zadeh bisc2004
TRANSCRIPT
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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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LAZ 8/17/200422
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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
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TEST QUERY
Definition of Switzerland - wordIQ Dictionary & Encyclopedia
Culture of Switzerland
General information about Switzerland
Hike the mountains of Switzerland
Fragmented Ecosystems: People and Forests in the Mountains of ...
Web Results 1 - 10 of about 249,000 for number of mountains in Switzerland. (0.30 seconds)
NUMBER OF MOUNTAINS IN SWITZERLAND
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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.
Canada’s Smallest Satellite: The Canadian Advanced Nanospace ...
Bw Poco Inn And Suites in Port Coquitlam, Canada
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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)
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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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LAZ 8/17/20046161
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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LAZ 8/17/20048585
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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
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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 =
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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