>From Computation with Measurements to Computation with Perceptions
--- A Paradigm Shift ---
Speaker :
Lotfi A. Zadeh
Professor in the Graduate School and
Director, Berkeley Initiative in Soft Computing (BISC),
Computer Science Division
University of California, Berkeley
E-mail: zadeh@cs.berkeley.edu
Date: Thursday, September 16th, 1999
Time: 4-5pm
Location : 310 Soda Hall
Abstract
One of the most deep-seated traditions in science has been and continues to
be that of according much more respect to numbers than to words. The essence
of this tradition was stated succinctly by Lord Kelvin in 1883: "I often
say that when you can measure what you are talking about and express it in
numbers, you know something about it; but when you cannot measure it,
when you cannot express it in numbers, your knowledge is of a meagre and
unsatisfactory kind."
In a world that is changing as rapidly as ours, no tradition can have
permanence and no dogma can remain beyond challenge forever. What Lord
Kelvin did not foresee is the advent of the computer age and the ballistic
ascent in the capability of computers to process huge volumes of information
at high speed, low cost and high reliability. Paradoxically, it is this
capability that reverses the direction of inequality in the respectability
of words and numbers. This is the crux of the paradigm shift that is alluded
to in the title of my talk.
It is a truism that the quest for precision has led to brilliant successes.
There is so much that we can do today that even Jules Verne could not have
predicted. We have cellular phones and the Internet; we have eyeprint
identification systems and the GPS; we can clone animals and transplant
organs. But alongside the brilliant successes we see many problem-areas where
progress has been slow and many problems which cannot be solved by any
prolongation of existing theories, methodologies and technologies. A case in
point is the problem of automation of driving in city traffic. This is easy
for humans and an intractable problem for machines.
Driving in city traffic is an example of the remarkable human capability to
perform a wide variety of physical and mental tasks without any measurements
and any computations. Everyday examples of such tasks are parking a car,
playing golf, deciphering sloppy handwriting and summarizing a story.
Underlying this capability is the brain's crucial ability to reason with
perceptions -- perceptions of time, distance, speed, force, direction, shape,
intent, likelihood, truth and other attributes of physical and mental objects.
In science, it is a long-standing tradition to deal with perceptions by
converting them into measurements. But what is becoming increasingly evident
is that, to a much greater extent than is generally recognized, conversion of
perceptions into measurements is infeasible, unrealistic or counter
productive. With the vast computational power at our command, what is becoming
feasible is a countertraditional move from measurements to perceptions. What
this implies is a major enlargement of the role of natural languages in
scientific theories. This is the essence of the paradigm shift which,
in my view, is likely to take place in coming years.
The theory which is put forth in my talk is focused on the development of
what is referred to as the computational theory of perceptions (CTP) -- a
theory which comprises a conceptual framework and a methodology for computing
and reasoning with perceptions. The base for CTP is the methodology of
computing with words (CW). In CW, the objects of computation are words and
propositions drawn from a natural language. A typical problem in CW is the
following. Assume that a function f, Y=f(X), is described in words as:
if X is small then Y is small; if X is medium than Y is large;
if X is large then Y is small, where small, medium and large are labels of
fuzzy sets. The question is: What are the maximum and maximizing values
of Y and X respectively?
The point of departure in the computational theory of perceptions is the
assumption that perceptions are described as propositions in a natural
language, e.g., "Michelle is slim," "it is likely to rain tomorrow,"
"economy is improving," "it is very unlikely that there will be a significant
increase in the price of oil in the near future." In this perspective, natural
languages may be viewed as systems for describing perceptions. Furthermore,
computing and reasoning with perceptions is reduced to computing and
reasoning with words.
To be able to compute with perceptions it is necessary to have a means of
representing their meaning in a way that lends itself to computation.
Conventional approaches to meaning representation cannot serve this purpose
because the intrinsic imprecision of perceptions puts them well beyond the
expressive power of predicate logic and related systems. In the computational
theory of perceptions, meaning representation is based on what is referred
to as constraint-centered semantics of natural languages (CSNL).
A concept which plays a central role in CSNL is that of a generalized
constraint. Conventional constraints are crisp and are expressed as ,
where X is a variable and C is a crisp set. In a generic form, a generalized
unconditional constraint is expressed as X isr R, where X is the constrained
variable; R is the constraining (fuzzy) relation which is called the
generalized value of X; and isr, pronounces as ezar, is a variable copula in
which the value of the discrete variable r defines the way in which R
constrains X. Among the basic types of constraints are the following: equality
constraints (r:=); possibilistic constraints (r:blank); veristic constraints
(r:v); probabilistic constraints (r:p); random set constraints (r:rs);
usuality constraints (r:u); and fuzzy graph constraints (r:fg).
In constraint-centered semantics, a proposition, p, is viewed as an answer
to a question, q, which is implicit in p. The meanings of p and q are
represented as generalized constraints, which play the roles of canonical
forms of p and q, CF(p) and CF(q), respectively. CF(q) is expressed as:
X isr ?R, read as "What is the generalized value of X?" Correspondingly,
CF(p) is expressed as: X isr R, read as "The generalized value of X isr R."
The process of expressing p and q in their canonical forms plays a central
role in constraint-centered semantics and is referred to as explicitation.
Explicitation may be viewed as translation of p and q into expressions in
GCL -- the Generalized Constraint Language.
In the computational theory of perceptions, representation of meaning is a
preliminary to reasoning with perceptions -- a process which starts with a
collection of perceptions which constitute the initial data set (IDS) and
terminates in a proposition or a collection of propositions which play the
role of an answer to a query, that is, the terminal data set (TDS). Canonical
forms of propositions in IDS constitute the initial constraint set (ICS).
The key part of the reasoning process is goal-directed propagation of
generalized constraints from ICS to a terminal constraint set (TCS) which
plays the role of the canonical form of TDS. The rules governing generalized
constraint propagation in the computational theory of perceptions coincide
with the roles of inference in fuzzy logic. The principal generic rules are:
conjunctive rule; disjunctive rule; projective rule; surjective rule;
inversive rule; compositional rule; and the extension principle. The generic
rules are specialized by assigning specific values to the copula variable,
r, in X isr R.
The principal aim of the computational theory of perceptions is the
development of an automated capability to reason with perception-based
information. Existing theories do not have this capability and rely instead
on conversion of perceptions into measurements -- a process which in many
cases is infeasible, unrealistic or counterproductive. In this perspective,
addition of the machinery of the computational theory of perceptions to
existing theories may eventually lead to theories which have a superior
capability to deal with real-world problems and make it possible to conceive
and design systems with a much higher MIQ (Machine IQ) than those we have
today.
**********************************************************************
Please direct questions with regard to the contents of the talk
and request for papers to the speaker.
**********************************************************************
-- --------------------------------------------------------------------------- Frank Hoffmann UC Berkeley Computer Science Division Department of EECS Email: fhoffman@cs.berkeley.edu phone: 1-510-642-8282 URL: http://http.cs.berkeley.edu/~fhoffman fax: 1-510-642-5775 --------------------------------------------------------------------------- If you ever want to remove yourself from this mailing list, you can send mail to <Majordomo@EECS.Berkeley.EDU> with the following command in the body of your email message: unsubscribe bisc-group or from another account, unsubscribe bisc-group <your_email_adress> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Do NOT send unsubscribe requests to bisc-group@cs.berkeley.edu !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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