Web Intelligence, World Knowledge and Fuzzy Logic

Lotfi A. Zadeh Computer Science Division

Department of EECSUC Berkeley

University of South Florida

April 1, 2004URL: http://www-bisc.cs.berkeley.edu

URL: 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 objectives

Improvement of quality of searchImprovement 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

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

X: constrained variable, implicit in pR: constraining relation, implicit in pr: index of modality, defines the modality of the

constraint, implicit in pX 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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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 ...

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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 (GOOGLE) smallest port in Canada: failure

Searched the web for smallest port Canada.  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

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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)

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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

Exampleq: How old is Carol?p1: Carol is several years older than Rayp2: 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’sp1: does not constrain Ray’s age

p2: Ray is about forty years oldp2: does not constrain Ray’s age

(p1, p2) constrains Ray’s age

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RELEVANCE, REDUNDANCE AND DELETABILITY

Name A1 Aj An DName1 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

Namer

. aij .d1

.d1

Namei+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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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, 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)

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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 Berkeleygeneralized:

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

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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))

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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

CONTINUED

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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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TEST PROBLEMS

MEASUREMENT-BASED VS PERCEPTION-BASED

INFORMATION

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•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

INFORMATION

measurement-based numerical

perception-based linguistic

MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION

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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

X approximately X

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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

1

hmax

hmin

hr

upper bound

lower bound

rN/100 N rankrhr+(i-r)hmin have hmax

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CONTINUED

most Swedes are tall is most

average height

constraint propagation

du)u()u(g tallhh

max

min∫

fraction of tall Swedesdu)u(ugmax

min

hh∫

du)u()u(g tallhh

max

min∫ is most

is ? havedu)u(ugmax

min

hh∫

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CONTINUED

Solution: application of extension principle

)du)u(g(u)((sup)v(μ tallhhmostgh

maxminave

∫=

1du)u(gmaxmin

hh =∫

subject to

du)u(ugv max

min

hh∫=

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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?

THE BALLS-IN-BOX PROBLEM

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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?

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CONTINUED

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?

box

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COMPUTATION (version 1)

measurement-basedX = number of black ballsY2 number of white ballsX 0.7 • 20 = 14X + Y = 20X = 3YX = 15; Y = 5p =5/20 = .25

(integer programming)

perception-basedX = number of black ballsY = number of white ballsX = most × 20*X = several *YX + Y = 20*P = Y/N

(fuzzy integer programming)

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FUZZY INTEGER PROGRAMMING

x

Y

1

X= several × y

X= most × 20*

X+Y= 20*

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NEW TOOLS

CN

IA PNL

CWP+ +

computing with numbers

computing with intervals

precisiated natural language

computing with words and perceptions

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 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)

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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.

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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)• ...//////////...//: psfgrsupvblank≤r ⊃⊂=

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GC-FORM (GENERALIZED CONSTRAINT FORM OF TYPE 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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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

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THE BASIC IDEA

P NL GCL

p NL(p)

GCL PFL

PF(p)

GC(p)

GC(p)

perception description of perception

precisiation of perception

precisiation of perception

abstraction

precisiationdescription

GCL (Generalized Constrain Language) is maximally expressive

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REASONING IN PNLReasoning (computation) is carried out through generalized constraint propagation

deduction rules = rules governing generalized constraint propagation

X isr R(X,Y) iss SY ist T

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CONTINUED

Deduction rules are protoformalProtoform of p: deep structure of pEva is tall Height(Eva) is tall A(B) is C

most Swedes are tallCount(tall.Swedes/Swedes) is mostCount (A/B) is Q

PFL: Protoform Language

p GC(p) PF(p)

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CONTINUED

IDS TDS

NL GCL PFL NL

initial dataset terminal dataset

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PROTOFORM LANGUAGE

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THE CONCEPT OF A PROTOFORM

CWP PNLPFL Protoform Language

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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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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

Eva much younger

Age PatAge

usuallyabout 6 pm

Time (Robert returns from work)

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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

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

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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

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CONTINUED

semantic network representation of E

E*

significant increase price oil

modifier variation attribute

mod var attr

future

near

epoch

mod

E

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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)

variationsignificant.increase

near.futureepoch

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CONTINUED

Precisiation (f.b.-concept)

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

Price

significant increase

current

presentTime

near.future

Price

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CONTINUED

precisiation of very unlikely

µ

V

likely

10

1

unlikely = ant(likely)

very unlikely = 2ant(likely)

µvery.unlikely (v) = (µlikely (1-v))2

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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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THE TALL SWEDES PROBLEM

p: most Swedes are tallQ: What is the average height of Swedes?Tryp* p**: Count (B/A) is Qq* q**: F(C/A) is ?R

answer to q** cannot be inferred from p**level of summarization of p has to be reduced

Swedesheight attribute

functional of height attribute

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PROTOFORMAL SEARCH RULES

examplequery: 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 LEXICONFORMAT OF RELATIONS

perception-based relationA1 … Am

G1 Gm

lexine attributes

granular values

Make Price

ford G

chevy

carexample

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

Examplep: most Swedes are tallq: 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

LAZ 3/9/20048686

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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)

QA’s are B’s or Count(A/B) is Q

PF(p)

abstraction

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PROTOFORMAL (PROTOFORM-BASED) DEDUCTION

precisiation abstraction

Deduction Database

instantiationretranslation

GC(p) PF(p)

PF(q)

p

q

antecedent

proposition

consequent

proposition

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protoformal rule

symbolic part computational part

FORMAT OF PROTOFORMAL DEDUCTION RULES

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PROTOFORM DEDUCTION RULE: GENERALIZED MODUS PONENS

X is AIf X is B then Y is CY is D

D = A°(B×C)

D = A°(BC)

computational 1

computational 2

symbolic

(fuzzy graph; Mamdani)

(implication; conditional relation)

classical

AA B B

fuzzy logic

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

))v,u()u((max)v( BAuBA ∧=

symbolic part

computational part

))du)u(g)u(((max)u( AU

BqD ∫=

du)u(g)u(vU

C∫ =subject to:

1du)u(gU

=∫

Prob (X is A) is BProb (X is C) is D

PROTOFORMAL RULES OF DEDUCTIONexamples

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COUNT-AND MEASURE-RELATED RULES

Q A’s are B’s

ant (Q) A’s are not B’s r0

1

1

ant (Q)Q

Q A’s are B’s

Q1/2 A’s are 2B’sr0

1

1

Q

Q1/2

most Swedes are tall ave (height) Swedes is ?h

Q A’s are B’s ave (B|A) is ?C

))a(N(sup)v( iBiQaave ∑1

)(1 ii aNv

),...,( 1 Naaa ,

crisp

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CONTINUED

not(QA’s are B’s) (not Q) A’s are B’s

Q1 A’s are B’sQ2 (A&B)’s are C’sQ1 Q2 A’s are (B&C)’s

Q1 A’s are B’sQ2 A’s are C’s(Q1 +Q2 -1) A’s are (B&C)’s

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REASONING WITH PERCEPTIONS: DEDUCTION MODULE

GC-formGC(p)

perceptionsp

GC-formsGC(p)

terminal data set

terminal protoform

set

initial protoform

set

protoformsPF(p)

translation explicitationprecisiation

IDS IGCS initial data set initial generalized

constraint set

IGCS IPS

TPS TDSIPS

abstraction deinstantiation

goal-directeddeduction

deinstantiation

initial protoform set

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PROTOFORMAL CONSTRAINT PROPAGATION

Dana is youngAge (Dana) is young X is A

p GC(p) PF(p)

Tandy is a few years older than Dana

Age (Tandy) is (Age (Dana)) Y is (X+B)

X is AY is (X+B)Y is A+B

Age (Tandy) is (young+few)

)uv(+)u((sup=)v( BAuB+A -

+few

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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 AdvancedXNorthern Light Power

No infoGoogleYahoo

XWeb Crawler

Open TextNo infoLycos

XInfoseekXHotBot

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