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Page 1: Zadeh Bisc2004

Web Intelligence, World Knowledge and Fuzzy Logic

Lotfi A. Zadeh

Computer Science Division Department of EECS

UC Berkeley

September 14, 2004

UC Berkeley

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

Email: [email protected]

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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 objectives Improvement of quality of search

Improvement in assessment of relevance

Upgrading a search engine to a question-answering system

Upgrading a search engine to a question-answering system requires a quantum jump in WIQ

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QUANTUM JUMP IN WIQ

Can a quantum jump in WIQ be achieved through the use of existing tools such as the Semantic Web and ontology-centered systems--tools which are based on bivalent logic and bivalent-logic-based probability theory?

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CONTINUED

It is beyond question that, in recent years, very impressive progress has been made through the use of such tools. But, a view which is advanced in the following is that bivalent-logic- based methods have intrinsically limited capability to address complex problems which arise in deduction from information which is pervasively ill-structured, uncertain and imprecise.

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COMPUTING AND REASONING WITH PERCEPTION-BASED INFORMATION?

1. 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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CONTINUED

1. The meaning of a proposition, p, in a natural language, NL, is represented as a generalized constraint

X: constrained variable, implicit in p

R: constraining relation, implicit in p

r: index of modality, defines the modality of the constraint, implicit in p

X isr R: Generalized Constraint Form of p, GC(p)

p X isr Rrepresentationprecisiation

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RELEVANCE

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

And yet, there is no definition of relevance Relevance is a matter of degree Relevance cannot be defined within the

conceptual structure of bivalent logic 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

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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

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TEST QUERY

The Mountains of California, by John Muir (1894) - John Muir ...

Number of Black Bears in the San Gabriel Mountains AllFusion Harvest Change Manager Helps DesertDocs Manage Mountains ...

Launching of the International Year of Mountains (IYM), 11 ...

Preliminary Meeting Notice and Agenda Santa Monica Mountains ...

Web Results 1 - 10 of about 1,040,000 for number of mountains in CA. (0.31 seconds)

NUMBER OF MOUNTAINS IN CALIFORNIA

Google

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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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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

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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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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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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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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 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 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, REDUNDANCE AND DELETABILITY

dr

.

dl

.

d2

d1

.

d1

D

amnamjam1Namen

....

alnaljal1Namel

....

ak+1, nak+1, jak+1, 1Namek+1

aknakjak1Namek

....

aina1ja11Name1

AnAjA1Name

DECISION TABLE

Aj: j th symptom

aij: value of j th symptom of Name

D: diagnosis

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REDUNDANCE DELETABILITY

.

d2

.

D

....

arn*ar1Namer

....

AnAjA1Name

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)

d2

.

d2

d1

.

d1

D

.aij.Name

i+s

.aij.Name

r

AnAjA1Name

(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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THE MAJOR OBSTACLE

Existing methods do not have the capability to operate on world knowledge

To operate on world knowledge, what is needed is the machinery of fuzzy logic and perception-based probability theory

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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EXAMPLES OF WORLD KNOWLEDGE

Paris is the capital of France (specific, crisp) California has a temperate climate (perception-based) Robert is tall (specific, perception-based) It is hard to find parking near the campus between

9am and 5pm (specific, perception-based) Usually Robert returns from work at about 6pm

(specific, perception-based) Child-bearing age is from about 16 to about 42

(perception-based)

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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 aHow is a* defined?

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PRECISIATION OF “approximately a,” a*

x

x

x

x

a

a

20 25p

0

0

1

0

0

1

bimodal distribution

p

fuzzy graph

probability distribution

interval

x 0

a

possibility distribution

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the web is, in the main, a repository of specific world knowledge

Semantic Web and ontology-based systems serve to enhance the performance of search engines by adding to the web a collection of relevant fragments of world knowledge

the problem is that much of world knowledge, and especially general world knowledge, consists of perceptions

WORLD KNOWLEDGE

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perceptions are intrinsically imprecise imprecision of perceptions is a concomitant of

the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information

perceptions are f-granular in the sense that (a) the boundaries of perceived classes are unsharp; and (b) the values of perceived attributes are granular, with a granule being a clump of values drawn together by indistinguishability, similarity, proximity or functionality

CONTINUED

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f-granularity of perceptions stands in the way of representing the meaning of perceptions through the use of conventional bivalent-logic-based languages

to deal with perceptions and world knowledge, new tools are needed

of particular relevance to enhancement of web intelligence are Precisiated Natural Language (PNL) and Protoform Theory (PFT)

CONTINUED

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NEW TOOLS

CN

IA PNL

CW+ +

computing with numbers

computing with intervals

precisiated natural language

computing with words

PTp

CTP: computational theory of perceptionsPFT: protoform theoryPTp: perception-based probability theoryTHD: theory of hierarchical definability

CTP THD PFT

probability theory

PT

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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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PRECISIATION OF “approximately a,” a*

x

x

x

x

a

a

20 25p

0

0

1

0

0

1

bimodal distribution

p

fuzzy graph

probability distribution

interval

x 0

a

possibility distribution

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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 VIA TRANLSATION INTO GCL

predicate logic, Prolog, SQL, … may be viewed as precisiation languages

example of precisiation

all men are mortal x(man(x) mortal(x)) principal attributes of PL: expressive power

deductive power

p p*

NL GCL

precisiation

translation

precisiation of p

GC-formGC(p)

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CONTINUED

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/NEAR[City] SMALL[City]

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GENERALIZED-CONSTRAINT-FORM(GC(p))

annotation

p X/A isr R/B annotated GC(p)

suppression

X/A isr R/B

X isr R is a deep structure (protoform) of p

instantiation

abstractionX isr R

A isr B

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CONTINUED

existing precisiation languages have a very limited expressive power

examples: Eva is young most Swedes are tall

are not precisiable through translation into predicate logic

the probability that a proposition picked at random from a book is precisiable through translation into predicate logic is of the order of 0.01

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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 shortba )()(

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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

GmG1

Am…A1lexine attributes

granular values

Gford

chevy

PriceMakecar

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

p r i c e ( c a r ) i s C

p r i c e ( B ) i s C

c o l o r ( c a r ) i s C

A ( c a r ) i s C

A ( c a r ) i s l o w

A ( B ) i s l o w

A ( B ) i s C

module

submodule

set of cars and their prices

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PROTOFORM-BASED DEDUCTION

p

qp*

q*

NL GCL

precisiation p**

q**

PFL

summarization

precisiation abstraction

answera

r** World KnowledgeModule

WKM DM

deduction module

Page 87: Zadeh Bisc2004

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

examples: (a) compositional rule of inference

PROTOFORM-BASED (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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THE TALL SWEDES PROBLEM

p: Most Swedes are tallq: What is the average height of SwedesPNL-based solution

4. PF(p): Count(A/B) is QPF(q): H(A) is Cno match in Deduction Databaseexcessive summarization

8. PF(p): Count(P[H is A] / P) is QHave is C

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CONTINUED

Name H

Name 1 h1

. . . .

Name N hn

P:

Name H µa

Namei hi µA(hi)P[H is A]:

))((sup)( iAihave hN1

v ),...,( N1 hhh ,

subject to: ii h

N1

v

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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 =

Page 93: Zadeh Bisc2004

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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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CONTINUED

Actually, elementary fuzzy logic techniques are used in many search engines

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USE OF FUZZY LOGIC* IN SEARCH ENGINES

XExcite!

Alta Vista

XFast Search Advanced

XNorthern Light Power

No infoGoogle

Yahoo

XWeb Crawler

Open Text

No infoLycos

XInfoseek

XHotBot

Fuzzy logic in any form

Search engine

* (currently, only elementary fuzzy logic tools are employed)

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CONTINUED

But what is needed is application of advanced concepts and techniques which are outlined in this presentation