no title

Michelle T. Lin (
Wed, 14 Oct 1998 00:35:42 +0200 (MET DST)

To: BISC Group <bisc-group@cs>
From: L. A. Zadeh <zadeh@cs>

For your information, following is my response to some of the
comments made about AI.

Warm regards,

Lotfi Zadeh


From: L. A. Zadeh <>

Following is my response to the questions raised by John
McCarthy, John Sowa and Chuck Thorpe. My response is late because I
was away on travel.

I believe that the real challenge to AI is to come up with
solutions to problems which are solved routinely by humans without any
measurements and any computations.

A good example of problems of this type is the problem of
automation of parking and driving a car.

Parking a car, even in a tight spot, is easy for humans but
quite difficult for machines. The problem of exiting from a tight
spot is, for humans, easier than that of parking. For machines the
reverse is true because the goal state is harder to describe.

The problem of exiting from a valet-serviced garage in which
the cars are tightly parked -- but there is a way of exiting without
moving other cars -- is, in my view, an order of magnitude more complex
than that of parallel parking. The reason is that in the case of a
valet-serviced garage the state space is much more complex. When
other cars have to be moved, the problem of exiting becomes much more
difficult for machines to solve. In my view, the problem of exiting
from a valet-serviced garage is, today, beyond the capability of any
AI system even if no cars have to be moved.

Turning to the automation of driving, let us consider a range
of problems such as: (1) freeway driving with no traffic; (2) freeway
driving with light traffic; (3) freeway driving with moderate traffic;
(4) freeway driving with heavy traffic; (5) city driving in Helsinki;
(6) city driving in London; (7) city driving in Rome; (8) city driving
in Istanbul.

We know that automation of (1) is achievable. Beyond (1), (2)
might be possible, with some qualifications. (3) is not possible
today but might be in the future. Beyond (3), the problems are
intractable, with no solution in sight. Would anybody claim that the
problem of automation of driving in Istanbul can be solved today or in
foreseeable future?

Turning to summarization, in my view the ability to summarize
is a acid test of knowledge and understanding. Clearly, machine
summarization is orders of magnitude more complea than machine
translation. For AI, it is the ultimate challenge.

The first obstacle on the way to solution is that we do not
know how to define what is a summary. Second, summarization cannot be
carried out by chunking into sentences, as translation can be. Third,
summarization is end-use and length dependent. But more importantly,
summarization requires both local and global understanding whereas
translation requires, for the most part, only local understanding.

The above does not mean that we cannot come up with special
purpose, restricted-use summarization programs. We have done so
already in some cases and will be able to do better in the future.
But the ability to construct general purpose summarization programs
which can come close to human ability to summarize is not in sight. It is
understood that summarization by omission is not acceptable.

I am not familiar with how Microsoft's AutoSummarize program --
mentioned by John McCarthy -- works, but I would not have difficulty in
devising a test that it would flunk badly. Here is an easy one.

The following is a short story I picked more or less at random
from the SF Chronicle. It carries an 8-word headline that is not
shown. Would Microsoft program come up with an approximation to this

A rocket exploded just yards from a convoy carrying Cambodian
leader Hun Sen today, killing four people - including two children -
but leaving Hun Sen uninjured. An aide called it an assassination
attempt. Three other people were injured by the explosion, which
occurred as Hun Sen was en route to the king's residence in the
north-western town of Siem Reap for the beginning of ceremonies to
swear in a new parliament. The swearing-in proceeded as scheduled.
Hun Sen looked unperturbed after arriving at the residence of King
Norodon Sihanouk, who spoke to the 122 lawmakers before they headed to
the famous 12th century temple Angkor Wat for the ceremonies. Colonel
Than Chay, local deputy police commander, said the lead vehicles of
Hun Sen's security detail had already passed by and the car carrying
Hun Sen was less than 10 yards away when the explosion occurred.
Police said three more unexploded rockets were found at the side of
the road.

Turning to fuzzy logic (FL) and GCL (Generalized Constraint
Language), there is a common misconception about fuzzy logic that has
to be clarified first.

Fuzzy logic is more than a logical system. It has four
principal facets: the logical facet, FL/L; the set-theoretic facet,
FLIS; the relational facet, FL/R; and the epistemic facet, FL/E. When
fuzzy logic is viewed as a logical system, it should be understood
that we are talking about FL/L. But what should be recognized is that
at this juncture most of the applications of fuzzy logic relate to
FL/R. FL/R is concerned in the main with manipulation of imprecise
dependencies. In manipulation of imprecise dependencies, the principal
tools are the concepts of a linguistic variable, fuzzy rule sets and
fuzzy graphs. These concepts are absent in standard logical systems.

So far as FL/L is concerned, it is a generalization od
predicate logic and is in no way in conflict with it. What it adds to
predicate logic is a much higher expressive power which is associated
with GCL. To say that anything that can be done with FL/L can be done
without it is not correct.

Here is a very simple example. Let us consider the classical
syllogism: all men are mortal; Socrates is a man; therefore Socrates
is mortal, and generalize it to: most young men are healthy; Charles
is a young man; therefore it is likely that Charles is healthy. How
would predicate logic handle this very simple example of commonsense
reasoning? How would it handle a slightly more complicated case in
which the second premise is: it is likely that Charles is a young
man. For those who might be interested in pursuing it further, I am
including an abstract of my talk "What is Fuzzy Logic? What are its


What is Fuzzy Logic? What are its Applications?

Lotfi A. Zadeh

Applications of fuzzy logic are growing rapidly in number,
variety and visibility. And yet there are many misconceptions about
what fuzzy logic is and a lack of understanding of the nature of its
applications. There are the issues that are addressed in my talk.

What is fuzzy logic? This question does not have a simple
answer because fuzzy logic, or FL for short, has many distinct facets
-- facets which overlap and have unsharp boundaries.

To a first approximation, fuzzy logic is a body of concepts,
constructs and techniques which relate to modes of reasoning which are
approximate rather than exact. Much -- perhaps most -- of human
reasoning is approximate in nature. In this perspective, the role
model for fuzzy logic is the human mind. By contrast, classical logic
is normative in spirit in the sense that it is aimed at serving as a
role model for human reasoning rather than having the human mind as
its role model. Fundamentally, however, fuzzy logic is a
generalization of classical logic and rests on the same foundations.

Among the many facets of fuzzy logic there are four that stand
out in importance. They are: (i) the logical facet, FL/L; (ii) the
set-theoretic facet, FL/S; (iii) the relational facet, FL/R; and (iv)
the epistemic facet, FL/E.

The logical facet of FL, FL/L, is a logical system or, more
accurately, a collection of logical systems which includes as a
special case both two-valued and multiple-valued systems. As in any
logical system, at the core of the logical facet of FL lies a system
of rules of inference. In FL/L, however, the rules of inference play
the role of rules which govern propagation of various types of fuzzy
constraints. Concomitantly, a proposition, p, is viewed as a fuzzy
constraint on an explicitly or implicitly defined variable. The
logical facet of FL plays a pivotal role in the applications of FL to
knowledge representation and to inference from information which is
imprecise, incomplete, uncertain or partially true.

The set-theoretic facet of FL, FL/S, is concerned with classes
or sets whose boundaries are not sharply defined. The initial
development of FL was focused on this facet. Most of the applications
of FL in mathematics have been and continue to be related to the
set-theoretic facet. Among examples of such applications are: fuzzy
topology, fuzzy groups, fuzzy differential equations and fuzzy

The relational facet of FL, FL/R, is concerned in the main
with representation and manipulation of imprecisely defined functions
and relations. It is this facet of FL that plays a pivotal role in
its applications to systems analysis and control. The three basic
concepts that lie at the core of this facet of FL are those of a
linguistic variable, fuzzy if-then rule and fuzzy graph. The
relational facet of FL provides a foundation for the fuzzy -
logic-based methodology of computing with words (CW).

The epistemic facet of FL, FL/E, is linked to its logical
facet and is focused on the applications of FL to knowledge
representation, information systems, fuzzy databases and the theories
of possibility and probability. A particularly important application
area for the epistemic facet of FL relates to the conception and
design of information/intelligent systems.

At the core of FL lie two basic concepts: (a)
fuzziness/fuzzification; and (b) granularity/granulation. Fuzziness
is a condition which relates to classes whose boundaries are unsharply
defined, while fuzzification refers to replacing a crisp set, that is,
a set with sharply defined boundaries, with a set whose boundaries are
fuzzy. For example, the number 5 is fuzzified when it is transformed
into approximately 5.

In a similar spirit, granularity relates to clumpiness of
structure while granulation refers to partitioning an object into a
collection of granules, with a granule being a clump of objects
(points) drawn together by indistinguishability, similarity, proximity
or functionality. For example, the granules of an article might be
the introduction, section 1, section 2, etc. Similarly, the granules
of a human body might be the head, neck, chest, stomach, legs, etc.
Granulation may be crisp or fuzzy; dense or sparse; and physical or

A concept which plays a pivotal role in fuzzy logic is that of
fuzzy information granulation, or fuzzy IG, for short. In crisp IG,
the granules are crisp while in fuzzy IG the granules are fuzzy. For
example, when the variable Age is granulated into the time intervals
{0,1}, {1,2}, {2,3}, ..., the granules {0,1}, {1,2}, {2,3}, ... are
crisp; when Age is treated as a linguistic variable, the fuzzy sets
labeled young, middle-aged and old, are fuzzy granules which play the
role of linguistic values of Age. The importance of fuzzy logic --
especially in the realm of applications -- derives in large measure
from the fact that FL is the only methodology that provides a
machinery for fuzzy information granulation.

There are three basic concepts that play key roles in the
applications of fuzzy logic and are unique to it. They are (a) the
concept of a linguistic variable, that is, a variable whose values are
words rather than numbers; (b) the concept of a fuzzy if-then rule;
and (c) the concept of a fuzzy graph. Collectively, these concepts
provide a machinery for manipulation of imprecisely defined functions
and relations.

At this juncture, most of the practical applications of fuzzy
logic relate to control systems and, especially, to intelligent
control. However, there are also many applications in a wide variety
of other fields, ranging from consumer products and quality control to
automobiles, trains, manufacturing, robotics, financial engineering
and biomedical instrumentation. Increasingly, in many of its
applications fuzzy logic is used in combination with the methodologies
of neurocomputing, evolutionary computing, probabilistic computing and
machine learning. Association of fuzzy logic with these methodologies
gives rise to what is referred to as soft computing (SC). The
importance of soft computing derives from the fact that it provides a
foundation for the conception, design, construction and utilization of
information/intelligent systems.


Warm regards to all,


Lotfi A. Zadeh
Professor in the Graduate School and Director,
Berkeley Initiative in Soft Computing (BISC)
CS Division, Department of EECS
University of California
Berkeley, CA 94720-1776
Tel/office: (510) 642-4959 Fax/office: (510) 642-1712
Tel/home: (510) 526-2569 Fax/home: (510) 526-2433

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