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Web Intelligence, World Knowledge and Fuzzy Logic Lotfi A. Zadeh Computer Science Division

Web Intelligence, World Knowledge and Fuzzy Logic Lotfi A. Zadeh Computer Science Division Department of EECS UC Berkeley November 11, 2004 Santa Clara URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/ Email: Zadeh@cs.berkeley.edu. BACKDROP. PREAMBLE.

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Web Intelligence, World Knowledge and Fuzzy Logic Lotfi A. Zadeh Computer Science Division

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  1. Web Intelligence, World Knowledge and Fuzzy Logic Lotfi A. Zadeh Computer Science Division Department of EECSUC Berkeley November 11, 2004 Santa Clara URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/ Email: Zadeh@cs.berkeley.edu

  2. BACKDROP LAZ 11/2/2004

  3. 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 engines—with Google at the top—fall into this category. In the context of the Web, MIQ becomes Web IQ, or WIQ, for short. LAZ 11/2/2004

  4. WEB INTELLIGENCE (WIQ) • Principal objectives • Improvement of quality of search • Improvement in assessment of relevance • Upgrading a search engine to a question-answering system LAZ 11/2/2004

  5. FROM SEARCH ENGINES TO QUESTION-ANSWERING SYSTEMS • In recent years, substantial progress has been made in improving performance of search engines through the use of the semantic web, ontology-based systems and related approaches. But upgrading a search engine to a question-answering systems requires a quantum jump in WIQ. A basic question which awaits an answer is: Can a search engine be upgraded to a question-answering system through the use of methods based on bivalent logic and bivalent-logic-based probability theory? In the following it is argued that the answer is No. LAZ 11/2/2004

  6. DIGRESSIONQUALITATIVE COMPLEXITY SCALE TASKS, PROBLEMS AND DEFINITIONS hard intractable limit of a particular method or technology class of tasks, problems or definitions difficulty easy tractable LAZ 11/2/2004

  7. EXAMPLES summarization automation of driving a car book Istanbul Rome New York Princeton limit of what is achievable with current technology current performance freeway, light traffic stereotypical document freeway, no traffic LAZ 11/2/2004

  8. 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. This goal is not achievable through the use of existing bivalent-logic-based approaches. The major obstacle is world knowledge. World knowledge cannot be dealt with effectively through the use of existing tools. LAZ 11/2/2004

  9. THE MAJOR OBSTACLE: WORLD KNOWLEDGE • World knowledge is the knowledge which humans acquire through experience, education and communication • World knowledge plays an essential role in search, assessment of relevance, deduction and summarization • Much of world knowledge is perception-based • Perception-based information is intrinsically imprecise • Imprecise of perception is a consequence of (a) the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information; and (b) in general, perceptions, are summaries of observations and experience LAZ 11/2/2004

  10. WORLD KNOWLEDGE • Few professors are rich • Almost all professors have the PhD degree • It is not likely to rain in San Francisco in midsummer • Swedes are tall • Usually Robert returns from work at about 6 pm • There are no mountains in Holland • Usually Princeton means Princeton University • Check out time is 1pm LAZ 11/2/2004

  11. IMPRECISION OF WORLD KNOWLEDGE • Imprecision of world knowledge cannot be dealt with through prolongation of methods based on bivalent logic and bivalent-logic-based probability theory. What is needed is a change in course—a change which amounts to abandonment of bivalence and adoption of new tools drawn from fuzzy logic LAZ 11/2/2004

  12. FROM STATISTICAL TO GRANULAR • Abandonment of bivalence entails an abandonment of the traditional view that information and uncertainty are statistical in nature • Instead, a more general view which is adopted that information and uncertainty are, or are allowed to be, granular • Informally, a granule is a clump of points drawn together by indistinguishability, equivalence, similarity, proximity or functionality • More precisely, a granule is defined by a generalized constraint. The concept of a generalized constraint is the centerpiece of the new tools granule LAZ 11/2/2004

  13. NEW TOOLS computing with numbers computing with words + + CW CN PNL IA precisiated natural language computing with intervals CTP PFT UTU THD PT CTP: computational theory of perceptions PFT: protoform theory PTp: perception-based probability theory THD: theory of hierarchical definability UTU: Unified Theory of uncertainty PTp probability theory LAZ 11/2/2004

  14. THE CENTERPIECE OF NEW TOOLS IS THE CONCEPT OF A GENERALIZED CONSTRAINT (ZADEH 1986) LAZ 11/2/2004

  15. GENERALIZED CONSTRAINT (Zadeh 1986) • Bivalent constraint (hard, inelastic, categorical:) X  C constraining bivalent relation • Generalized constraint: X isr R constraining non-bivalent (fuzzy) relation index of modality 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) r:  | = |  |  |  | … | blank | p | v | u | rs | fg | ps |… bivalent non-bivalent (fuzzy) LAZ 11/2/2004

  16. SIMPLE EXAMPLES • “Check-out time is 1 pm,” is a generalized constraint on check-out time • “Speed limit is 100km/h” is a generalized constraint on speed • “Vera is a divorce with two young children,” is a generalized constraint on Vera’s age LAZ 11/2/2004

  17. GENERALIZED CONSTRAINT—MODALITY r X isr R r: = equality constraint: X=R is abbreviation of X is=R r: ≤ inequality constraint: X ≤ R r: subsethood constraint: X  R r: blank possibilistic constraint; X is R; R is the possibility distribution of X r: v veristic constraint; X isv R; R is the verity distribution of X r: p probabilistic constraint; X isp R; R is the probability distribution of X LAZ 11/2/2004

  18. 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 11/2/2004

  19. CONSTRAINT QUALIFICATION • p isr R means r value of p is R in particular p isp R Prob(p) is R (probability qualification) p isv R Tr(p) is R (truth (verity) qualification) p is R Poss(p) is R (possibility qualification) examples (X is small) isp likely (X is small) is likely (X is small) isv very true ( X is small) is very true (X isu R) Prob(X is R) is usually LAZ 11/2/2004

  20. GENERALIZED CONSTRAINT LANGUAGE (GCL) • GCL is an abstract language • GCL is generated by combination, qualification and propagation of generalized constraints • 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 A then Y is B • the language of fuzzy if-then rules is a sublanguage of GCL • deduction= generalized constraint propagation LAZ 11/2/2004

  21. EXAMPLE OF DEDUCTION • compositional rule of inference in FL X is A (X,Y) is B Y is A°B • = min (t-norm) • = max (t-conorm) LAZ 11/2/2004

  22. THE CONCEPT OF PRECISIATION LAZ 11/2/2004

  23. PRECISIATION = TRANSLATION INTO GCL NL GCL p p* precisiation 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] GC-form GC(p) translation LAZ 11/2/2004

  24. PRECISIATION s-precisiation g-precisiation • conventional (degranulation) • * a a • approximately a GCL-based (granulation) precisiation *a precisiation X isr R p proposition GC-form common practice in probability theory LAZ 11/2/2004

  25. PRECISIATION OF “approximately a,” *a  1 singleton s-precisiation 0 a x  1 interval 0 a x p probability distribution 0 g-precisiation a x  possibility distribution 0 a x  1 fuzzy graph 0 20 25 LAZ 11/2/2004 x

  26. CONTINUED p bimodal distribution g-precisiation GCL-based (maximal generality) 0 x precisiation *a X isr R GC-form LAZ 11/2/2004

  27. COMPUTATIONAL THEORY OF PERCEPTIONS (CTP) LAZ 11/2/2004

  28. KEY IDEAS • Perceptions play a key role in human cognition • Humans have a remarkable capability to perform a wide variety of physical and mental tasks using perceptions, without any measurements and any computations. CTP is aimed at automation of this capability • In CTP, 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 LAZ 11/2/2004

  29. THE BALLS-IN-BOX PROBLEM Version 1. Measurement-based A flat box contains a layer of black and white balls. You can see the balls and are allowed as much time as you need to count them • q1: What is the number of white balls? • q2: What is the probability that a ball drawn at random is white? • q1 and q2 remain the same in the next version LAZ 11/2/2004

  30. CONTINUED Version 2. Perception-based You are allowed n seconds to look at the box. n seconds is not enough to allow you to count the balls You describe your perceptions in a natural language p1: there are about 20 balls p2: most are black p3: there are several times as many black balls as white balls PT’s solution? LAZ 11/2/2004

  31. CONTINUED Version 3. Measurement-based The balls have the same color but different sizes You are allowed as much time as you need to count the balls q1: How many balls are large? q2: What is the probability that a ball drawn at random is large PT’s solution? LAZ 11/2/2004

  32. CONTINUED Version 4. Perception-based You are allowed n seconds to look at the box. n seconds is not enough to allow you to count the balls Your perceptions are: p1: there are about 20 balls p2: most are small p3: there are several times as many small balls as large balls q1: how many are large? q2: what is the probability that a ball drawn at random is large? LAZ 11/2/2004

  33. CONTINUED Version 5. Perception-based My perceptions are: p1: there are about 20 balls p2: most are large p3: if a ball is large then it is likely to be heavy q1: how many are heavy? q2: what is the probability that a ball drawn at random is not heavy? LAZ 11/2/2004

  34. A SERIOUS LIMITATION OF PT • Version 4 points to a serious short coming of PT • In PT there is no concept of cardinality of a fuzzy set • How many large balls are in the box? 0.6 0.8 0.4 0.9 0.9 0.5 • There is no underlying randomness LAZ 11/2/2004

  35. a box contains 20 black and white balls over seventy percent 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 picked at random is white? 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? MEASUREMENT-BASED PERCEPTION-BASED version 2 LAZ 11/2/2004

  36. measurement-based X = number of black balls Y2 number of white balls X  0.7 • 20 = 14 X + Y = 20 X = 3Y X = 15 ; Y = 5 p =5/20 = .25 perception-based X = number of black balls Y = number of white balls X = most × 20* X = several *Y X + Y = 20* P = Y/N COMPUTATION (version 2) LAZ 11/2/2004

  37. FUZZY INTEGER PROGRAMMING Y X= most × 20* X+Y= 20* X= several × y x 1 LAZ 11/2/2004

  38. RELEVANCE LAZ 11/2/2004

  39. 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 11/2/2004

  40. RELEVANCE KEY POINTS • The concept of relevance has a position of centrality in search and question-answering • And yet, there is no operational definition of relevance • Relevance is not a bivalent concept; relevance is a matter of degree • 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 11/2/2004

  41. 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 • Existing bivalent-logic-based search engines do not perform well in assessment of relevance LAZ 11/2/2004

  42. TEST QUERY NUMBER OF CARS IN CALIFORNIA Google  Web Results 1 - 10 of about 2,950,000 forNumberofcarsinCalifornia. (0.75 seconds) A Student's Guide to Alternative Fuel Vehicles - Hydrogen The Energy Story - Chapter 18: Energy for Transportation Electric Cars for California California Car Rentals - Cheap Rental Cars in California Lawmakers look to drive out car-title loans LAZ 11/2/2004

  43. 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 ... LAZ 11/2/2004

  44. TEST QUERY (GOOGLE) • largest port in Switzerland: failure Searched the web for largestportSwitzerland.  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 11/2/2004

  45. 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 11/2/2004

  46. TEST QUERY (GOOGLE) • population of largest city in Spain: failure • largest city in Spain: Madrid, success • population of Madrid: success LAZ 11/2/2004

  47. 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 11/2/2004

  48. FUZZY CONCEPTS • Relevance • Causality • Summary • Cluster • Mountain • Valley • In the existing literature, there are no operational definitions of these concepts LAZ 11/2/2004

  49. 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) LAZ 11/2/2004

  50. 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 11/2/2004

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