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Zadeh Bisc2004 Zadeh Bisc2004 Presentation Transcript

  • 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 . edu URL: http://zadeh.cs.berkeley.edu/ Email: [email_address]
  • BACKDROP
  • 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
  • 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
  • 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?
  • 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.
  • COMPUTING AND REASONING WITH PERCEPTION-BASED INFORMATION?
    • 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
  • 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)
    p X isr R representation precisiation
  • 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
  • CONTINUED
    • ?q p = (p 1 , …, p n )
    • 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
  • 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 Google
  • 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 Google
  • 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 ...
  • 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
  • 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
  • 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)
    Google
  • TEST QUERY (GOOGLE)
    • population of largest city in Spain: failure
    • largest city in Spain: Madrid, success
    • population of Madrid: success
  • 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
  • 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
  • DIGRESSION: COINTENSION C human perception of C p(C) definition of C d(C) intension of p(C) intension of d(C) CONCEPT cointension: coincidence of intensions of p(C) and d(C)
  • 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
  • QUERY RELEVANCE
    • Example
    • q: How old is Carol?
    • p 1 : Carol is several years older than Ray
    • p 2 : 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
  • 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
  • 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
  • CONTINUED
    • Problem with relevance
    • q: How old is Ray?
    • p 1 : Ray’s age is about the same as Alan’s
    • p 1 : does not constrain Ray’s age
    • p 2 : Ray is about forty years old
    • p 2 : does not constrain Ray’s age
    • (p 1 , p 2 ) constrains Ray’s age
  • RELEVANCE, REDUNDANCE AND DELETABILITY DECISION TABLE A j : j th symptom a ij : value of j th symptom of Name D: diagnosis d r . d l . d 2 d 1 . d 1 D a mn a mj a m1 Name n . . . . a ln a lj a l1 Name l . . . . a k+1, n a k+1, j a k+1, 1 Name k+1 a kn a kj a k1 Name k . . . . a in a 1j a 11 Name 1 A n A j A 1 Name
  • REDUNDANCE DELETABILITY A j is conditionally redundant for Name r , A, is a r1 , A n is a rn If D is d s for all possible values of A j in * A j is redundant if it is conditionally redundant for all values of Name
    • compactification algorithm (Zadeh, 1976); Quine-McCluskey algorithm
    . d 2 . D . . . . a rn * a r1 Name r . . . . A n A j A 1 Name
  • RELEVANCE A j is irrelevant if it A j is uniformative for all a rj D is ?d if A j is a rj constraint on A j induces a constraint on D example: (blood pressure is high) constrains D (A j is a rj ) is uniformative if D is unconstrained irrelevance deletability
  • IRRELEVANCE (UNINFORMATIVENESS) (A j is a ij ) is irrelevant (uninformative) d 2 . d 2 d 1 . d 1 D . a ij . Name i+s . a ij . Name r A n A j A 1 Name
  • EXAMPLE A 1 and A 2 are irrelevant (uninformative) but not deletable A 2 is redundant (deletable) 0 A 1 A 1 A 2 A 2 0 D: black or white D: black or white
  • 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
  • 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
  • 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)
  • VERA’S AGE
    • q: How old is Vera?
    • p 1 : Vera has a son, in mid-twenties
    • p 2 : Vera has a daughter, in mid-thirties
    • wk: the child-bearing age ranges from about 16 to about 42
    WORLD KNOWLEDGE—THE AGE EXAMPLE
  • CONTINUED 16* 16* 16* 41* 42* 42* 42* 51* 51* 67* 67* 77* range 1 range 2 p 1 : p 2 : (p 1 , p 2 ) 0 0 (p 1 , p 2 ):  a =  ° 51*  ° 67* timelines a*: approximately a How is a* defined?
  • PRECISIATION OF “approximately a,” a* x x x x a a 20 25 p 0 0 1 0 0 1 bimodal distribution  p  fuzzy graph probability distribution interval x 0 a possibility distribution 
    • 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
    • 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
    • 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
  • NEW TOOLS CN IA PNL CW + + computing with numbers computing with intervals precisiated natural language computing with words PTp CTP: computational theory of perceptions PFT: protoform theory PTp: perception-based probability theory THD: theory of hierarchical definability CTP THD PFT probability theory PT
  • PRECISIATED NATURAL LANGUAGE PNL
  • 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
  • PRINCIPAL FUNCTIONS OF PNL
    • perception description language
    • knowledge representation language
    • definition language
    • specification language
    • deduction language
  • 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
  • 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 precisiation
  • 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
  • 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
  • PRECISIATION OF “approximately a,” a* x x x x a a 20 25 p 0 0 1 0 0 1 bimodal distribution  p  fuzzy graph probability distribution interval x 0 a possibility distribution 
  • 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
  • PRECISIATION OF CONCEPTS
    • Relevance
    • Causality
    • Similarity
    • Rationality
    • Optimality
    • Reasonable doubt
  • 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-form GC(p)
  • 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]
  • 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 abstraction X isr R A isr B
  • 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
  • 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
  • CONTINUED
    •  Count(tall.Swedes/Swedes) =
    • constraint on h
    is most
  • CALIBRATION / PRECISIATION most Swedes are tall h: height density function
    • precisiation
    1 0 height  height 1 0 fraction  most 0.5 1 1
    • calibration
    • Frege principal of compositionality
  • DEDUCTION 1 0 fraction 1 q: How many Swedes are not tall q*: is ? Q solution: 1-most most
  • DEDUCTION q: How many Swedes are short q*: is ? Q solution: is most is ? Q extension principle subject to
  • CONTINUED q: What is the average height of Swedes? q*: is ? Q solution: is most is ? Q extension principle subject to
  • PROTOFORM LANGUAGE PFL
  • 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
  • CONTINUED object p object space summarization abstraction protoform protoform space summary of p S(p) A(S(p)) PF(p)
    • PF(p): abstracted summary of p
    • deep structure of p
    • protoform equivalence
    • protoform similarity
  • 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
  • THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS Fuzzy Logic Bivalent Logic protoform ontology conceptual graph skeleton Montague grammar
  • PROTOFORMS
    • 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
    PF-equivalence class object space protoform space
  • EXAMPLES
    • 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 6:15pm
    • Prob{Time(Return(Robert)} is 6:15*} is usually
    • Prob{A(B) is C} is D
    usually 6:15* Return(Robert) Time abstraction instantiation
  • 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 X 0 object Y X 0 i-protoform option 1 option 2 0 1 2 gain
  • 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))
  • 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
  • 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
    • largest port in Canada?
    • second tallest building in San Francisco
    PROTOFORM OF A QUERY X A B ?X is selector (attribute (A/B)) San Francisco buildings height 2 nd tallest
  • 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))
  • ORGANIZATION OF WORLD KNOWLEDGE EPISTEMIC (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 R ii , …, R in
    • entries in R ij are bimodal-distribution-valued attributes of i
    • values of attributes are, in general, granular and context-dependent
    network of nodes and links w ij = granular strength of association between i and j i j r ij K(i) lexine w ij
  • EPISTEMIC LEXICON lexine i lexine j r ij : 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 r ij
  • EPISTEMIC LEXICON FORMAT OF RELATIONS perception-based relation lexine attributes granular values car example G: 20*%  15k* + 40*% [15k*, 25k*] + • • • granular count G m G 1 A m … A 1 G ford chevy Price Make
  • 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)
  • 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
  • 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?
  • 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?
  • 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 t 1
    • if I choose (b), I will arrive in D at time t 2
    • t 1 is earlier than t 2
    • therefore, I should choose (a) ?
    A C B D (a) (b)
  • PROTOFORM EQUIVALENCE options gain c 1 2 a b 0
  • PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION PF-submodule PF-module PF-module knowledge base
  • EXAMPLE module submodule set of cars and their prices
  • PROTOFORM-BASED DEDUCTION
  • PROTOFORM-BASED DEDUCTION p q p* q* NL GCL precisiation p** q** PFL summarization precisiation abstraction answer a r** World Knowledge Module WKM DM deduction module
    • 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 computational (b) extension principle X is A Y = f(X) Y = f(A) symbolic Subject to: computational
  • 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(P[H is A] / P) is Q
    • H ave is C
  • CONTINUED Name H Name 1 h 1 . . . . Name N h n P: Name H µ a Name i h i µ A (h i ) P[H is A]: , subject to:
    • 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: computational symbolic
  • GENERALIZATIONS OF THE EXTENSION PRINCIPLE f(X) is A g(X) is B Subject to: information = constraint on a variable given information about X inferred information about X
  • CONTINUED f(X 1 , …, X n ) is A g(X 1 , …, X n ) is B Subject to: (X 1 , …, X n ) is A g j (X 1 , …, X n ) is Y j , j=1, …, n (Y 1 , …, Y n ) is B Subject to:
  • 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
  • CONTINUED
    • Actually, elementary fuzzy logic techniques are used in many search engines
  • USE OF FUZZY LOGIC* IN SEARCH ENGINES X Excite! Alta Vista X Fast Search Advanced X Northern Light Power No info Google Yahoo X Web Crawler Open Text No info Lycos X Infoseek X HotBot Fuzzy logic in any form Search engine * (currently, only elementary fuzzy logic tools are employed)
  • CONTINUED
    • But what is needed is application of advanced concepts and techniques which are outlined in this presentation