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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 University of South Florida April 1, 2004 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 University of South Florida April 1, 2004 URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/ Email: Zadeh@cs.berkeley.edu

  2. BACKDROP LAZ 3/9/2004

  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 3/9/2004

  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 • Upgrading a search engine to a question-answering system requires a quantum jump in WIQ LAZ 3/9/2004

  5. 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 3/9/2004

  6. CONTINUED • It is beyond question that, in recent years, very impressive progress has been made through the use of such tools. But, a view which is advanced in the following is that bivalent-logic- based methods have intrinsically limited capability to address complex problems which arise in deduction from information which is pervasively ill-structured, uncertain and imprecise. LAZ 3/9/2004

  7. COMPUTING AND REASONING WITH PERCEPTION-BASED INFORMATION? KEY IDEAS • Perceptions are dealt with not directly but through their descriptions in a natural language • Note: A natural language is a system for describing perceptions • A perception is equated to its descriptor in a natural language LAZ 3/9/2004

  8. CONTINUED • The meaning of a proposition, p, in a natural language, NL, is represented as a generalized constraint X: constrained variable, implicit in p R: constraining relation, implicit in p r: index of modality, defines the modality of the constraint, implicit in p X isr R: Generalized Constraint Form of p, GC(p) representation p X isr R precisiation LAZ 3/9/2004

  9. 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 3/9/2004

  10. 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 3/9/2004

  11. 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 3/9/2004

  12. 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 3/9/2004

  13. TEST QUERY (GOOGLE) • smallest port in Canada: failure Searched the web for smallestportCanada.  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 3/9/2004

  14. 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 3/9/2004

  15. TEST QUERY (GOOGLE) • population of largest city in Spain: failure • largest city in Spain: Madrid, success • population of Madrid: success LAZ 3/9/2004

  16. 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 LAZ 3/9/2004

  17. 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 3/9/2004

  18. 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 3/9/2004

  19. 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 3/9/2004

  20. 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 3/9/2004

  21. 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 3/9/2004

  22. 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 LAZ 3/9/2004

  23. 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 3/9/2004

  24. RELEVANCE, REDUNDANCE AND DELETABILITY DECISION TABLE Aj: j th symptom aij: value of j th symptom of Name D: diagnosis LAZ 3/9/2004

  25. REDUNDANCE DELETABILITY Aj is conditionally redundant for Namer, A, is ar1, An is arn If D is ds for all possible values of Aj in * Aj is redundant if it is conditionally redundant for all values of Name • compactification algorithm (Zadeh, 1976); Quine-McCluskey algorithm LAZ 3/9/2004

  26. RELEVANCE D is ?d if Aj is arj constraint on Aj induces a constraint on D example: (blood pressure is high) constrains D (Aj is arj) is uniformative if D is unconstrained Aj is irrelevant if it Aj is uniformative for all arj irrelevance deletability LAZ 3/9/2004

  27. IRRELEVANCE (UNINFORMATIVENESS) (Aj is aij) is irrelevant (uninformative) LAZ 3/9/2004

  28. EXAMPLE A2 D: black or white 0 A1 A1 and A2 are irrelevant (uninformative) but not deletable A2 D: black or white 0 A1 A2 is redundant (deletable) LAZ 3/9/2004

  29. THE MAJOR OBSTACLE WORLD KNOWLEDGE • Existing methods do not have the capability to operate on world knowledge • To operate on world knowledge, what is needed is the machinery of fuzzy logic and perception-based probability theory LAZ 3/9/2004

  30. 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 3/9/2004

  31. 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 3/9/2004

  32. 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 3/9/2004

  33. 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 3/9/2004

  34. CONTINUED • 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 LAZ 3/9/2004

  35. CONTINUED • perceptions are intrinsically imprecise • imprecision of perceptions is a concomitant of the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information • perceptions are f-granular in the sense that (a) the boundaries of perceived classes are unsharp; and (b) the values of perceived attributes are granular, with a granule being a clump of values drawn together by indistinguishability, similarity, proximity or functionality LAZ 3/9/2004

  36. 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) LAZ 3/9/2004

  37. TEST PROBLEMSMEASUREMENT-BASED VS PERCEPTION-BASED INFORMATION LAZ 3/9/2004

  38. MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION INFORMATION measurement-based numerical perception-based linguistic • 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 LAZ 3/9/2004

  39. 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 THE TALL SWEDES PROBLEM X approximately X LAZ 3/9/2004

  40. 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 upper bound hmax hr lower bound hmin 1 rank rN/100 N rhr+(i-r)hmin  have hmax LAZ 3/9/2004

  41. CONTINUED • most Swedes are tall is most • average height • constraint propagation fraction of tall Swedes is most is ? have LAZ 3/9/2004

  42. CONTINUED • Solution: application of extension principle subject to LAZ 3/9/2004

  43. THE BALLS-IN-BOX PROBLEM 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? LAZ 3/9/2004

  44. 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 3/9/2004

  45. CONTINUED box 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? LAZ 3/9/2004

  46. 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 (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) COMPUTATION (version 1) LAZ 3/9/2004

  47. FUZZY INTEGER PROGRAMMING Y X= most × 20* X+Y= 20* X= several × y x 1 LAZ 3/9/2004

  48. NEW TOOLS computing with numbers computing with words and perceptions + + CWP CN PNL IA precisiated natural language computing with intervals CTP PFT PTp THD PT CTP: computational theory of perceptions PFT: protoform theory PTp: perception-based probability theory THD: theory of hierarchical definability probability theory LAZ 3/9/2004

  49. PRECISIATED NATURAL LANGUAGE PNL LAZ 3/9/2004

  50. 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 3/9/2004

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