7 20 14
- X Y 20
- X 3Y
- X 15 Y 5
- p 5/20 .25

- perception-based
- X number of black balls
- Y number of white balls
- X most 20
- X several Y
- X Y 20
- P Y/N

FUZZY INTEGER PROGRAMMING

Y

X most 20

XY 20

X several y

x

1

RELEVANCE

TEST QUERY

WHAT IS THE NUMBER OF CARS IN CALIFORNIA

Web Results 1 - 10 of about 3,470,000 for What

is the number of cars in California. (0.44

seconds)

Electric Cars for California NRDC Nature's

Voice - California Drives a New Solution to

Global California Driving -- The

Law California Driving Guide -- The

Basics Guide to Automobile Repair Agreements

Cars and Trucks and Global Warming

TEST QUERY

COMBINED POPULATION OF THE THREE LARGEST CITIES

IN JAPAN

Web Results 1 - 10 of about 526,000 for combined

population of the three largest cities in Japan.

(0.35 seconds)

Highest lowest biggest smallest tallest deepest

oldest youngest ... top 100 cities sin Japan by

population - Society - Crime in Japan ...

Country Profile PDF TUSN Living in Japan

Geography Global Change and Urbanization

TEST QUERY

- Number of Ph.D.s in computer science produced by

European universities in 1996 - For Job Hunters in Academe, 1999 Offers Signs of

an Upturn - Fifth Inter-American Workshop on Science and

Engineering ...

TEST QUERY (GOOGLE)

- What is the number of fish in California?
- Web Results 1 - 10 of about 3,650,000 for number

of fish in California. (0.26 seconds) - Turner's Outdoorsman 2
- California Explores the Ocean
- The Amazing Grunion
- Steinhart Aquarium - California Academy of

Sciences

TEST QUERY

- distance between largest city in Spain and

largest city in Portugal failure - largest city in Spain Madrid (success)
- largest city in Portugal Lisbon (success)
- distance between Madrid and Lisbon (success)

RELEVANCE

- The concept of relevance has a position of

centrality in summarization, search and

question-answering - There is no formal, cointensive definition of

relevance - Reason
- Relevance is not a bivalent conceptit is a fuzzy

concept - A cointensive definitive of relevance cannot be

formalized within the conceptual structure of

bivalent logic

FUZZY CONCEPTS

- Relevance
- Causality
- Summary
- Cluster
- Mountain
- Valley
- In the existing literature, there are no

operational definitions of these concepts

DIGRESSION COINTENSION

CONCEPT

C

human perception of C p(C)

definition of C d(C)

intension of p(C)

intension of d(C)

cointension coincidence of intensions of p(C)

and d(C)

QUERY RELEVANCE

- Example
- q How old is Carol?
- p1 Carol is several years older than Ray
- p2 Ray has two sons the younger is in his

middle twenties and the older is in his middle

thirties - This example cannot be dealt with through the use

of standard probability theory, PT - What is needed is perception-based probability

theory, PTp

PTpBASED SOLUTION

- Describe your perception of Rays age in a

natural language - Precisiate your description through the use of

PNL (Precisiated Natural Language) - Result Bimodal distribution of Age (Ray)
- unlikely \\ Age(Ray)
- likely \\ 55 ? Age Ray ? 65
- unlikely \\ Age(Ray) 65
- Age(Carol) Age(Ray) several

CONTINUED

- More generally
- q is represented as a generalized constraint
- q X isr ?R
- Informal definition
- p is relevant to q if knowledge of p constrains X
- degree of relevance is covariant with the degree

to which p constrains X

constraining relation

modality of constraint

constrained variable

CONTINUED

- Problem with relevance
- q How old is Ray?
- p1 Rays age is about the same as Alans
- p1 does not constrain Rays age
- p2 Ray is about forty years old
- p2 does not constrain Rays age
- (p1, p2) constrains Rays age

RELEVANCE AND i-RELEVANCE

- p is i-relevant to q if p is relevant to q in

isolation - P is i-irrelevant to q if p is irrelevant in

isolation

RELEVANCE, REDUNDANCE AND DELETABILITY

DECISION TABLE

Aj j th symptom aij value of j th

symptom of Name D diagnosis

REDUNDANCE DELETABILITY

Aj is conditionally redundant for Namer, A, is

ar1, An is arn If D is ds for all possible values

of Aj in

Aj is redundant if it is conditionally redundant

for all values of Name

- compactification algorithm (Zadeh, 1976)

Quine-McCluskey algorithm

RELEVANCE

D is ?d if Aj is arj

constraint on Aj induces a constraint on

D example (blood pressure is high) constrains

D (Aj is arj) is uniformative if D is

unconstrained

Aj is irrelevant if it Aj is uniformative for all

arj

irrelevance deletability

IRRELEVANCE (UNINFORMATIVENESS)

(Aj is aij) is irrelevant (uninformative)

EXAMPLE

A2

D black or white

0

A1

A1 and A2 are irrelevant (uninformative) but not

deletable

A2

D black or white

A1

0

A2 is redundant (deletable)

RELEVANCE AND WORLD KNOWLEDGE

- Assessment of relevance is an intrinsically

complex problem. To deal with this problem what

is needed is a better understanding of issues

related to representation of, and inference from,

world knowledge

WORLD KNOWLEDGE

WORLD KNOWLEDGE

- World knowledge is the knowledge acquired through

experience, education and communication - World knowledge has a position of centrality in

human cognition - Centrality of world knowledge in human cognition

entails its centrality in web intelligence and,

especially, in assessment of relevance,

summarization, knowledge organization, ontology,

search and deduction

VERAS AGE

WORLD KNOWLEDGETHE AGE EXAMPLE

- q How old is Vera?
- p1 Vera has a son, in mid-twenties
- p2 Vera has a daughter, in mid-thirties
- wk the child-bearing age ranges from about 16 to

about 42

CONTINUED

range 1

timelines

p1

0

16

41

42

67

range 2

p2

0

16

42

51

77

(p1, p2)

16

42

51

67

(p1, p2) ?a ? 51 ? 67

a approximately a How is a defined?

WORLD KNOWLEDGE AND PRECISIATED NATURAL LANGUAGE

PNL

WHAT IS PNL?

- PNL is not merely a languageit is a system aimed

at a wide-ranging enlargement of the role of

natural languages in scientific theories and,

more particularly, in enhancement of machine IQ

PRINCIPAL FUNCTIONS OF PNL

- perception description language
- knowledge representation language
- definition language
- specification language
- deduction language

PRECISIATED NATURAL LANGUAGE (PNL) AND COMPUTING

WITH WORDS (CW)

CW

GrC

Granular Computing Computational Theory of

Perceptions Protoform Theory Theory of

Hierarchical Definability

CTP

PNL

PFT

THD

CW Granular Computing Generalized-Constraint-B

ased Semantics of Natural Languages

PRECISIATION AND GRANULAR COMPUTING

KEY IDEA

- example
- most Swedes are tall
- Count(tall.Swedes/Swedes) is most is most
- h count density function
- h(u)du fraction of Swedes whose height lies

in the interval u, udu - In granular computing, the objects of computation

are not values of variables but constraints on

values of variables

precisiation

THE CONCEPT OF PRECISIATION

- e expression in a natural language, NL
- e propositioncommandquestion
- Conversation between A and B in NL
- A e
- B I understood e but can you be more precise?
- A e precisiation of e

PRECISIATION

- Usually it does not rain in San Francisco in

midsummer - Brian is much taller than most of his close

friends - Carol loves music
- It is very unlikely that there will be a

significant increase in the price of oil in the

near future - It is not quite true that Mary is very rich

NEED FOR PRECISIATION

- fuzzy commands, instructions
- take a few steps
- slow down
- proceed with caution
- raise your glass
- use with adequate ventilation
- fuzzy commands and instructions cannot be

understood by a machine - to be understood by a machine, fuzzy commands and

instructions must be precisiated

PRECISIATION OF CONCEPTS

- Relevance
- Causality
- Similarity
- Rationality
- Optimality
- Reasonable doubt

PRECISIATION OF PROPOSITIONS

- example
- p most Swedes are tall
- p ?Count(tall.Swedes/Swedes) is most
- further precisiation
- h(u) height density function
- h(u)du fraction of Swedes whose height is in u,

udu, a ? u ? b

CONTINUED

- ?Count(tall.Swedes/Swedes)
- constraint on h

is most

CALIBRATION / PRECISIATION

- calibration

?height

?most

1

1

0

0

height

fraction

0.5

1

1

- precisiation

most Swedes are tall

h count density function

- Frege principle of compositionalityprecisiated

version - precisiation of a proposition requires

precisiations - (calibrations) of its constituents

DEDUCTION

q How many Swedes are not tall q is ? Q

solution

1-most

most

1

0

1

fraction

DEDUCTION

q How many Swedes are short q is ? Q

solution is most

is ? Q

extension principle

subject to

CONTINUED

q What is the average height of Swedes? q

is ? Q solution is most

is ? Q

extension principle

subject to

PROTOFORM LANGUAGE

PFL

THE CONCEPT OF A PROTOFORM

PREAMBLE

- As we move further into the age of machine

intelligence and automated reasoning, a daunting

problem becomes harder and harder to master. How

can we cope with the explosive growth in

knowledge, information and data. How can we

locate and infer from decision-relevant

information which is embedded in a large

database. - Among the many concepts that relate to this

issue there are four that stand out in

importance organization, representation, search

and deduction. In relation to these concepts, a

basic underlying concept is that of a protoforma

concept which is centered on the confluence of

abstraction and summarization

CONTINUED

object space

object p

protoform space

summary of p

protoform

summarization

abstraction

S(p)

A(S(p))

PF(p)

- PF(p) abstracted summary of p
- deep structure of p
- protoform equivalence
- protoform similarity

WHAT IS A PROTOFORM?

- protoform abbreviation of prototypical form
- informally, a protoform, A, of an object, B,

written as APF(B), is an abstracted summary of B - usually, B is lexical entity such as proposition,

question, command, scenario, decision problem,

etc - more generally, B may be a relation, system,

geometrical form or an object of arbitrary

complexity - usually, A is a symbolic expression, but, like B,

it may be a complex object - the primary function of PF(B) is to place in

evidence the deep semantic structure of B

THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS

Fuzzy Logic

Bivalent Logic

ontology

conceptual graph

protoform

skeleton

Montague grammar

PROTOFORMS

object space

protoform space

PF-equivalence class

- at a given level of abstraction and

summarization, objects p and q are PF-equivalent

if PF(p)PF(q) - example
- p Most Swedes are tall Count (A/B) is Q
- q Few professors are rich Count (A/B) is Q

EXAMPLES

instantiation

- Monika is young Age(Monika) is young A(B) is C
- Monika is much younger than Robert
- (Age(Monika), Age(Robert) is much.younger
- D(A(B), A(C)) is E
- Usually Robert returns from work at about 615pm
- ProbTime(Return(Robert) is 615 is usually
- ProbA(B) is C is D

abstraction

usually

615

Return(Robert)

Time

EXAMPLES

gain

Alan has severe back pain. He goes to see a

doctor. The doctor tells him that there are two

options (1) do nothing and (2) do surgery. In

the case of surgery, there are two possibilities

(a) surgery is successful, in which case Alan

will be pain free and (b) surgery is not

successful, in which case Alan will be paralyzed

from the neck down. Question Should Alan elect

surgery?

2

1

0

option 2

option 1

Y

Y

object

i-protoform

X

0

X

0

PROTOFORMAL SEARCH RULES

- example
- query What is the distance between the largest

city in Spain and the largest city in Portugal? - protoform of query ?Attr (Desc(A), Desc(B))
- procedure
- query ?Name (A)Desc (A)
- query Name (B)Desc (B)
- query ?Attr (Name (A), Name (B))

MULTILEVEL STRUCTURES

- An object has a multiplicity of protoforms
- Protoforms have a multilevel structure
- There are three principal multilevel structures
- Level of abstraction (?)
- Level of summarization (?)
- Level of detail (?)
- For simplicity, levels are implicit
- A terminal protoform has maximum level of

abstraction - A multilevel structure may be represented as a

lattice

ABSTRACTION LATTICE

example

most Swedes are tall

Q Swedes are tall

most As are tall

most Swedes are B

Q Swedes are B

Q As are tall

most As are Bs

Q Swedes are B

Q As are Bs

Count(B/A) is Q

PROTOFORM OF A QUERY

- largest port in Canada?
- second tallest building in San Francisco

B

A

X

?X is selector (attribute (A/B))

San Francisco

buildings

height

2nd tallest

PROTOFORMAL SEARCH RULES

- example
- query What is the distance between the largest

city in Spain and the largest city in Portugal? - protoform of query ?Attr (Desc(A), Desc(B))
- procedure
- query ?Name (A)Desc (A)
- query Name (B)Desc (B)
- query ?Attr (Name (A), Name (B))

ORGANIZATION OF WORLD KNOWLEDGEEPISTEMIC

(KNOWLEDGE-DIRECTED) LEXICON (EL)

(ONTOLOGY-RELATED)

j

rij

wij granular strength of association between i

and j

wij

i

K(i)

network of nodes and links

lexine

- i (lexine) object, construct, concept

(e.g., car, Ph.D. degree) - K(i) world knowledge about i (mostly

perception-based) - K(i) is organized into n(i) relations Rii, ,

Rin - entries in Rij are bimodal-distribution-valued

attributes of i - values of attributes are, in general, granular

and context-dependent

EPISTEMIC LEXICON

lexinej

rij

lexinei

rij i is an instance of j (is or isu) i is a

subset of j (is or isu) i is a superset of

j (is or isu) j is an attribute of i i causes

j (or usually) i and j are related

EPISTEMIC LEXICON

FORMAT OF RELATIONS

perception-based relation

lexine

attributes

granular values

example

car

G 20 \ ? 15k 40 \ 15k, 25k

granular count

PROTOFORM OF A DECISION PROBLEM

- buying a home
- decision attributes
- measurement-based price, taxes, area, no. of

rooms, - perception-based appearance, quality of

construction, security - normalization of attributes
- ranking of importance of attributes
- importance function w(attribute)
- importance function is granulated L(low),

M(medium), H(high)

PROTOFORM EQUIVALENCE

- A key concept in protoform theory is that of

protoform-equivalence - At specified levels of abstraction, summarization

and detail, p and q are protoform-equivalent,

written in PFE(p, q), if p and q have identical

protoforms at those levels - Example
- p most Swedes are tall
- q few professors are rich
- Protoform equivalence serves as a basis
- for protoform-centered mode of knowledge

organization

PF-EQUIVALENCE

- Scenario A
- Alan has severe back pain. He goes to see a

doctor. The doctor tells him that there are two

options (1) do nothing and (2) do surgery. In

the case of surgery, there are two possibilities

(a) surgery is successful, in which case Alan

will be pain free and (b) surgery is not

successful, in which case Alan will be paralyzed

from the neck down. Question Should Alan elect

surgery?

PF-EQUIVALENCE

- Scenario B
- Alan needs to fly from San Francisco to St.

Louis and has to get there as soon as possible.

One option is fly to St. Louis via Chicago and

the other through Denver. The flight via Denver

is scheduled to arrive in St. Louis at time a.

The flight via Chicago is scheduled to arrive in

St. Louis at time b, with aconnection time in Denver is short. If the flight

is missed, then the time of arrival in St. Louis

will be c, with cb. Question Which option is

best?

THE TRIP-PLANNING PROBLEM

- I have to fly from A to D, and would like to get

there as soon as possible - I have two choices (a) fly to D with a

connection in B or - (b) fly to D with a connection in C
- if I choose (a), I will arrive in D at time t1
- if I choose (b), I will arrive in D at time t2
- t1 is earlier than t2
- therefore, I should choose (a) ?

B

(a)

A

D

C

(b)

PROTOFORM EQUIVALENCE

gain

c

1

2

0

options

a

b

PROTOFORM EQUIVALENCE

- Backpain trip planning divorce job change

PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION

knowledge base

PF-module

PF-module

PF-submodule

EXAMPLE

module

submodule

set of cars and their prices

PROTOFORMAL DEDUCTION

PROTOFORMAL DEDUCTION

NL

GCL

PFL

p q

p q

p q

precisiation

summarization

precisiation

abstraction

WKM

DM

r

World Knowledge Module

a

answer

deduction module

PROTOFORMAL DEDUCTION

- Rules of deduction in the Deduction Database

(DDB) are protoformal - examples (a) compositional rule of inference

X is A (X, Y) is B Y is AB

symbolic

computational

(b) extension principle

X is A Y f(X) Y f(A)

Subject to

symbolic

computational

RULES OF DEDUCTION

- Rules of deduction are basically rules governing

generalized constraint propagation - The principal rule of deduction is the extension

principle

X is A f(X,) is B

Subject to

computational

symbolic

GENERALIZATIONS OF THE EXTENSION PRINCIPLE

information constraint on a variable

f(X) is A g(X) is B

given information about X

inferred information about X

Subject to

CONTINUED

f(X1, , Xn) is A g(X1, , Xn) is B

Subject to

(X1, , Xn) is A gj(X1, , Xn) is Yj , j1,

, n (Y1, , Yn) is B

Subject to

PROTOFORMAL DEDUCTION

- Example
- most Swedes are tall 1/n?Count(GA is R)

is Q

Height

PROTOFORMAL DEDUCTION RULE

1/n?Count(GA is R) is Q

1/n?Count(GA is S) is T

?µR(Ai) is Q

?µS(Ai) is T

µT(v) supA1, , An(µQ(?i µR(Ai))

subject to

v ? µS(Ai)

SUMMATION

- addition of significant question-answering

capability to search engines is a complex,

open-ended problem - incremental progress, but not much more, is

achievable through the use of bivalent-logic-base

d methods - to achieve significant progress, it is imperative

to develop and employ new tools based on

computing with words, protoform theory,

precisiated natural language and computational

theory of perceptions - The centerpiece of the new tools is the concept

of a generalized constraint

APPENDIX

KEY POINTTHE ROLE OF FUZZY LOGIC

- Existing approaches to the enhancement of web

intelligence are based on classical,

Aristotelian, bivalent logic and

bivalent-logic-based probability theory. In our

approach, bivalence is abandoned. What is

employed instead is fuzzy logica logical system

which subsumes bivalent logic as a special case. - Fuzzy logic is not fuzzy
- Fuzzy logic is a precise logic of fuzziness and

imprecision - The centerpiece of fuzzy logic is the concept of

a generalized constraint.

- In bivalent logic, BL, truth is bivalent,

implying that every proposition, p, is either

true or false, with no degrees of truth allowed - In multivalent logic, ML, truth is a matter of

degree - In fuzzy logic, FL
- everything is, or is allowed to be, to be

partial, i.e., a matter of degree - everything is, or is allowed to be, imprecise

(approximate) - everything is, or is allowed to be, granular

(linguistic) - everything is, or is allowed to be, perception

based

CONTINUED

- The generality of fuzzy logic is needed to cope

with the great complexity of problems related to

search and question-answering in the context of

world knowledge to deal computationally with

perception-based information and natural

languages and to provide a foundation for

management of uncertainty and decision analysis

in realistic settings

- Feb. 24, 2004
- Factual Information About the Impact of Fuzzy

Logic - PATENTS
- Number of fuzzy-logic-related patents applied for

in Japan 17,740 - Number of fuzzy-logic-related patents issued in

Japan 4,801 - Number of fuzzy-logic-related patents issued in

the US around 1,700

- PUBLICATIONS
- Count of papers containing the word fuzzy in

title, as cited in INSPEC and MATH.SCI.NET

databases. (Data for 2002 are not complete) - Compiled by Camille Wanat, Head, Engineering

Library, UC Berkeley, - November 20, 2003
- Number of papers in INSPEC and MathSciNet which

have "fuzzy" in their titles - INSPEC - "fuzzy" in the title
- 1970-1979 569
- 1980-1989 2,404
- 1990-1999 23,207
- 2000-present 9,945
- Total 36,125
- MathSciNet - "fuzzy" in the title
- 1970-1979 443
- 1980-1989 2,465
- 1990-1999 5,479

- JOURNALS (fuzzy or soft computing in

title) - Fuzzy Sets and Systems
- IEEE Transactions on Fuzzy Systems
- Fuzzy Optimization and Decision Making
- Journal of Intelligent Fuzzy Systems
- Fuzzy Economic Review
- International Journal of Uncertainty, Fuzziness

and Knowledge-Based Systems - Journal of Japan Society for Fuzzy Theory and

Systems - International Journal of Fuzzy Systems
- Soft Computing
- International Journal of Approximate

Reasoning--Soft Computing in Recognition and

Search - Intelligent Automation and Soft Computing
- Journal of Multiple-Valued Logic and Soft

Computing - Mathware and Soft Computing
- Biomedical Soft Computing and Human Sciences
- Applied Soft Computing

APPLICATIONS The range of application-areas of

fuzzy logic is too wide for exhaustive listing.

Following is a partial list of existing

application-areas in which there is a record of

substantial activity.

- Industrial control
- Quality control
- Elevator control and scheduling
- Train control
- Traffic control
- Loading crane control
- Reactor control
- Automobile transmissions
- Automobile climate control
- Automobile body painting control
- Automobile engine control
- Paper manufacturing
- Steel manufacturing
- Power distribution control
- Software engineerinf
- Expert systems
- Operation research
- Decision analysis

- Financial engineering
- Assessment of credit-worthiness
- Fraud detection
- Mine detection
- Pattern classification
- Oil exploration
- Geology
- Civil Engineering
- Chemistry
- Mathematics
- Medicine
- Biomedical instrumentation
- Health-care products
- Economics
- Social Sciences
- Internet
- Library and Information Science

- Product Information Addendum 1
- This addendum relates to information about

products which employ fuzzy logic singly or in

combination. The information which is presented

came from SIEMENS and OMRON. It is fragmentary

and far from complete. Such addenda will be sent

to the Group from time to time.SIEMENS

washing machines, 2 million units sold

fuzzy guidance for navigation systems (Opel,

Porsche) OCS Occupant Classification

System (to determine, if a place in a car is

occupied by - a person or something else to control the

airbag as well as the intensity of the - airbag). Here FL is used in the product as

well as in the design process - (optimization of parameters).
- fuzzy automobile transmission (Porsche,

Peugeot, Hyundai) - OMRON fuzzy logic blood pressure meter,

7.4 million units sold, approximate retail value - 740 million dollars
- Note If you have any information about products

and or manufacturing which may be of relevance

please communicate it to Dr. Vesa Niskanen

vesa.a.niskanen_at_helsinki.fi and Masoud Nikravesh

Nikravesh_at_cs.berkeley.edu .

- Product Information Addendum 2
- This addendum relates to information about

products which employ fuzzy logic singly or in

combination. The information which is presented

came from Professor Hideyuki Takagi, Kyushu

University, Fukuoka, Japan. Professor Takagi is

the co-inventor of neurofuzzy systems. Such

addenda will be sent to the Group from time to

time. Facts on FL-based systems in Japan (as

of 2/06/2004) - 1. Sony's FL camcordersTotal amount of

camcorder production of all companies in

1995-1998 times Sony's market share is the

following. Fuzzy logic is used in all Sony's

camcorders at least in these four years, i.e.

total production of Sony's FL-based camcorders is

2.4 millions products in these four years. - 1,228K units X 49 in 1995 1,315K

units X 52 in 1996 1,381K units X 50 in

1997 1,416K units X 51 in 1998 - 2. FL control at Idemitsu oil factoriesFuzzy

logic control is running at more than 10 places

at 4 oil factories of Idemitsu Kosan Co. Ltd

including not only pure FL control but also the

combination of FL and conventional control.

They estimate that the effect of their FL control

is more than 200 million YEN per year and it

saves more than 4,000 hours per year.

- 3. Canon
- Canon used (uses) FL in their cameras,

camcorders, copy machine, and stepper alignment

equipment for semiconductor production. But, they

have a rule not to announce their production and

sales data to public.Canon holds 31 and 31

established FL patents in Japan and US,

respectively.4. Minolta camerasMinolta has a

rule not to announce their production and sales

data to public, too.whose name in US market was

Maxxum 7xi. It used six FL systems in acamera

and was put on the market in 1991 with 98,000 YEN

(body pricewithout lenses). It was produced

30,000 per month in 1991. Its sistercameras,

alpha-9xi, alpha-5xi, and their successors used

FL systems, too.But, total number of production

is confidential.

- 5. FL plant controllers of Yamatake

CorporationYamatake-Honeywell (Yamatake's

former name) put FUZZICS, fuzzy software package

for plant operation, on the market in 1992. It

has been used at the plants of oil, oil chemical,

chemical, pulp, and other industries where it is

hard for conventional PID controllers to describe

the plan process for these more than 10

years.They planed to sell the FUZZICS 20 - 30

per year and total 200 million YEN.As this

software runs on Yamatake's own control systems,

the software package itself is not expensive

comparative to the hardware control systems.6.

OthersNames of 225 FL systems and products

picked up from news articles in 1987 - 1996 are

listed at http//www.adwin.com/elec/fuzzy/note_10.

html in Japanese.) - Note If you have any information about products

and or manufacturing which may be of relevance

please communicate it to Dr. Vesa Niskanen

vesa.a.niskanen_at_helsinki.fi and Masoud Nikravesh

Nikravesh_at_cs.berkeley.edu , with cc to me.

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