Web Intelligence, World Knowledge and Fuzzy Logic

Lotfi A. Zadeh

Computer Science Division Department of EECS

UC Berkeley

November 11, 2004

Santa Clara

URL: http://www-bisc.cs.berkeley.eduURL: http://zadeh.cs.berkeley.edu/

Email: Zadeh@cs.berkeley.edu

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In moving further into the age of machine intelligence and automated reasoning, we have reached a point where we can speak, without exaggeration, of systems which have a high machine IQ (MIQ). The Web, and especially search engines—with Google at the top—fall into this category. In the context of the Web, MIQ becomes Web IQ, or WIQ, for short.

PREAMBLE

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WEB INTELLIGENCE (WIQ)

Principal objectivesImprovement of quality of search

Improvement in assessment of relevance

Upgrading a search engine to a question-answering system

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FROM SEARCH ENGINES TO QUESTION-ANSWERING SYSTEMS

In recent years, substantial progress has been made in improving performance of search engines through the use of the semantic web, ontology-based systems and related approaches. But upgrading a search engine to a question-answering systems requires a quantum jump in WIQ. A basic question which awaits an answer is: Can a search engine be upgraded to a question-answering system through the use of methods based on bivalent logic and bivalent-logic-based probability theory? In the following it is argued that the answer is No.

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DIGRESSIONQUALITATIVE COMPLEXITY SCALE

TASKS, PROBLEMS AND DEFINITIONS

limit of a particular method or technology

class of tasks, problems or definitionsdifficulty

easy

hard intractable

tractable

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EXAMPLES

summarization automation of driving a car

book

stereotypical document

Istanbul

New York

limit of what is achievable with current technology

freeway, light traffic

freeway, no traffic

Rome

Princeton

current performance

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HISTORICAL NOTE

1970-1980 was a period of intense interest in question-answering and expert systems

There was no discussion of search enginesExample: 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 obstacle is world knowledge. World knowledge cannot be dealt with

effectively through the use of existing tools.

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THE MAJOR OBSTACLE: WORLD KNOWLEDGE

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 Imprecise of perception is a consequence of (a) the

bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information; and (b) in general, perceptions, are summaries of observations and experience

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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

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IMPRECISION OF WORLD KNOWLEDGE

Imprecision of world knowledge cannot be dealt with through prolongation of methods based on bivalent logic and bivalent-logic-based probability theory. What is needed is a change in course—a change which amounts to abandonment of bivalence and adoption of new tools drawn from fuzzy logic

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FROM STATISTICAL TO GRANULAR

Abandonment of bivalence entails an abandonment of the traditional view that information and uncertainty are statistical in nature

Instead, a more general view which is adopted that information and uncertainty are, or are allowed to be, granular

Informally, a granule is a clump of points drawn together by indistinguishability, equivalence, similarity, proximity or functionality

More precisely, a granule is defined by a generalized constraint. The concept of a generalized constraint is the centerpiece of the new tools

granule

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NEW TOOLS

CN

IA PNL

CW+ +

computing with numbers

computing with intervals

precisiated natural language

computing with words

UTU

CTP: computational theory of perceptionsPFT: protoform theoryPTp: perception-based probability theoryTHD: theory of hierarchical definabilityUTU: Unified Theory of uncertainty

CTP THD PFT

probability theory

PTPTp

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THE CENTERPIECE OF NEW TOOLS IS THE CONCEPT OF A

GENERALIZED CONSTRAINT (ZADEH 1986)

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• X= (X1 , …, Xn )• X may have a structure: X= Location (Residence(Carol))• X may be a function of another variable: X=f(Y)• X may be conditioned: (X/Y)

GENERALIZED CONSTRAINT (Zadeh 1986)

• Bivalent constraint (hard, inelastic, categorical:)

X Cconstraining bivalent relation

X isr R

constraining non-bivalent (fuzzy) relation

index of modality

constrained variable

Generalized constraint:

r: | = | | | | … | blank | p | v | u | rs | fg | ps |…

bivalent non-bivalent (fuzzy)

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SIMPLE EXAMPLES

“Check-out time is 1 pm,” is a generalized constraint on check-out time

“Speed limit is 100km/h” is a generalized constraint on speed

“Vera is a divorce with two young children,” is a generalized constraint on Vera’s age

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GENERALIZED CONSTRAINT—MODALITY r

X isr R

r: = equality constraint: X=R is abbreviation of X is=Rr: ≤ inequality constraint: X ≤ Rr: subsethood constraint: X Rr: blank possibilistic constraint; X is R; R is the possibility

distribution of Xr: v veristic constraint; X isv R; R is the verity

distribution of Xr: p probabilistic constraint; X isp R; R is the

probability distribution of X

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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: ps Pawlak set constraint: X isps ( X, X) means that X is a set and X and X are the lower and upper approximations to X

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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 (X is small) is likely

(X is small) isv very true ( X is small) is very true

(X isu R) Prob(X is R) is usually

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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

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EXAMPLE OF DEDUCTION

compositional rule of inference in FL

X is A

(X,Y) is B

Y is A°B

)),()(()( uvμuμvvμ BAuBA

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

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PRECISIATION = TRANSLATION INTO GCL

annotationp X/A isr R/B GC-form of p

examplep: Carol lives in a small city near San FranciscoX/Location(Residence(Carol)) is R/NEAR[City] SMALL[City]

p p*

NL GCL

precisiation

translationGC-formGC(p)

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conventional (degranulation)

* a a

approximately a

GCL-based (granulation)

PRECISIATION

s-precisiation g-precisiation

precisiationprecisiation X isr R

p

GC-formproposition

common practice in probability theory

*a

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PRECISIATION OF “approximately a,” *a

x

x

x

a

a

20 250

1

0

0

1

p

fuzzy graph

probability distribution

interval

x 0

a

possibility distribution

x a0

1

s-precisiation singleton

g-precisiation

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CONTINUED

x

p

0

bimodal distribution

GCL-based (maximal generality)

precisiation X isr R

GC-form

*a

g-precisiation

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1. Perceptions play a key role in human cognition

2. 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

3. 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

A perception is equated to its descriptor in a natural language

KEY IDEAS

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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

THE BALLS-IN-BOX PROBLEM

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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 ballsYou 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

PT’s solution?

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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

PT’s solution?

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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?

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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?

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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?

0.5

• There is no underlying randomness

0.9

0.80.6

0.9

0.4

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MEASUREMENT-BASED

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?

PERCEPTION-BASED

version 2

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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

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FUZZY INTEGER PROGRAMMING

x

Y

1

X= several × y

X= most × 20*

X+Y= 20*

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RELEVANCE

relevance

query relevance topic relevance

examples

query: How old is Ray proposition: Ray has three grown up children topic: numerical analysis topic: differential equations

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RELEVANCE

The concept of relevance has a position of centrality in search and question-answering

And yet, there is no operational definition of relevance

Relevance is not a bivalent concept; relevance is a matter of degree

Informally, p is relevant to a query q, X isr ?R, if p constrains X

Example

q: How old is Ray? p: Ray has two children

KEY POINTS

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CONTINUED

?q p = (p1, …, pn)

If p is relevant to q then any superset of p is relevant to q

A subset of p may or may not be relevant to q

Monotonicity, inheritance

Existing bivalent-logic-based search engines do not perform well in assessment of relevance

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TEST QUERY

NUMBER OF CARS IN CALIFORNIA

Google

 Web Results 1 - 10 of about 2,950,000 for Number of cars in California. (0.75 seconds)

A Student's Guide to Alternative Fuel Vehicles - Hydrogen

The Energy Story - Chapter 18: Energy for Transportation

Electric Cars for California

California Car Rentals - Cheap Rental Cars in California

Lawmakers look to drive out car-title loans

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TEST QUERY

Number of Ph.D.’s in computer science produced by European universities in 1996

Google:

For Job Hunters in Academe, 1999 Offers Signs of an Upturn

Fifth Inter-American Workshop on Science and Engineering ...

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TEST QUERY (GOOGLE)

largest port in Switzerland: failure

Searched the web for largest port Switzerland.  Results 1 - 10 of about 215,000. Search took 0.18 seconds.

THE CONSULATE GENERAL OF SWITZERLAND IN CHINA - SHANGHAI FLASH N ...

EMBASSY OF SWITZERLAND IN CHINA - CHINESE BUSINESS BRIEFING N° ...

Andermatt, Switzerland Discount Hotels - Cheap hotel and motel ...

Port Washington personals online dating post

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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)

Google

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TEST QUERY (GOOGLE)

population of largest city in Spain: failure

largest city in Spain: Madrid, success

population of Madrid: success

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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 concept A cointensive definitive of relevance cannot

be formalized within the conceptual structure of bivalent logic

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FUZZY CONCEPTS

Relevance Causality Summary Cluster Mountain Valley

In the existing literature, there are no operational definitions of these concepts

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DIGRESSION: COINTENSION

C

human perception of Cp(C)

definition of Cd(C)

intension of p(C) intension of d(C)

CONCEPT

cointension: coincidence of intensions of p(C) and d(C)

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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, or through the use of techniques used in existing search engines

What is needed is perception-based probability theory, PTp

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PTp—BASED SOLUTION

(a) Describe your perception of Ray’s age in a natural language

(b) Precisiate your description through the use of PNL (Precisiated Natural Language)

Result: Bimodal distribution of Age (Ray)unlikely \\ Age(Ray) < 65* +likely \\ 55* Age Ray 65* +unlikely \\ Age(Ray) > 65*

Age(Carol) = Age(Ray) + several

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CONTINUED

More generallyq is represented as a generalized constraint

q: X isr ?R

Informal definitionp is relevant to q if knowledge of p

constrains Xdegree of relevance is covariant with the

degree to which p constrains X

constraining relationmodality of constraint

constrained variable

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CONTINUED

Problem with relevance

q: How old is Ray?

p1: Ray’s age is about the same as Alan’s

p1: does not constrain Ray’s age

p2: Ray is about forty years old

p2: does not constrain Ray’s age

(p1, p2) constrains Ray’s age

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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

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RELEVANCE, REDUNDANCE AND DELETABILITY

Name A1 Aj An D

Name1 a11 a1j ain d1

. . . . .Namek ak1 akj akn d1

Namek+1 ak+1, 1 ak+1, j ak+1, n d2

. . . . .Namel al1 alj aln dl

. . . . .Namen am1 amj amn dr

DECISION TABLE

Aj: j th symptom

aij: value of j th symptom of Name

D: diagnosis

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REDUNDANCE DELETABILITY

Name A1 Aj An D

. . . . .Namer ar1 * arn d2

. . . . .

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

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RELEVANCE

Aj is irrelevant if it Aj is uniformative for all arj

D is ?d if Aj is arj

constraint on Aj induces a constraint on Dexample: (blood pressure is high) constrains D(Aj is arj) is uniformative if D is unconstrained

irrelevance deletability

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IRRELEVANCE (UNINFORMATIVENESS)

Name A1 Aj An D

Name

r

. aij .

d1

.

d1

Name

i+s

. aij .

d2

.

d2

(Aj is aij) is irrelevant (uninformative)

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EXAMPLE

A1 and A2 are irrelevant (uninformative) but not deletable

A2 is redundant (deletable)

0 A1

A1

A2

A2

0

D: black or white

D: black or white

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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

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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

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VERA’S AGE

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

WORLD KNOWLEDGE—THE AGE EXAMPLE

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CONTINUED

16*

16*

16*

41* 42*

42*

42*

51*

51* 67*

67*

77*

range 1

range 2

p1:

p2:

(p1, p2)

0

0

(p1, p2): a= ° 51* ° 67*

timelines

a*: approximately a How is a* defined?

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WORLD KNOWLEDGE AND PRECISIATED

NATURAL LANGUAGE

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WHAT IS PNL?

PNL is not merely a language—it 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

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PRINCIPAL FUNCTIONS OF PNL

perception description language

knowledge representation language

definition language

specification language

deduction language

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PRECISIATED NATURAL LANGUAGE (PNL) AND COMPUTING WITH WORDS (CW)

PNL

GrC

CTP

PFT

THD

CW

Granular Computing

Computational Theory of Perceptions

Protoform Theory

Theory of Hierarchical definability

CW = Granular Computing + Generalized-Constraint-Based Semantics of Natural Languages

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PRECISIATION AND GRANULAR COMPUTING

example

most Swedes are tall

Count(tall.Swedes/Swedes) is most is most

h: height density function

h(u)du = fraction of Swedes whose height lies in the interval [u, u+du]

In granular computing, the objects of computation are not values of variables but constraints on values of variables

KEY IDEA

duuuh tall

b

a )()(

))()(()( duuuhh tall

b

amost

precisiation

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THE CONCEPT OF PRECISIATION

e: expression in a natural language, NL

e proposition|command|question|…

Conversation between A and B in NL

A: e

B: I understood e but can you be more precise?

A: e*: precisiation of e

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PRECISIATION

Usually it does not rain in San Francisco in midsummer

Brian is much taller than most of his close friends

Clinton loves women

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

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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

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PRECISIATION OF CONCEPTS

Relevance Causality Similarity Rationality Optimality Reasonable doubt

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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, u+du], a u b

1duuhb

a )(

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CONTINUED

Count(tall.Swedes/Swedes) =

constraint on h

duuuh tall

b

a )()(

duuuh tall

b

a )()( is most

))()(()( duuuhh tall

b

amost

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CALIBRATION / PRECISIATION

))()(()( duuuhh tallbamost most Swedes are tall

h: height density function

• precisiation

1

0height

height

1

0fraction

most

0.5 11

• calibration

• Frege principal of compositionality

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DEDUCTION

1

0fraction1

q: How many Swedes are not tall

q*: is ? Q

solution:

duuuh tallnotba )()( .

duu1uh tallba ))()((

most1duuuhduuh tallba

ba )()()(

1-mostmost

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DEDUCTION

q: How many Swedes are short

q*: is ? Q

solution: is most

duuuh shortba )()(

)()( uuh tallba

)()( uuh shortba is ? Q

extension principle

)))()(((sup)( duuuhv tallbamostuQ

subject to

duuuhv short

b

a )()(

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CONTINUED

q: What is the average height of Swedes?

q*: is ? Q

solution: is most

uduuhba )(

duuuh tallba )()(

uduuhba )( is ? Q

extension principle

)))()(((sup)( duuuhv tallbamosthQ

subject to

uduuhv ba )(

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PROTOFORM LANGUAGE

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THE CONCEPT OF A PROTOFORM

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 protoform—a concept which is centered on the confluence of abstraction and summarization

PREAMBLE

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CONTINUED

object

p

object space

summarization abstractionprotoform

protoform spacesummary of p

S(p) A(S(p))

PF(p)

PF(p): abstracted summary of pdeep structure of p

• protoform equivalence• protoform similarity

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WHAT IS A PROTOFORM?

protoform = abbreviation of prototypical form

informally, a protoform, A, of an object, B, written as A=PF(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

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THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS

Fuzzy Logic Bivalent Logic

protoform

ontology

conceptualgraph

skeleton

Montaguegrammar

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PROTOFORMS

at a given level of abstraction and summarization, objects p and q are PF-equivalent if PF(p)=PF(q)

examplep: Most Swedes are tall Count (A/B) is Qq: Few professors are rich Count (A/B) is Q

PF-equivalenceclass

object space protoform space

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EXAMPLES

Monika is young Age(Monika) is young A(B) is C

Monika is much younger than Robert(Age(Monika), Age(Robert) is much.youngerD(A(B), A(C)) is E

Usually Robert returns from work at about 6:15pmProb{Time(Return(Robert)} is 6:15*} is usuallyProb{A(B) is C} is D

usually6:15*

Return(Robert)Time

abstraction

instantiation

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EXAMPLES

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?

Y

X0

object

Y

X0

i-protoform

option 1

option 2

01 2

gain

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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))

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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

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ABSTRACTION LATTICE

examplemost Swedes are tall

Q Swedes are tall most A’s are tall most Swedes are B

Q Swedes are B Q A’s are tall most A’s are B’s Q Swedes are B

Q A’s are B’s

Count(B/A) is Q

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largest port in Canada? second tallest building in San Francisco

PROTOFORM OF A QUERY

X

AB

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

San Francisco

buildingsheight2nd tallest

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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))

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ORGANIZATION OF WORLD KNOWLEDGEEPISTEMIC (KNOWLEDGE-DIRECTED) LEXICON (EL)

(ONTOLOGY-RELATED)

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

network of nodes and links

wij= granular strength of association between i and j

i

jrij

K(i)lexine

wij

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EPISTEMIC LEXICON

lexinei

lexinej

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 ii causes j (or usually)i and j are related

rij

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EPISTEMIC LEXICON

FORMAT OF RELATIONS

perception-based relation

A1 … Am

G1 Gm

lexine attributes

granular values

Make Price

ford G

chevy

car

example

G: 20*% \ 15k* + 40*% \ [15k*, 25k*] + • • •

granular count

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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)

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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

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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?

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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 a<b. However, the connection time in Denver is short. If the flight is missed, then the time of arrival in St. Louis will be c, with c>b. Question: Which option is best?

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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) ?

A

C

B

D

(a)

(b)

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PROTOFORM EQUIVALENCE

options

gain

c

1 2

a

b

0

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PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION

PF-submodule

PF-module

PF-module

knowledge base

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EXAMPLE

price (car) is C

price (B) is C

color (car) is C

A (car) is C

A (car) is low

A (B ) is low

A (B) is C

module

submodule

set of cars and their prices

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PROTOFORMAL DEDUCTION

p

qp*

q*

NL GCL

precisiation p**

q**

PFL

summarization

precisiation abstraction

answera

r** World KnowledgeModule

WKM DM

deduction module

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Rules of deduction in the Deduction Database (DDB) are protoformal

examples: (a) compositional rule of inference

PROTOFORMAL DEDUCTION

X is A

(X, Y) is B

Y is A°B

symbolic

))v,u()u(sup()v( BAB

computational

(b) extension principle

X is A

Y = f(X)

Y = f(A)

symbolic

Subject to:

))u((sup)v( Auy

)u(fv

computational

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Rules of deduction are basically rules governing generalized constraint propagation

The principal rule of deduction is the extension principle

RULES OF DEDUCTION

X is A

f(X,) is B Subject to:

)u((sup)v( AuB

computationalsymbolic

)u(fv

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GENERALIZATIONS OF THE EXTENSION PRINCIPLE

f(X) is A

g(X) is B

Subject to:

))u(f((sup)v( AuB

)u(gv

information = constraint on a variable

given information about X

inferred information about X

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CONTINUED

f(X1, …, Xn) is A

g(X1, …, Xn) is B Subject to:

))u(f((sup)v( AuB

)u(gv

(X1, …, Xn) is A

gj(X1, …, Xn) is Yj , j=1, …, n

(Y1, …, Yn) is B

Subject to:

))u(f((sup)v( AuB

)u(gv n,...,1j =

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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-based methods

to achieve significant progress, it is imperative to develop and employ techniques based on computing with words, protoform theory, precisiated natural language and computational theory of perceptions

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KEY POINT—THE 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 logic—a logical system which subsumes bivalent logic as a special case. More specifically:

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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

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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

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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

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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 title1970-1979: 5691980-1989: 2,4041990-1999: 23,2072000-present: 9,945Total: 36,125 MathSciNet - "fuzzy" in the title1970-1979: 4431980-1989: 2,4651990-1999: 5,4792000-present: 2,865Total: 11,252

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JOURNALS (“fuzzy” or “soft computing” in title) 1. Fuzzy Sets and Systems 2. IEEE Transactions on Fuzzy Systems 3. Fuzzy Optimization and Decision Making 4. Journal of Intelligent & Fuzzy Systems 5. Fuzzy Economic Review 6. International Journal of Uncertainty, Fuzziness and

Knowledge-Based Systems7. Journal of Japan Society for Fuzzy Theory and Systems 8. International Journal of Fuzzy Systems 9. Soft Computing 10. International Journal of Approximate Reasoning--Soft

Computing in Recognition and Search 11. Intelligent Automation and Soft Computing 12. Journal of Multiple-Valued Logic and Soft Computing 13. Mathware and Soft Computing 14. Biomedical Soft Computing and Human Sciences 15. Applied Soft Computing

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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.

1. Industrial control2. Quality control3. Elevator control and scheduling4. Train control5. Traffic control6. Loading crane control7. Reactor control8. Automobile transmissions9. Automobile climate control10. Automobile body painting control11. Automobile engine control12. Paper manufacturing13. Steel manufacturing14. Power distribution control15. Software engineerinf16. Expert systems17. Operation research18. Decision analysis

19. Financial engineering20. Assessment of credit-worthiness21. Fraud detection22. Mine detection23. Pattern classification24. Oil exploration25. Geology26. Civil Engineering27. Chemistry28. Mathematics29. Medicine30. Biomedical instrumentation31. Health-care products32. Economics33. Social Sciences34. Internet35. Library and Information Science

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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@helsinki.fi and Masoud Nikravesh Nikravesh@cs.berkeley.edu .

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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 camcorders

Total 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 factories

Fuzzy 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.

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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 cameras

Minolta 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.

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5. FL plant controllers of Yamatake Corporation

Yamatake-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. Others

Names 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@helsinki.fi and Masoud Nikravesh Nikravesh@cs.berkeley.edu , with cc to me.

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WORLD KNOWLEDGE

There is an extensive literature on world knowledge. But there are two key aspects of world knowledge which are not addressed in the literature

1. Much of world knowledge is perception-based Icy roads are slippery Usually it does not rain in San Francisco in midsummer

2. Most concepts are fuzzy rather than bivalent, i.e., most concepts are a matter of degree rather than categorical

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EXAMPLES

causality Information retrieval

economic

physical

question-answering

search