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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, 2004URL: http://www-bisc.cs.berkeley.edu
URL: http://zadeh.cs.berkeley.edu/
Email: [email protected]
LAZ 3/9/200433
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
LAZ 3/9/200444
WEB INTELLIGENCE (WIQ)
Principal objectivesImprovement 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 3/9/200455
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 3/9/200466
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 3/9/200477
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
LAZ 3/9/200488
CONTINUED
2. 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
LAZ 3/9/200499
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 3/9/20041010
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 3/9/20041111
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 3/9/20041212
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
LAZ 3/9/20041313
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
LAZ 3/9/20041414
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 3/9/20041515
TEST QUERY (GOOGLE)
population of largest city in Spain: failure
largest city in Spain: Madrid, success
population of Madrid: success
LAZ 3/9/20041616
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
LAZ 3/9/20041717
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 3/9/20041818
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)
LAZ 3/9/20041919
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 3/9/20042020
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 3/9/20042121
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 3/9/20042222
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
LAZ 3/9/20042323
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 3/9/20042424
RELEVANCE, REDUNDANCE AND DELETABILITY
Name A1 Aj An D
Name1 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
LAZ 3/9/20042525
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
LAZ 3/9/20042626
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
LAZ 3/9/20042727
IRRELEVANCE (UNINFORMATIVENESS)
Name A1 Aj An D
Name
r
. aij .
d1
.
d1
Name
i+s
. aij .
d2
.
d2
(Aj is aij) is irrelevant (uninformative)
LAZ 3/9/20042828
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
LAZ 3/9/20042929
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
LAZ 3/9/20043030
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 3/9/20043131
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 3/9/20043232
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 3/9/20043333
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 3/9/20043434
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
LAZ 3/9/20043535
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
LAZ 3/9/20043636
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
LAZ 3/9/20043838
•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
LAZ 3/9/20043939
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
LAZ 3/9/20044040
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 rank
rhr+(i-r)hmin have hmax
LAZ 3/9/20044141
CONTINUED
most Swedes are tall is most
average height
constraint propagation
du)u()u(g tallh
hmax
min∫
fraction of tall Swedesdu)u(ugmax
min
h
h∫
du)u()u(g tallh
hmax
min∫ is most
is ? havedu)u(ugmax
min
h
h∫
LAZ 3/9/20044242
CONTINUED
Solution: application of extension principle
)du)u(g(u)((sup)v(μ tallhhmostgh
max
minave ∫=
1du)u(gmax
min
hh =∫
subject to
du)u(ugv max
min
h
h∫=
LAZ 3/9/20044343
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
LAZ 3/9/20044444
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 3/9/20044545
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
LAZ 3/9/20044646
COMPUTATION (version 1)
measurement-basedX = number of black balls
Y2 number of white ballsX 0.7 • 20 = 14X + Y = 20X = 3YX = 15; Y = 5p =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)
LAZ 3/9/20044848
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
LAZ 3/9/20045050
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 3/9/20045151
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 3/9/20045252
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 ⊃⊂=
LAZ 3/9/20045353
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
LAZ 3/9/20045454
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 3/9/20045555
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 3/9/20045656
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
LAZ 3/9/20045757
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 3/9/20045858
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)
LAZ 3/9/20046262
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 3/9/20046363
THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS
Fuzzy Logic Bivalent Logic
protoform
ontology
conceptualgraph
skeleton
Montaguegrammar
LAZ 3/9/20046464
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
usually
about 6 pm
Time (Robert returns from work)
LAZ 3/9/20046565
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 3/9/20046666
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
LAZ 3/9/20046767
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 3/9/20046868
CONTINUED
semantic network representation of E
E*
significant increase price oil
modifier variation attribute
mod var attr
future
near
epoch
mod
E
LAZ 3/9/20046969
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)
variation
significant.increase
near.futureepoch
LAZ 3/9/20047070
CONTINUED
Precisiation (f.b.-concept)
E*: Epoch (Variation (Price (oil)) is significant.increase) is near.future
Price
significant increase
current
presentTime
near.future
Price
LAZ 3/9/20047171
CONTINUED
precisiation of very unlikely
µ
V
likely
10
1
unlikely = ant(likely)
very unlikely = 2ant(likely)
µvery.unlikely (v) = (µlikely (1-v))2
LAZ 3/9/20047272
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
LAZ 3/9/20047373
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
Swedes
height attribute
functional of height attribute
LAZ 3/9/20047474
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 3/9/20047575
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
LAZ 3/9/20047676
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
LAZ 3/9/20047777
EPISTEMIC LEXICON
FORMAT OF RELATIONS
perception-based relation
A1 … Am
G1 Gm
lexine attributes
granular values
Make Price
ford G
chevy
car
example
G: 20*% \ 15k* + 40*% \ [15k*, 25k*] + • • •
granular count
LAZ 3/9/20047878
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)
LAZ 3/9/20047979
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
LAZ 3/9/20048080
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?
LAZ 3/9/20048181
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?
LAZ 3/9/20048282
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)
LAZ 3/9/20048484
PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION
PF-submodule
PF-module
PF-module
knowledge base
LAZ 3/9/20048585
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 3/9/20048787
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)
LAZ 3/9/20048888
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
LAZ 3/9/20048989
PROTOFORMAL (PROTOFORM-BASED) DEDUCTION
precisiation abstraction
Deduction Database
instantiationretranslation
GC(p) PF(p)
PF(q)
p
q
antecedent
proposition
consequent
proposition
LAZ 3/9/20049090
protoformal rule
symbolic part computational part
FORMAT OF PROTOFORMAL DEDUCTION RULES
LAZ 3/9/20049191
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
LAZ 3/9/20049292
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 DEDUCTION
examples
LAZ 3/9/20049393
COUNT-AND MEASURE-RELATED RULES
Q A’s are B’s
ant (Q) A’s are not B’sr0
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
LAZ 3/9/20049494
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
LAZ 3/9/20049595
REASONING WITH PERCEPTIONS: DEDUCTION MODULE
GC-formGC(p)
perceptions
pGC-forms
GC(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
LAZ 3/9/20049696
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
LAZ 3/9/20049797
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
LAZ 3/9/20049898
CONTINUED
Actually, elementary fuzzy logic techniques are used in many search engines
LAZ 3/9/20049999
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)