Web Intelligence, World Knowledge and Fuzzy Logic

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Web Intelligence, World Knowledge and Fuzzy
Logic Lotfi A. Zadeh Computer Science Divis
ion Department of EECSUC Berkeley Septembe
r 14, 2004 UC Berkeley URL http//www-bisc.
cs.berkeley.edu URL http//zadeh.cs.berkeley.edu
/ Email Zadeh_at_cs.berkeley.edu
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(No Transcript)
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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
engineswith Google at the topfall into this
category. In the context of the Web, MIQ becomes
Web IQ, or WIQ, for short.
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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?

6
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?
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

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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
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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
NUMBER OF MOUNTAINS IN CALIFORNIA
Google
Web Results 1 - 10 of about 1,040,000 for number
of mountains in CA. (0.31 seconds) 
The Mountains of California, by John Muir (1894)
- John Muir ... Number of Black Bears in the San
Gabriel Mountains AllFusion Harvest Change Man
ager Helps DesertDocs Manage Mountains
...Launching of the International Year of
Mountains (IYM), 11 ... Preliminary Meeting Noti
ce and Agenda Santa Monica Mountains ...
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TEST QUERY
NUMBER OF MOUNTAINS IN SWITZERLAND
Google
Web Results 1 - 10 of about 249,000 for number of
mountains in Switzerland. (0.30 seconds) 
Definition of Switzerland - wordIQ Dictionary
amp Encyclopedia Culture of Switzerland Gene
ral information about Switzerland
Hike the mountains of Switzerland
Fragmented Ecosystems People and Forests in the
Mountains of ...
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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 (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.
  
• Canadas 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 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

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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
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)
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RELEVANCE
relevance
query relevance
topic relevance
examples query How old is Ray propos
ition 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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PTpBASED SOLUTION

• (a) Describe your perception of Rays 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)
• likely \\ 55 ? Age Ray ? 65
• unlikely \\ Age(Ray) 65
• Age(Carol) Age(Ray) several

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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
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CONTINUED

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

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RELEVANCE, REDUNDANCE AND DELETABILITY
DECISION TABLE
Aj j th symptom aij value of j th sy
mptom of
Name D diagnosis
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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

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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
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IRRELEVANCE (UNINFORMATIVENESS)
(Aj is aij) is irrelevant (uninformative)
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EXAMPLE
A2
D black or white
0
A1
A1 and A2 are irrelevant (uninformative) but not
deletable
A2
D black or white
A1
0
A2 is redundant (deletable)
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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

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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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VERAS AGE
WORLD KNOWLEDGETHE AGE EXAMPLE

• q How old is Vera?
• p1 Vera has a son, in mid-twenties
• p2 Vera has a daughter, in mid-thirties
• wk the child-bearing age ranges from about 16 to
  about 42

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CONTINUED
range 1
timelines
p1
0
16
41
42
67
range 2
p2
0
16
42
51
77
(p1, p2)
16
42
51
67
(p1, p2) ?a ? 51 ? 67
a approximately a How is a defined?
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PRECISIATION OF approximately a, a
?
1
interval
0
a
x
p
probability distribution
0
a
x
?
possibility distribution
0
a
x
?
1
fuzzy graph
0
20
25
x
p
bimodal distribution
0
x
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WORLD KNOWLEDGE

• 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
  

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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

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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)

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NEW TOOLS
computing with numbers
computing with words


CW
CN
PNL
IA
precisiated natural language
computing with intervals
PTp
CTP
THD
PFT
PT
CTP computational theory of perceptions
PFT protoform theory PTp perception-based
probability theory THD theory of hierarch
ical definability
probability theory
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PRECISIATED NATURAL LANGUAGE
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WHAT IS PNL?

• PNL is not merely a languageit is a system aimed
  at a wide-ranging enlargement of the role of
  natural languages in scientific theories and,
  more particularly, in enhancement of machine IQ

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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)
CW
GrC
Granular Computing Computational Theory of Pe
rceptions Protoform Theory Theory of Hierarc
hical
definability
CTP
PNL
PFT
THD
CW Granular Computing Generalized-Constraint-B
ased
Semantics of Natural Languages
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PRECISIATION AND GRANULAR COMPUTING
KEY IDEA

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

precisiation
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THE CONCEPT OF PRECISIATION

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

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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
?
1
interval
0
a
x
p
probability distribution
0
a
x
?
possibility distribution
0
a
x
?
1
fuzzy graph
0
20
25
x
p
bimodal distribution
0
x
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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
NL
GCL
p
p
precisiation
GC-form GC(p)
translation
precisiation of p

• 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

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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/NEARCity ?
  SMALLCity

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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

abstraction
X isr R
A isr B
instantiation
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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,
  udu, a ? u ? b

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CONTINUED

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

is most
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CALIBRATION / PRECISIATION

• calibration

?height
?most
1
1
0
0
height
fraction
0.5
1
1

• precisiation

most Swedes are tall
h height density function

• Frege principal of compositionality

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DEDUCTION
q How many Swedes are not tall
q is ? Q
solution
1-most
most
1
0
1
fraction
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DEDUCTION
q How many Swedes are short q is ? Q sol
ution is most
is ? Q
extension principle
subject to
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CONTINUED
q What is the average height of Swedes?
q is ? Q
solution is most
is ? Q
extension principle
subject to
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PROTOFORM LANGUAGE
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THE CONCEPT OF A PROTOFORM
PREAMBLE

• As we move further into the age of machine
  intelligence and automated reasoning, a daunting
  problem becomes harder and harder to master. How
  can we cope with the explosive growth in
  knowledge, information and data. How can we
  locate and infer from decision-relevant
  information which is embedded in a large
  database.
• Among the many concepts that relate to this
  issue there are four that stand out in
  importance organization, representation, search
  and deduction. In relation to these concepts, a
  basic underlying concept is that of a protoforma
  concept which is centered on the confluence of
  abstraction and summarization

63
CONTINUED
object space
object p
protoform space
summary of p
protoform
summarization
abstraction
S(p)
A(S(p))
PF(p)

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

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WHAT IS A PROTOFORM?

• protoform abbreviation of prototypical form
• informally, a protoform, A, of an object, B,
  written as APF(B), is an abstracted summary of
  B
  
• usually, B is lexical entity such as proposition,
  question, command, scenario, decision problem,
  etc
  
• more generally, B may be a relation, system,
  geometrical form or an object of arbitrary
  complexity
  
• usually, A is a symbolic expression, but, like B,
  it may be a complex object
  
• the primary function of PF(B) is to place in
  evidence the deep semantic structure of B

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THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS
Fuzzy Logic
Bivalent Logic
ontology
conceptual graph
protoform
skeleton
Montague grammar
66
PROTOFORMS
object space
protoform space
PF-equivalence class

• at a given level of abstraction and
  summarization, objects p and q are PF-equivalent
  if PF(p)PF(q)
  
• example
• p Most Swedes are tall Count (A/B) is Q
• q Few professors are rich Count (A/B) is Q

67
EXAMPLES
instantiation

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

abstraction
usually
615
Return(Robert)
Time
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EXAMPLES
gain
Alan has severe back pain. He goes to see a
doctor. The doctor tells him that there are two
options (1) do nothing and (2) do surgery. In
the case of surgery, there are two possibilities
(a) surgery is successful, in which case Alan
will be pain free and (b) surgery is not
successful, in which case Alan will be paralyzed
from the neck down. Question Should Alan elect
surgery?
2
1
0
option 2
option 1
Y
Y
object
i-protoform
X
0
X
0
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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))

70
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 As are tall
most Swedes are B
Q Swedes are B
Q As are tall
most As are Bs
Q Swedes are B
Q As are Bs
Count(B/A) is Q
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PROTOFORM OF A QUERY

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

B
A
X
?X is selector (attribute (A/B))
San Francisco
buildings
height
2nd tallest
73
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)
j
rij
wij granular strength of association between i
and j
wij
i
K(i)
network of nodes and links
lexine

• i (lexine) object, construct, concept
  (e.g., car, Ph.D. degree)
  
• K(i) world knowledge about i (mostly
  perception-based)
  
• K(i) is organized into n(i) relations Rii, ,
  Rin
  
• entries in Rij are bimodal-distribution-valued
  attributes of i
  
• values of attributes are, in general, granular
  and context-dependent

75
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
76
EPISTEMIC LEXICON
FORMAT OF RELATIONS
perception-based relation
lexine
attributes
granular values
example
car
G 20 \ ? 15k 40 \ 15k, 25k
granular count
77
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)

78
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

79
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?

80
PF-EQUIVALENCE

• Scenario B
• Alan needs to fly from San Francisco to St.
  Louis and has to get there as soon as possible.
  One option is fly to St. Louis via Chicago and
  the other through Denver. The flight via Denver
  is scheduled to arrive in St. Louis at time a.
  The flight via Chicago is scheduled to arrive in
  St. Louis at time b, with aconnection time in Denver is short. If the flight
  is missed, then the time of arrival in St. Louis
  will be c, with cb. Question Which option is
  best?

81
THE TRIP-PLANNING PROBLEM

• I have to fly from A to D, and would like to get
  there as soon as possible
  
• I have two choices (a) fly to D with a
  connection in B or
  
• (b) fly to D with a connection in C
• if I choose (a), I will arrive in D at time t1
• if I choose (b), I will arrive in D at time t2
• t1 is earlier than t2
• therefore, I should choose (a) ?

B
(a)
A
D
C
(b)
82
PROTOFORM EQUIVALENCE
gain
c
1
2
0
options
a
b
83
PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION
knowledge base
PF-module
PF-module
PF-submodule
84
EXAMPLE
module
submodule
set of cars and their prices
85
(No Transcript)
86
PROTOFORM-BASED DEDUCTION
NL
GCL
PFL
p q
p q
p q
precisiation
summarization
precisiation
abstraction
WKM
DM
r
World Knowledge Module
a
answer
deduction module
87
PROTOFORM-BASED (PROTOFORMAL) DEDUCTION

• Rules of deduction in the Deduction Database
  (DDB) are protoformal
  
• examples (a) compositional rule of inference

X is A (X, Y) is B Y is AB
symbolic
computational
(b) extension principle
X is A Y f(X) Y f(A)
Subject to
symbolic
computational
88
THE TALL SWEDES PROBLEM

• p Most Swedes are tall
• q What is the average height of Swedes
• PNL-based solution
• PF(p) Count(A/B) is Q
• PF(q) H(A) is C
• no match in Deduction Database
• excessive summarization
• PF(p) ?Count(PH is A / P) is Q
• Have is C

89
CONTINUED
Name H Name 1 h1 . . . . Name N
hn
P
Name H µa Namei hi µA(hi)
PH is A
,
subject to
90
RULES OF DEDUCTION

• Rules of deduction are basically rules governing
  generalized constraint propagation
  
• The principal rule of deduction is the extension
  principle
  

X is A f(X,) is B
Subject to
computational
symbolic
91
GENERALIZATIONS OF THE EXTENSION PRINCIPLE
information constraint on a variable
f(X) is A g(X) is B
given information about X
inferred information about X
Subject to
92
CONTINUED
f(X1, , Xn) is A g(X1, , Xn) is B
Subject to
(X1, , Xn) is A gj(X1, , Xn) is Yj , j1,
, n
(Y1, , Yn) is B
Subject to
93
SUMMATION

• addition of significant question-answering
  capability to search engines is a complex,
  open-ended problem
  
• incremental progress, but not much more, is
  achievable through the use of bivalent-logic-base
  d methods
  
• to achieve significant progress, it is imperative
  to develop and employ techniques based on
  computing with words, protoform theory,
  precisiated natural language and computational
  theory of perceptions

94
CONTINUED

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

95
USE OF FUZZY LOGIC IN SEARCH ENGINES
Fuzzy logic in any form
Search engine
X
Excite!
Alta Vista
X
HotBot
X
Infoseek
No info
Lycos
Open Text
X
Web Crawler
Yahoo
No info
Google
X
Northern Light Power
X
Fast Search Advanced
(currently, only elementary fuzzy logic tools
are employed)
96
CONTINUED

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