1. 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]

2. BACKDROP

3. 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

11. 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

12. 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

20. 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)

21. 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

26. 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

28. 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

29. 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

30. 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

35. 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?

36. 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 

40. 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

41. PRECISIATED NATURAL LANGUAGE PNL

44. 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

48. 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 

58. DEDUCTION 1 0 fraction 1 q: How many Swedes are not tall q*: is ? Q solution: 1-most most

59. DEDUCTION q: How many Swedes are short q*: is ? Q solution: is most is ? Q extension principle subject to

60. CONTINUED q: What is the average height of Swedes? q*: is ? Q solution: is most is ? Q extension principle subject to

61. PROTOFORM LANGUAGE PFL

65. THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS Fuzzy Logic Bivalent Logic protoform ontology conceptual graph skeleton Montague grammar

68. 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

71. 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

75. 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

76. 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

82. PROTOFORM EQUIVALENCE options gain c 1 2 a b 0

83. PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION PF-submodule PF-module PF-module knowledge base

84. EXAMPLE module submodule set of cars and their prices

85. PROTOFORM-BASED DEDUCTION

86. 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

89. 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:

91. 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

92. 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:

95. 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)