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A New Frontier in Computation—Computation with Information Described in Natural Language Lotfi A. Zadeh Computer Scienc

A New Frontier in Computation—Computation with Information Described in Natural Language Lotfi A. Zadeh Computer Science Division Department of EECS UC Berkeley ISAI Beijing, China August 1, 2006 URL: http://www-bisc.cs.berkeley.edu URL: http://www.cs.berkeley.edu/~zadeh/

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A New Frontier in Computation—Computation with Information Described in Natural Language Lotfi A. Zadeh Computer Scienc

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  1. A New Frontier in Computation—Computation with Information Described in Natural Language Lotfi A. Zadeh Computer Science Division Department of EECSUC Berkeley ISAI Beijing, China August 1, 2006 URL: http://www-bisc.cs.berkeley.edu URL: http://www.cs.berkeley.edu/~zadeh/ Email: Zadeh@eecs.berkeley.edu

  2. PREAMBLE • What is meant by Computation with Information Described in Natural Language, or NL-Computation, for short? • Does NL-Computation constitute a new frontier in computation? • Do existing bivalent-logic-based approaches to natural language processing provide a basis for NL-Computation? • What are the basic concepts and ideas which underlie NL-Computation? • These are some of the issues which are addressed in the following. LAZ 7/28/2006

  3. A HISTORICAL NOTE • NL-Computation is a culmination of my long-standing interest in exploring what I have always believed to be a central issue in fuzzy logic, namely, the relationship between fuzzy logic and natural languages. My principal papers on this theme are the following. LAZ 7/28/2006

  4. TIMELINE • 1971 Quantitave Fuzzy Semantics • 1973, 1975 Lynguistic Variables and Fuzzy-if-then rules • 1978 Theory of Approximate Reasoning • 1978 PRUF-a meaning representation language for natural languages • 1979 Fuzzy Sets and Information Granularity • 1982 Test-score semantics for natural languages and meaning representation via PRUF • 1986 Generalized Constraint • 1996 Fuzzy Logic=Computing with Words • 1999 From computing with numbers to computing with words --from manipulation of measurements to manipulation of perceptions • 2005 Generalized Theory of Uncertainty (GTU) LAZ 7/28/2006

  5. BASIC STRUCTURE OF NL-COMPUTATION Basically, NL-Computation is a system of computation in which the objects of computation are words and propositions drawn from a natural language COMPUTATION PRECISIATION NL Pre1(p) Pren(p) p q information solution reduction ans(q/p) question Pre1(q) Pren(q) final solution reduction to a standard problem bridge from NL to MATH (generalized-constraint-based) (generalized-constraint-based) LAZ 7/28/2006

  6. KEY IDEAS IN NL-COMPUTATION FUNDAMENTAL THESIS • Information = generalized constraint • proposition is a carrier of information MEANING POSTULATE • proposition = generalized constraint • In our approach, NL-Computation is reduced to computation with generalized constraints, that is, to generalized-constraint-based computation. NL-Computation is based on fuzzy logic. NL-Computation is closely related to Computing with Words (CW) LAZ 7/28/2006

  7. FUZZY LOGIC—KEY POINTS • “Fuzzy logic” is not fuzzy logic • Fuzzy logic is a precise logic of imprecision The principal distinguishing features of fuzzy logic are: • In fuzzy logic everything is, or is allowed to be graduated, that is, be a matter of degree or, equivalently fuzzy • In fuzzy logic everything is allowed to be granulated LAZ 7/28/2006

  8. ANALOGY • In bivalent logic, one writes with a ballpoint pen • In fuzzy logic, one writes with a spray pen which has a precisely defined spray pattern • This simple analogy suggests many mathematical problems • What is the maximum value of f? • Precisiation/imprecisiation principle Y X LAZ 7/28/2006

  9. EXAMPLE OF NL-COMPUTATION Trip planning I am planning to drive from Berkeley to Santa Barbara, with stopover for lunch in Monterey. Usually, it takes about two hours to get to Monterey. Usually it takes about one hour to have lunch. It is likely that it will take about six hours to get from Monterey to Santa Barbara. At what time should I leave Berkeley to get to Santa Barbara, with high probability, before about 6 pm? LAZ 7/28/2006

  10. LOOKAHEAD • in NL-Computation, computations are for the most part protoformal, that is, the objects of computation are protoforms (deep structures). example C5=C1+C2+C3+C4 • what we have is partial (granular) information about the Ci which is expressed as a generalized constraint i(Ci)=GC(Ci) example: usually (C2 is about 2 hours) C3 C5 C1 C2 C4 LAZ 7/28/2006

  11. A BASIC CONCEPT IN NL-COMPUTATION: PROTOFORM EQUIVALENCE protoform = abstracted summary surface structure most Swedes are tall most balls are large deep structure Count (G[A is B]/G[A]) is Q protoform LAZ 7/28/2006

  12. A BASIC CONCEPT IN NL-COMPUTATION: INFORMATION GRANULARITY A granular value of X a singular value of X universe of discourse • singular: X is a singleton • granular: X isr A granule • a granule is defined by a generalized constraint example: X: unemployment a: 7.3% A: high LAZ 7/28/2006

  13. ATTRIBUTES OF A GRANULE • Probability measure • Possibility measure • Verity measure • Length • Volume • Entropy LAZ 7/28/2006

  14. PRECISIATION 1 X: time of departure U: travel time from Berkeley to Monterey V: duration of lunch W: travel time from Monterey to Santa Barbara X is a fuzzy variable; U, V, and W are imprecisely described fuzzy random variables *a: approximately a Prob(((?X + U + V + W)  *18)) is high LAZ 7/28/2006

  15. SIMPLIFIED PROBLEM—LOOKAHEAD Problem ? Z=*a + usually(*b) precisiation granular computing X Y : granular values LAZ 7/28/2006

  16. PRECISIATION OF “approximately a,” *a  1 singleton s-precisiation 0 a x  1 cg-precisiation interval 0 a x p probability distribution 0 g-precisiation a x  possibility distribution 0 a x  1 fuzzy graph 0 20 25 LAZ 7/28/2006 x

  17. CONTINUED p bimodal distribution g-precisiation 0 x LAZ 7/28/2006

  18. CONTINUED A A *a is A u B B *b is B u usually usually is C u 0 1 usually (*b) p(v) is usually LAZ 7/28/2006

  19. CONTINUED p(v) p*(v)=p(v-u) v subject to: LAZ 7/28/2006

  20. EXTENSION PRINCIPLE (Zadeh 1965, 1975) Y=f(X) singular values granulation Y*=f*(X*) granular values example f(X) is A g(X) is B B=supu(A(f(u)) subject to v=g(u) LAZ 7/28/2006

  21. MAMDANI Y=f(X) granular f f*: if X is Ai then Y is Bi, i=1, …, n f* is Ii AiBi X is a Y is iAi(a)Bi LAZ 7/28/2006

  22. EXAMPLES OF NL-COMPUTATION Balls-in-box A box contains about twenty balls of various sizes. Most are large. What is the number of small balls? What is the probability that a ball drawn at random is neither small nor large? Temperature Usually the temperature is not very low and not very high. What is the average temperature? Tall Swedes Most Swedes are tall. How many are short? What is the average height of Swedes? Flight delay Usually most United Airlines flights from San Francisco leave on time. What is the probability that my flight will be delayed? LAZ 7/28/2006

  23. CONTINUED Maximization f is a function from reals to reals described as: If X is small then Y is small; if X is medium then Y is large; if X is large then Y is small. What is the maximum of f? Expected value X is a real valued random variable. Usually, X is much larger than approximately a, and much smaller than approximately b, where a and b are real numbers, with a < b. What is the expected value of X? LAZ 7/28/2006

  24. BASIC POINTS • Much of human knowledge is expressed in natural language • A natural language is basically a system for describing perceptions • Perceptions are intrinsically imprecise, reflecting the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information • Imprecision of perceptions is passed on to natural languages, resulting in semantic imprecision • Semantic imprecision of natural languages stands in the way of application of machinery of natural languages processing to computation with information described in natural language LAZ 7/28/2006

  25. NL-CAPABILITY • NL-capability = capability to compute with information described in natural language • Existing scientific theories do not have NL-capability • In particular, probability theory does not have NL-capability LAZ 7/28/2006

  26. THE CONCEPTS OF PRECISIATION AND COINTENSIVE PRECISIATION LAZ 7/28/2006

  27. UNDERSTANDING VS. PRECISIATION • Understanding precedes precisiation • I understand what you said, but can you be more precise • Beyond reasonable doubt • Use with adequate ventilation • Unemployment is high unemployment is over 5% • Where do you draw the line? Paraphrase: The US Constitution is an invitation to argue over where to draw the line • Where to draw the line is a key issue in legal arguments precisiation LAZ 7/28/2006

  28. THE CONCEPT OF -PRECISION / PRECISIATION • In NL-Computation, precision is a concept with many facets. This perception of precisition leads to the concept of -precision/precisiation, where  is an indexical variable whose values are labels of facets of precision •  = v (value) v-precise, v-precisiation v-imprecise, v-imprecisiation •  = m (meaning) m-precise, m-precisiation m-imprecise, m-imprecisiation •  = mh + mm + s + g + gc +bl + fl + … LAZ 7/28/2006

  29. WHAT IS PRECISE? PRECISE v-precise m-precise • precise value • p: X is a Gaussian random variable with mean m and variance 2. m and 2 are precisely defined real numbers • p is v-imprecise and m-precise • p: X is in the interval [a, b]. a and b are precisely defined real numbers • p is v-imprecise and m-precise precise meaning m-precise = mathematically well-defined LAZ 7/28/2006

  30. PRECISIATION AND IMPRECISIATION v-imprecisiation 1 1 0 0 a v-precisiation a x x m-precise m-precise v-precise v-imprecise 1 If X is small then Y is small If X is medium then Y is large If X is large then Y is small v-imprecisiation 0 x v-imprecise v-precise m-imprecise m-precise LAZ 7/28/2006

  31. IMPRECISIATION/ SUMMARIZATION OF FUNCTIONS L If X is small then Y is small If X is medium then Y is large If X is large then Y is small v-imprecisiation M summarization S 0 S M L If X is small then Y is small If X is medium then Y is large If X is large then Y is small (X, Y) is small  small + medium  large + large  small mm-precisiation fuzzy graph LAZ 7/28/2006

  32. SUMMARIZATION OF T-NORMS S M L • To facilitate the chore of an appropriate t-norm, each t-norm should be associated with a summary S M L LAZ 7/28/2006

  33. granule L M S 0 S M L APPROXIMATION VS. SUMMARIZATION • summarization may be viewed as a form of imprecisiation y y approximation 0 0 x x y summarization 0 x LAZ 7/28/2006

  34. V-PRECISIATION A X: variable g-precisiation a X s-precisiation s-precisiation 7.3% unemployment high g-precisiation • s-precisiation is used routinely in scientific theories and especially in probability theory • defuzzification may be viewed as an instance of s-precisiation LAZ 7/28/2006

  35. PRECISIATION/IMPRECISIATION PRINCIPLE (Zadeh 2005) a*: approximately a • simple version f(*a)= *f(a) Y Y X X LAZ 7/28/2006

  36. PRECISE SOLUTION level set undominated LAZ 7/28/2006

  37. THE CONCEPTS OF PRECISIEND AND PRECISIAND precisiend precisiand object of precisiation precisiation result of precisiation variable X X v-precisiand v-precisiation value of X lexeme ℓ concept Pre (ℓ) proposition m-precisiation m-precisiand question command model of meaning LAZ 7/28/2006

  38. MODALITIES OF m-PRECISIATION m-precisiation mh-precisiation mm-precisiation machine-oriented human-oriented m-precisiation ℓ precisiand of ℓ (Pre(ℓ)) LAZ 7/28/2006

  39. PRECISIATION AND DISAMBIGUATION • Examples: • Overeating causes obesity most of those who overeat become obese Count(become.obese/overeat) is most • Obesity is caused by overeating most of those who are obese were overeating Count(were.overeating/obese) is most LAZ 7/28/2006

  40. PRECISIATION/ DISAMBIGUATION P: most tall Swedes P(A) is? POPULATION (Swedes) tall Swedes A P1: most of tall Swedes P2: mostly tall Swedes mh-precisiation P mm-precisiation P1 Count(A/tall.Swedes) is most P2 Count(tall.Swedes/A) is most mm-precisiation LAZ 7/28/2006

  41. BASIC STRUCTURE OF DEFINITIONS definiens definiendum (idea/perception) concept mh-precisiand mm-precisiand mh-precisiation mm-precisiation cointension cointension cointension= wellness of fit of meaning Declining market with expectation of further decline We classify a bear market as a 30 percent decline after 50 days, or a 13 percent decline after 145 days. (Robert Shuster) mh-precisiation bear market mm-precisiation LAZ 7/28/2006

  42. EXAMPLES: MOUNTAIN, CLUSTER, STABILITY mh-precisiation A natural raised part of the earth’s surface, usually rising more or less abruptly, and larger than a hill mountain mm-precisiation ? LAZ 7/28/2006

  43. CONTINUED mh-precisiation A number of things of the same sort gathered together or growing together; bunch cluster mm-precisiation ? • the concepts of mountain and cluster are PF-equivalent, that is, have the same deep structure mh-precisiation The capacity of an object to return to equilibrium after having been displaced stability mm-precisiation Lyapuonov definition mm-precisiation fuzzy stability definition LAZ 7/28/2006

  44. RATIONALE FOR IMPRECISIATIONIMPRECISIATION PRINCIPLE p: X is V X: real-valued variable X: (X1, …, Xn) X: function X: relation … V is v-precise if V is a singleton (singular) v-imprecisiation: singular granular value of X variable LAZ 7/28/2006

  45. v-IMPRECISIATION v-imprecisiation forced: V is not known precisely deliberate: V need not be known precisely v-imprecisiation principle: Precision carries a cost. If there is a tolerance for imprecision, exploit it by employing v-imprecisiation to achieve lower cost, robustness, tractability, decision-relevance and higher level of confidence forced deliberate LAZ 7/28/2006

  46. EXAMPLE: V-IMPRECISIATION v-precise v-imprecise 1 If X is small then Y is small If X is medium then Y is large If X is large then Y is small deliberate 0 x perception forced LAZ 7/28/2006

  47. GRANULATION REVISITED • Granulation is a derivative of v-imprecisiation principle continuous quantized 1, 2, 3, 4, 5, … Age granulated young + middle-aged + old middle-aged µ µ old young 1 1 0 0 Age quantized Age granulated granulation = v-imprecisiation / m-precisiation LAZ 7/28/2006

  48. KEY POINT • Granulation plays a key role in human cognition • In human cognition, v-imprecisiation is followed by mh-precisiation. Granulation is mh-precisiation-based • In fuzzy logic, v-imprecisiation is followed by mm-precisiation. Granulation is mm-precisiation-based • mm-precisiation-based granulation is a major • contribution of fuzzy logic. No other logical • system offers this capability LAZ 7/28/2006

  49. DIGRESSION—EXTENSION VS. INTENSION • extension and intension are concepts drawn from logic and linguistics basic idea object =(name; (attribute1, value1), …, (attribute n, value n)) more compactly object = (name, (attribute, value)) n-ary n-ary name attribute name attribute value object attribute name attribute value LAZ 7/28/2006

  50. OPERATIONS ON OBJECTS function name-based extensional definition object intensional definition attribute-based (algorithmic) object: (Michael, (gender, male), …, (age, 25)) son (Michael) = Ron LAZ 7/28/2006

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