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Web Intelligence, World Knowledge and Fuzzy Logic Lotfi A. Zadeh Computer Science Division Department of EECS UC Berkeley University of South Florida April 1, 2004 URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/ Email: [email protected] BACKDROP. PREAMBLE.

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Web Intelligence, World Knowledge and Fuzzy Logic

Lotfi A. Zadeh Computer Science Division

Department of EECSUC Berkeley

University of South Florida

April 1, 2004

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

URL: http://zadeh.cs.berkeley.edu/

Email: [email protected]


BACKDROP

LAZ 3/9/2004


PREAMBLE

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.

LAZ 3/9/2004


Web intelligence wiq
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

LAZ 3/9/2004


Quantum jump in wiq
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?

LAZ 3/9/2004


Continued
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.

LAZ 3/9/2004


Computing and reasoning with perception based information
COMPUTING AND REASONING WITH PERCEPTION-BASED INFORMATION?

KEY IDEAS

  • 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

LAZ 3/9/2004


Continued1
CONTINUED

  • 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)

representation

p X isr R

precisiation

LAZ 3/9/2004


Relevance
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

LAZ 3/9/2004


Continued2
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

LAZ 3/9/2004


Limitations of search engines test queries
LIMITATIONS OF SEARCH ENGINESTEST QUERIES

  • 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 ...

LAZ 3/9/2004


Test query google
TEST QUERY (GOOGLE)

  • largest port in Switzerland: failure

    Searched the web for largestportSwitzerland.  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

LAZ 3/9/2004


Test query google1
TEST QUERY (GOOGLE)

  • smallest port in Canada: failure

    Searched the web for smallestportCanada.  Results 1 - 10 of about 77,100. Search took 0.43 seconds.

    Canada’s Smallest Satellite: The Canadian Advanced Nanospace ...

    Bw Poco Inn And Suites in Port Coquitlam, Canada

LAZ 3/9/2004


Test query google2
TEST QUERY (GOOGLE)

  • 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)

LAZ 3/9/2004


Test query google3
TEST QUERY (GOOGLE)

  • population of largest city in Spain: failure

  • largest city in Spain: Madrid, success

  • population of Madrid: success

LAZ 3/9/2004


Historical note
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

LAZ 3/9/2004


Relevance1
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

LAZ 3/9/2004


Digression cointension
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)

LAZ 3/9/2004


Relevance2
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

LAZ 3/9/2004


Query relevance
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

LAZ 3/9/2004


Ptp based solution
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

LAZ 3/9/2004


Continued3
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

LAZ 3/9/2004


Continued4
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

LAZ 3/9/2004


Relevance redundance and deletability
RELEVANCE, REDUNDANCE AND DELETABILITY

DECISION TABLE

Aj: j th symptom

aij: value of j th

symptom of

Name

D: diagnosis

LAZ 3/9/2004


Redundance deletability
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

LAZ 3/9/2004


Relevance3
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

LAZ 3/9/2004


Irrelevance uninformativeness
IRRELEVANCE (UNINFORMATIVENESS)

(Aj is aij) is irrelevant (uninformative)

LAZ 3/9/2004


Example
EXAMPLE

A2

D: black or white

0

A1

A1 and A2 are irrelevant (uninformative) but not deletable

A2

D: black or white

0

A1

A2 is redundant (deletable)

LAZ 3/9/2004


The major obstacle
THE MAJOR OBSTACLE

WORLD KNOWLEDGE

  • 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

LAZ 3/9/2004


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

LAZ 3/9/2004


Examples of world knowledge
EXAMPLES OF WORLD KNOWLEDGE

  • Paris is the capital of France (specific, crisp)

  • California has a temperate climate (perception-based, dispositional)

  • Robert is tall (specific, perception-based)

  • Robert is honest (specific, perception-based, dispositional)

  • It is hard to find parking near the campus between 9am and 5pm (specific, perception-based, dispositional)

  • Usually Robert returns from work at about 6pm (specific, perception-based, dispositional)

LAZ 3/9/2004


World knowledge examples
WORLD KNOWLEDGE: EXAMPLES

specific:

  • if Robert works in Berkeley then it is likely that Robert lives in or near Berkeley

  • if Robert lives in Berkeley then it is likely that Robert works in or near Berkeley

    generalized:

    if A/Person works in B/City then it is likely that A lives in or near B

    precisiated:

    Distance (Location (Residence (A/Person), Location (Work (A/Person) isu near

    protoform: F (A (B (C)), A (D (C))) isu R

LAZ 3/9/2004


Example1
EXAMPLE

Specific:

  • If Ray has a Ph.D. degree, then it is unlikely that Age(Ray) < 22*

    General:

  • Attr1(A/Person) is f(Attr2(Person))

LAZ 3/9/2004


Continued5
CONTINUED

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

  • Semantic Web and related 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

LAZ 3/9/2004


Continued6
CONTINUED

  • 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

LAZ 3/9/2004


Continued7
CONTINUED

  • 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)

LAZ 3/9/2004


Test problems measurement based vs perception based information
TEST PROBLEMSMEASUREMENT-BASED VS PERCEPTION-BASED INFORMATION

LAZ 3/9/2004


MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION

INFORMATION

measurement-based

numerical

perception-based

linguistic

  • it is 35 C°

  • Eva is 28

  • Tandy is three years

  • older than Dana

  • It is very warm

  • Eva is young

  • Tandy is a few

  • years older than Dana

  • it is cloudy

  • traffic is heavy

  • Robert is very honest

LAZ 3/9/2004


The tall swedes problem

MEASUREMENT-BASED

IDS p1: Height of Swedes ranges from hmin to hmax

p2: Over 70% are taller than htall

TDS q1: What fraction are less than htall

q2: What is the average height of Swedes

PERCEPTION-BASED

p1: Height of Swedes ranges from approximately hmin to approximately hmax

p2: Most are tall

(taller than approximately htall)

q1: What fraction are not tall

(shorter than approximately htall)

q2: What is the average height of Swedes

THE TALL SWEDES PROBLEM

X approximately X

LAZ 3/9/2004


The tall swedes problem1
THE TALL SWEDES PROBLEM

  • measurement-based version

    • height of Swedes ranges from hmin to hmax

    • over r% of Swedes are taller than hr

    • what is the average height, have , of Swedes?

height

upper bound

hmax

hr

lower bound

hmin

1

rank

rN/100

N

rhr+(i-r)hmin  have hmax

LAZ 3/9/2004


Continued8
CONTINUED

  • most Swedes are tall is most

  • average height

  • constraint propagation

fraction of tall Swedes

is most

is ? have

LAZ 3/9/2004


Continued9
CONTINUED

  • Solution: application of extension principle

subject to

LAZ 3/9/2004


THE BALLS-IN-BOX PROBLEM

Version 1. Measurement-based

  • a box contains 20 black and white balls

  • over 70% 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 drawn at random is white?

  • I draw a ball at random. If it is white, I win $20; if it is black, I lose $5. Should I play the game?

LAZ 3/9/2004


Continued10
CONTINUED

Version 2. Perception-based

  • 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?

  • I draw a ball at random. If it is white, I win $20; if it is black, I lose $5. Should I play the game?

LAZ 3/9/2004


Continued11
CONTINUED

box

Version 3. Perception-based

  • a box contains about 20 black balls of various sizes

  • most are large

  • there are several times as many large balls as small balls

  • what is the number of small balls?

  • what is the probability that a ball drawn at random is small?

LAZ 3/9/2004


Computation version 1

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

(integer programming)

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)

COMPUTATION (version 1)

LAZ 3/9/2004


Fuzzy integer programming
FUZZY INTEGER PROGRAMMING

Y

X= most × 20*

X+Y= 20*

X= several × y

x

1

LAZ 3/9/2004


NEW TOOLS

computing with numbers

computing with words and perceptions

+

+

CWP

CN

PNL

IA

precisiated natural language

computing with intervals

CTP

PFT

PTp

THD

PT

CTP: computational

theory of perceptions

PFT: protoform theory

PTp: perception-based

probability theory

THD: theory of hierarchical

definability

probability theory

LAZ 3/9/2004


PRECISIATED NATURAL LANGUAGE

PNL

LAZ 3/9/2004


WHAT IS PRECISIATED NATURAL LANGUAGE (PNL)? PRELIMINARIES

  • a proposition, p, in a natural language, NL, is precisiable if it translatable into a precisiation language

  • in the case of PNL, the precisiation language is the Generalized Constraint Language, GCL

  • precisiation of p, p*, is an element of GCL (GC-form)

LAZ 3/9/2004


WHAT IS PNL?

  • PNL is a sublanguage of precisiable propositions in NL which is equipped with two dictionaries: (1) NL to GCL; (2) GCL to PFL (Protoform Language); and (3) a modular multiagent database of rules of deduction (rules of generalized constrained propagation) expressed in PFL.

LAZ 3/9/2004


GENERALIZED CONSTRAINT

  • standard constraint: X  C

  • generalized constraint: X isr R

X isr R

copula

GC-form (generalized constraint form of type r)

type identifier

constraining relation

constrained variable

  • 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)

LAZ 3/9/2004


GC-FORM (GENERALIZED CONSTRAINT FORM OF TYPE r)

X isr R

r: = equality constraint: X=R is abbreviation of X is=R

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

distribution of X

r: p probabilistic constraint; X isp R; R is the

probability distribution of X

LAZ 3/9/2004


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

LAZ 3/9/2004


Generalized constraint language gcl
GENERALIZED CONSTRAINT LANGUAGE (GCL)

  • GCL is generated by combination, qualification and propagation of generalized constraints

  • in GCL, rules of deduction are the rules governing generalized constraint propagation

  • 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 small then Y is large

  • the language of fuzzy if-then rules is a sublanguage of PNL

LAZ 3/9/2004


The basic idea
THE BASIC IDEA

P

GCL

NL

precisiation

description

p

NL(p)

GC(p)

description of perception

precisiation of perception

perception

PFL

GCL

abstraction

GC(p)

PF(p)

precisiation of perception

GCL (Generalized Constrain Language) is maximally expressive

LAZ 3/9/2004


Reasoning in pnl
REASONING IN PNL

Reasoning (computation) is carried out through generalized constraint propagation

deduction rules = rules governing generalized constraint propagation

X isr R

(X,Y) iss S

Y ist T

LAZ 3/9/2004


Continued12
CONTINUED

Deduction rules are protoformal

Protoform of p: deep structure of p

Eva is tall Height(Eva) is tall A(B) is C

most Swedes are tall Count(tall.Swedes/Swedes) is most Count (A/B) is Q

PFL: Protoform Language

p

GC(p)

PF(p)

LAZ 3/9/2004


Continued13
CONTINUED

NL

PFL

GCL

NL

IDS

TDS

initial dataset

terminal dataset

LAZ 3/9/2004


PROTOFORM LANGUAGE

PFL

LAZ 3/9/2004


The concept of a protoform
THE CONCEPT OF A PROTOFORM

PNL

CWP

PFL

Protoform Language

LAZ 3/9/2004


What is a protoform
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

LAZ 3/9/2004


The concept of protoform and related concepts
THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS

Fuzzy Logic

Bivalent Logic

ontology

conceptual

graph

protoform

skeleton

Montague

grammar

LAZ 3/9/2004


Translation from nl to pfl
TRANSLATION FROM NL TO PFL

examples

Most Swedes are tall Count (A/B) is Q

Eva is much younger than Pat (A (B), A (C)) is R

usually Robert returns from work at about 6pm

Prob {A is B} is C

much younger

Age

Pat

Age

Eva

usually

about 6 pm

Time (Robert returns from work)

LAZ 3/9/2004


Multilevel structures
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

LAZ 3/9/2004


Abstraction lattice
ABSTRACTION LATTICE

example

most 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

LAZ 3/9/2004


Levels of summarization
LEVELS OF SUMMARIZATION

example

p: it is very unlikely that there will be a significant increase in the price of oil in the near future

PF(p): Prob(E) is A

very.unlikely

significant increase in the price of oil in the near future

LAZ 3/9/2004


Continued14
CONTINUED

semantic network representation of E

E

E*

modifier

variation

attribute

mod

attr

var

significant

increase

price

oil

epoch

future

mod

near

LAZ 3/9/2004


Continued15
CONTINUED

E: significant increase in the price of oil in the near future

f: function of time

PF(E): (B(f) is C, D(f) is E)

significant.increase

variation

near.future

epoch

LAZ 3/9/2004


Continued16
CONTINUED

Precisiation (f.b.-concept)

E*: Epoch (Variation (Price (oil)) is significant.increase)

is near.future

Price

significant

increase

Price

current

present

Time

near.future

LAZ 3/9/2004


Continued17
CONTINUED

precisiation of very unlikely

µ

1

likely

unlikely = ant(likely)

very unlikely = 2ant(likely)

0

1

V

µvery.unlikely (v) = (µlikely (1-v))2

LAZ 3/9/2004


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

2nd tallest

height

LAZ 3/9/2004


The tall swedes problem2
THE TALL SWEDES PROBLEM

p: most Swedes are tall

Q: What is the average height of Swedes?

Try

p* p**: Count (B/A) is Q

q* q**: F(C/A) is ?R

answer to q** cannot be inferred from p**

level of summarization of p has to be reduced

Swedes

height attribute

functional of height attribute

LAZ 3/9/2004


Protoformal search rules
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))

LAZ 3/9/2004


Organization of world knowledge epistemic knowledge directed lexicon el ontology related
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

rij

j

wij= granular strength of association between i and j

wij

i

K(i)

network of nodes and links

lexine

LAZ 3/9/2004


Epistemic lexicon
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

LAZ 3/9/2004


Epistemic lexicon1
EPISTEMIC LEXICON

FORMAT OF RELATIONS

perception-based relation

lexine

attributes

granular values

example

car

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

granular count

LAZ 3/9/2004


Protoform of a decision problem
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
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
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 equivalence1
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
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

(b)

C

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Protoform equivalence1
PROTOFORM EQUIVALENCE

gain

c

1

2

0

options

a

b

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Protoform centered knowledge organization
PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION

knowledge base

PF-module

PF-module

PF-submodule

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Example2
EXAMPLE

module

submodule

set of cars and their prices

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PROTOFORM-BASED

DEDUCTION

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PROTOFORMS AND LOGICAL FORMS

  • p=proposition in a natural language

  • if p has a logical form, LF(p), then a protoform of p, PF(p), is an abstraction of LF(p)

    all men are mortal x(man(x) mortal(x)) x(A(x) B(x))

p

LF(p)

PF(p)

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CONTINUED

  • if p does not have a logical form but is in PNL, then a protoform of p is an abstraction of the generalized constraint form of p, GC(p)

most Swedes are tall ΣCount(tall.Swedes/Swedes) is most

p

GC(p)

abstraction

QA’s are B’s or Count(A/B) is Q

PF(p)

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PROTOFORMAL (PROTOFORM-BASED) DEDUCTION

precisiation

abstraction

antecedent

GC(p)

PF(p)

p

proposition

Deduction

Database

consequent

retranslation

instantiation

q

PF(q)

proposition

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FORMAT OF PROTOFORMAL DEDUCTION RULES

protoformal rule

symbolic part

computational part

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Protoform deduction rule generalized modus ponens
PROTOFORM DEDUCTION RULE: GENERALIZED MODUS PONENS

fuzzy logic

classical

X is A

If X is B then Y is C

Y is D

A

A B

B

symbolic

D = A°(B×C)

(fuzzy graph;

Mamdani)

computational 1

D = A°(BC)

(implication;

conditional

relation)

computational 2

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PROTOFORMAL RULES OF DEDUCTION

examples

X is A

(X, Y) is B

Y is AB

symbolic

part

computational part

Prob (X is A) is B

Prob (X is C) is D

subject to:

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COUNT-AND MEASURE-RELATED RULES

crisp

Q

1

ant (Q)

Q A’s are B’s

ant (Q) A’s are not B’s

r

0

1

Q A’s are B’s

Q1/2 A’s are 2B’s

1

Q

Q1/2

r

0

1

most Swedes are tall

ave (height) Swedes is ?h

Q A’s are B’s ave (B|A) is ?C

,

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CONTINUED

not(QA’s are B’s) (not Q) A’s are B’s

Q1 A’s are B’s

Q2 (A&B)’s are C’s

Q1 Q2 A’s are (B&C)’s

Q1 A’s are B’s

Q2 A’s are C’s

(Q1 +Q2 -1) A’s are (B&C)’s

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REASONING WITH PERCEPTIONS: DEDUCTION MODULE

initial data set

initial generalized

constraint set

IDS

IGCS

perceptions

p

GC-forms

GC(p)

translation

explicitation

precisiation

IGCS

IPS

initial protoform set

GC-form

GC(p)

protoforms

PF(p)

abstraction

deinstantiation

TDS

IPS

TPS

initial

protoform

set

terminal

protoform

set

terminal

data

set

goal-directed

deinstantiation

deduction

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PROTOFORMAL CONSTRAINT PROPAGATION

p

GC(p)

PF(p)

Age (Dana) is young

Dana is young

X is A

Age (Tandy) is (Age (Dana))

Tandy is a few years older than Dana

Y is (X+B)

+few

X is A

Y is (X+B)

Y is A+B

Age (Tandy) is (young+few)

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Summation
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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Continued18
CONTINUED

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

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Use of fuzzy logic in search engines
USE OF FUZZY LOGIC* IN SEARCH ENGINES

Search engine

Fuzzy logic in any form

Excite!

X

Alta Vista

HotBot

X

Infoseek

X

Lycos

No info

Open Text

Web Crawler

X

Yahoo

Google

No info

Northern Light Power

X

Fast Search Advanced

X

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

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Continued19
CONTINUED

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

LAZ 3/9/2004


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