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ZadehTalk

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Published on October 18, 2007

Author: Abbott

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Slide1:  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 Slide3:  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):  WEB INTELLIGENCE (WIQ) Principal objectives Improvement of quality of search Improvement in assessment of relevance Upgrading a search engine to a question-answering system FROM SEARCH ENGINES TO QUESTION-ANSWERING SYSTEMS:  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. DIGRESSION QUALITATIVE COMPLEXITY SCALE TASKS, PROBLEMS AND DEFINITIONS:  DIGRESSION QUALITATIVE COMPLEXITY SCALE TASKS, PROBLEMS AND DEFINITIONS limit of a particular method or technology class of tasks, problems or definitions difficulty easy hard intractable tractable EXAMPLES:  EXAMPLES summarization automation of driving a car book stereotypical document Istanbul New York limit of what is achievable with current technology freeway, light traffic freeway, no traffic Rome Princeton current performance HISTORICAL NOTE:  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. THE MAJOR OBSTACLE: WORLD KNOWLEDGE:  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 WORLD KNOWLEDGE:  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 IMPRECISION OF WORLD KNOWLEDGE:  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 FROM STATISTICAL TO GRANULAR:  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 Slide13:  NEW TOOLS CN IA PNL CW + + computing with numbers computing with intervals precisiated natural language computing with words UTU CTP: computational theory of perceptions PFT: protoform theory PTp: perception-based probability theory THD: theory of hierarchical definability UTU: Unified Theory of uncertainty CTP THD PFT probability theory PT PTp THE CENTERPIECE OF NEW TOOLS IS THE CONCEPT OF A GENERALIZED CONSTRAINT (ZADEH 1986):  THE CENTERPIECE OF NEW TOOLS IS THE CONCEPT OF A GENERALIZED CONSTRAINT (ZADEH 1986) Slide15:  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) GENERALIZED CONSTRAINT (Zadeh 1986) Bivalent constraint (hard, inelastic, categorical:) X  C constraining bivalent relation X isr R constraining non-bivalent (fuzzy) relation index of modality constrained variable Generalized constraint: r:  | = |  |  |  | … | blank | p | v | u | rs | fg | ps |… bivalent non-bivalent (fuzzy) SIMPLE EXAMPLES:  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 Slide17:  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 Slide18:  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 CONSTRAINT QUALIFICATION:  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 GENERALIZED CONSTRAINT LANGUAGE (GCL):  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 EXAMPLE OF DEDUCTION:  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) PRECISIATION = TRANSLATION INTO GCL:  PRECISIATION = TRANSLATION INTO GCL 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] p p* NL GCL precisiation translation GC-form GC(p) Slide24:  conventional (degranulation) * a a approximately a GCL-based (granulation) PRECISIATION s-precisiation g-precisiation precisiation precisiation X isr R p GC-form proposition common practice in probability theory *a PRECISIATION OF “approximately a,” *a:  PRECISIATION OF “approximately a,” *a x x x a a 20 25 0 1 0 0 1 p  fuzzy graph probability distribution interval x 0 a possibility distribution  x a 0 1   s-precisiation singleton g-precisiation CONTINUED:  CONTINUED x p 0 bimodal distribution GCL-based (maximal generality) precisiation X isr R GC-form *a g-precisiation Slide28:  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 KEY IDEAS Slide29:  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 THE BALLS-IN-BOX PROBLEM CONTINUED:  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? CONTINUED:  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? CONTINUED:  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? CONTINUED:  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? A SERIOUS LIMITATION OF PT:  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? 0.5 There is no underlying randomness 0.9 0.8 0.6 0.9 0.4 MEASUREMENT-BASED:  MEASUREMENT-BASED 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? PERCEPTION-BASED version 2 COMPUTATION (version 2):  COMPUTATION (version 2) 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 FUZZY INTEGER PROGRAMMING:  FUZZY INTEGER PROGRAMMING x Y 1 X= several × y X= most × 20* X+Y= 20* RELEVANCE:  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 RELEVANCE:  RELEVANCE 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 KEY POINTS CONTINUED:  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 TEST QUERY:  TEST QUERY NUMBER OF CARS IN CALIFORNIA Google  Web Results 1 - 10 of about 2,950,000 for Number of cars in California. (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 TEST QUERY:  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):  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 :  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):  TEST QUERY (GOOGLE) population of largest city in Spain: failure largest city in Spain: Madrid, success population of Madrid: success RELEVANCE:  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 FUZZY CONCEPTS:  FUZZY CONCEPTS Relevance Causality Summary Cluster Mountain Valley In the existing literature, there are no operational definitions of these concepts DIGRESSION: COINTENSION:  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) QUERY RELEVANCE:  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 PTp—BASED SOLUTION:  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:  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:  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 RELEVANCE AND i-RELEVANCE:  RELEVANCE AND i-RELEVANCE p is i-relevant to q if p is relevant to q in isolation P is i-irrelevant to q if p is irrelevant in isolation RELEVANCE, REDUNDANCE AND DELETABILITY:  RELEVANCE, REDUNDANCE AND DELETABILITY DECISION TABLE Aj: j th symptom aij: value of j th symptom of Name D: diagnosis REDUNDANCE DELETABILITY:  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 RELEVANCE:  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 D example: (blood pressure is high) constrains D (Aj is arj) is uniformative if D is unconstrained irrelevance deletability IRRELEVANCE (UNINFORMATIVENESS):  IRRELEVANCE (UNINFORMATIVENESS) (Aj is aij) is irrelevant (uninformative) EXAMPLE:  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 RELEVANCE AND WORLD KNOWLEDGE:  RELEVANCE AND WORLD KNOWLEDGE Assessment of relevance is an intrinsically complex problem. To deal with this problem what is needed is a better understanding of issues related to representation of, and inference from world knowledge 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 VERA’S AGE:  VERA’S AGE q: How old is Vera? p1: Vera has a son, in mid-twenties p2: 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:  CONTINUED 16* 16* 16* 41* 42* 42* 42* 51* 51* 67* 67* 77* range 1 range 2 p1: p2: (p1, p2) 0 0 (p1, p2): a=  ° 51*  ° 67* timelines a*: approximately a How is a* defined? Slide65:  WORLD KNOWLEDGE AND PRECISIATED NATURAL LANGUAGE WHAT IS 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:  PRINCIPAL FUNCTIONS OF PNL perception description language knowledge representation language definition language specification language deduction language Slide68:  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:  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:  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:  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 NEED FOR PRECISIATION:  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:  PRECISIATION OF CONCEPTS Relevance Causality Similarity Rationality Optimality Reasonable doubt PRECISIATION OF PROPOSITIONS:  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:  CONTINUED Count(tall.Swedes/Swedes) = constraint on h is most CALIBRATION / PRECISIATION:  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:  DEDUCTION 1 0 fraction 1 q: How many Swedes are not tall q*: is ? Q solution: 1-most most DEDUCTION:  DEDUCTION q: How many Swedes are short q*: is ? Q solution: is most is ? Q extension principle subject to CONTINUED:  CONTINUED q: What is the average height of Swedes? q*: is ? Q solution: is most is ? Q extension principle subject to Slide80:  PROTOFORM LANGUAGE THE CONCEPT OF A PROTOFORM:  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:  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?:  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:  THE CONCEPT OF PROTOFORM AND RELATED CONCEPTS Fuzzy Logic Bivalent Logic protoform ontology conceptual graph skeleton Montague grammar PROTOFORMS:  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:  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:  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:  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:  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:  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 Slide91:  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 2nd tallest PROTOFORMAL SEARCH RULES:  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):  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 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 j rij K(i) lexine wij EPISTEMIC LEXICON:  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 i i causes j (or usually) i and j are related rij EPISTEMIC LEXICON:  EPISTEMIC LEXICON FORMAT OF RELATIONS perception-based relation lexine attributes granular values car example G: 20*% \  15k* + 40*% \ [15k*, 25k*] + • • • granular count PROTOFORM OF A DECISION PROBLEM:  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:  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:  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:  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:  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) PROTOFORM EQUIVALENCE:  PROTOFORM EQUIVALENCE options gain c 1 2 a b 0 PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION:  PROTOFORM-CENTERED KNOWLEDGE ORGANIZATION PF-submodule PF-module PF-module knowledge base EXAMPLE:  EXAMPLE module submodule set of cars and their prices PROTOFORMAL DEDUCTION:  PROTOFORMAL DEDUCTION p q p* q* NL GCL precisiation p** q** PFL summarization precisiation abstraction answer a r** World Knowledge Module WKM DM deduction module Slide106:  Rules of deduction in the Deduction Database (DDB) are protoformal examples: (a) compositional rule of inference 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 Slide107:  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 Slide108:  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 Slide109:  CONTINUED f(X1, …, Xn) is A g(X1, …, Xn) is B Subject to: (X1, …, Xn) is A gj(X1, …, Xn) is Yj , j=1, …, n (Y1, …, Yn) is B Subject to: SUMMATION:  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 KEY POINT—THE ROLE OF FUZZY LOGIC:  KEY POINT—THE ROLE OF FUZZY LOGIC Existing approaches to the enhancement of web intelligence are based on classical, Aristotelian, bivalent logic and bivalent-logic-based probability theory. In our approach, bivalence is abandoned. What is employed instead is fuzzy logic—a logical system which subsumes bivalent logic as a special case. More specifically: Slide113:  In bivalent logic, BL, truth is bivalent, implying that every proposition, p, is either true or false, with no degrees of truth allowed In multivalent logic, ML, truth is a matter of degree In fuzzy logic, FL: everything is, or is allowed to be, to be partial, i.e., a matter of degree everything is, or is allowed to be, imprecise (approximate) everything is, or is allowed to be, granular (linguistic) everything is, or is allowed to be, perception based CONTINUED:  CONTINUED The generality of fuzzy logic is needed to cope with the great complexity of problems related to search and question-answering in the context of world knowledge; to deal computationally with perception-based information and natural languages; and to provide a foundation for management of uncertainty and decision analysis in realistic settings Slide115:  Feb. 24, 2004 Factual Information About the Impact of Fuzzy Logic    PATENTS Number of fuzzy-logic-related patents applied for in Japan: 17,740 Number of fuzzy-logic-related patents issued in Japan:  4,801 Number of fuzzy-logic-related patents issued in the US: around 1,700 Slide116:  PUBLICATIONS   Count of papers containing the word “fuzzy” in title, as cited in INSPEC and MATH.SCI.NET databases. (Data for 2002 are not complete) Compiled by Camille Wanat, Head, Engineering Library, UC Berkeley, November 20, 2003   Number of papers in INSPEC and MathSciNet which have "fuzzy" in their titles:   INSPEC - "fuzzy" in the title 1970-1979: 569 1980-1989: 2,404 1990-1999: 23,207 2000-present: 9,945 Total: 36,125   MathSciNet - "fuzzy" in the title 1970-1979: 443 1980-1989: 2,465 1990-1999: 5,479 2000-present: 2,865 Total: 11,252 Slide117:  JOURNALS (“fuzzy” or “soft computing” in title)   Fuzzy Sets and Systems IEEE Transactions on Fuzzy Systems Fuzzy Optimization and Decision Making Journal of Intelligent & Fuzzy Systems Fuzzy Economic Review International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Journal of Japan Society for Fuzzy Theory and Systems International Journal of Fuzzy Systems Soft Computing International Journal of Approximate Reasoning--Soft Computing in Recognition and Search Intelligent Automation and Soft Computing Journal of Multiple-Valued Logic and Soft Computing Mathware and Soft Computing Biomedical Soft Computing and Human Sciences Applied Soft Computing Slide118:  APPLICATIONS The range of application-areas of fuzzy logic is too wide for exhaustive listing. Following is a partial list of existing application-areas in which there is a record of substantial activity. Industrial control Quality control Elevator control and scheduling Train control Traffic control Loading crane control Reactor control Automobile transmissions Automobile climate control Automobile body painting control Automobile engine control Paper manufacturing Steel manufacturing Power distribution control Software engineerinf Expert systems Operation research Decision analysis Financial engineering Assessment of credit-worthiness Fraud detection Mine detection Pattern classification Oil exploration Geology Civil Engineering Chemistry Mathematics Medicine Biomedical instrumentation Health-care products Economics Social Sciences Internet Library and Information Science Slide119:  Product Information Addendum 1   This addendum relates to information about products which employ fuzzy logic singly or in combination. The information which is presented came from SIEMENS and OMRON. It is fragmentary and far from complete. Such addenda will be sent to the Group from time to time. SIEMENS:     * washing machines, 2 million units sold     * fuzzy guidance for navigation systems (Opel, Porsche)     * OCS: Occupant Classification System (to determine, if a place in a car is occupied by a person or something else; to control the airbag as well as the intensity of the airbag). Here FL is used in the product as well as in the design process (optimization of parameters). * fuzzy automobile transmission (Porsche, Peugeot, Hyundai)   OMRON:     * fuzzy logic blood pressure meter, 7.4 million units sold, approximate retail value $740 million dollars Note: If you have any information about products and or manufacturing which may be of relevance please communicate it to Dr. Vesa Niskanen vesa.a.niskanen@helsinki.fi and Masoud Nikravesh Nikravesh@cs.berkeley.edu . Slide120:  Product Information Addendum 2 This addendum relates to information about products which employ fuzzy logic singly or in combination. The information which is presented came from Professor Hideyuki Takagi, Kyushu University, Fukuoka, Japan. Professor Takagi is the co-inventor of neurofuzzy systems. Such addenda will be sent to the Group from time to time.   Facts on FL-based systems in Japan (as of 2/06/2004) 1. Sony's FL camcorders Total amount of camcorder production of all companies in 1995-1998 times Sony's market share is the following. Fuzzy logic is used in all Sony's camcorders at least in these four years, i.e. total production of Sony's FL-based camcorders is 2.4 millions products in these four years.      1,228K units X 49% in 1995      1,315K units X 52% in 1996      1,381K units X 50% in 1997      1,416K units X 51% in 1998 2. FL control at Idemitsu oil factories Fuzzy logic control is running at more than 10 places at 4 oil factories of Idemitsu Kosan Co. Ltd including not only pure FL control but also the combination of FL and conventional control. They estimate that the effect of their FL control is more than 200 million YEN per year and it saves more than 4,000 hours per year. Slide121:  3. Canon Canon used (uses) FL in their cameras, camcorders, copy machine, and stepper alignment equipment for semiconductor production. But, they have a rule not to announce their production and sales data to public. Canon holds 31 and 31 established FL patents in Japan and US, respectively. 4. Minolta cameras Minolta has a rule not to announce their production and sales data to public, too. whose name in US market was Maxxum 7xi. It used six FL systems in a camera and was put on the market in 1991 with 98,000 YEN (body price without lenses). It was produced 30,000 per month in 1991. Its sister cameras, alpha-9xi, alpha-5xi, and their successors used FL systems, too. But, total number of production is confidential. Slide122:  5. FL plant controllers of Yamatake Corporation Yamatake-Honeywell (Yamatake's former name) put FUZZICS, fuzzy software package for plant operation, on the market in 1992. It has been used at the plants of oil, oil chemical, chemical, pulp, and other industries where it is hard for conventional PID controllers to describe the plan process for these more than 10 years. They planed to sell the FUZZICS 20 - 30 per year and total 200 million YEN. As this software runs on Yamatake's own control systems, the software package itself is not expensive comparative to the hardware control systems. 6. Others Names of 225 FL systems and products picked up from news articles in 1987 - 1996 are listed at http://www.adwin.com/elec/fuzzy/note_10.html in Japanese.) Note: If you have any information about products and or manufacturing which may be of relevance please communicate it to Dr. Vesa Niskanen vesa.a.niskanen@helsinki.fi and Masoud Nikravesh Nikravesh@cs.berkeley.edu , with cc to me. WORLD KNOWLEDGE:  WORLD KNOWLEDGE There is an extensive literature on world knowledge. But there are two key aspects of world knowledge which are not addressed in the literature Much of world knowledge is perception-based Icy roads are slippery Usually it does not rain in San Francisco in midsummer Most concepts are fuzzy rather than bivalent, i.e., most concepts are a matter of degree rather than categorical EXAMPLES:  EXAMPLES causality Information retrieval economic physical question-answering search

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