Berkeley Initiative in Soft Computing (BISC)
Lotfi A. Zadeh
Almost all scientific theories are based on Aristotelean logic and
probability theory. Use of these theories has led to brilliant successes
that are visible to all. But what is less visible is that alongside
the brilliant successes lie many problem areas where progress has been
slow or nonexistent. We cannot automate driving in city traffic; we
cannot construct programs which can summarize nonstereotypical
stories,and our capacity to do economic forecasting without human
intervention leaves much to be desired.
To understand the reasons for the mixed picture, it is germane to
start with the thesis that, in general, a system for performing a
specified task may be viewed as having three principal components: (a)
hardware; (b) software: and (c) what may be called brainware -- a
complex of concepts, theories, methods and algorithms which govern the
functioning of hardware and software.
The capability of a system to perform a specified task is a
function of the capabilities of its hardware, software and brainware
components. In general, there is a tradeoff between these
capabilities. However, there are important classes of problems in which
the overall capability is limited primarily by the structure of
brainware and, more particularly, by the underlying systems for logical
reasoning and dealing with uncertainty.
What may be called the Intractability Principle is a thesis which
relates limits on performance to the structure of brainware. Stated
informally, the thesis has two parts, (a)negative; and (b)
positive,which are simmarized in the following.
(a) As the complexity of a problem increases, a critical
threshold is reached beyond which solution cannot be achieved through
the use of techniques based on two-valued logical systems and
(b) Beyond the critical threshold, ahievement of solution
necessitates the use of fuzzy-logic-based methodology of computing with
words (CW) and perception-based theory of probabilistic reasoning (PTp).
The basic idea which underlies the Intractability Principle is
that problems which lie beyond the critical threshold are intractable by
conventional measurement-based methods .What is not widely recognized is
that many problems which are simple for humans fall into this category.
Here are a few examples.
(a) Automation of driving a car. In this case, on one end of the
complexity scale we have automation of driving on a freeway with no
traffic. On the other end, is automation of driving in Istambul. Humans
can do this without any measurements and any computations. At this
juncture, no conceivable system can solve the problem.
(b) Machine -execution of the instruction: Make a right turn at
the intersection. In this case, at one end of the scale we have an
intersection on the outskirts of Princeton. On the other end, an
intersection in the center of New York.
(c) Summarization. On one end of the scale is a short
stereotypical story. On the other end, is a book. As a task,
summarization is an order of magnitude more complex than machine
There are two key points that require comment. First, in most
real-world problems that are simple for humans, the critical threshold
is not a remote limit that is of no concern. On the contrary, it
underscores the intrinsic limitation of techniqus based on Aristotelian
logic and proability theory to deal with problems in which
decision-relevant information is, for the most part, perception-based.
The second point relates to the pivotal role of the methodology
of computing with words in making it possible to solve problems which
lie beyond the critical threshold. The crux of the matter is that in
most problems which lie beyond the critical threshold, perception-based
information is described by propositions expressed in a natural
language, e.g., " usually traffic is very heavy in late afternoon." In
general, such propositions are f-granular in the sense that (a) the
boundaries of perceived classes are unsharp; and (b) the values of
attributes are granulated ,with a granule being a clump of values drawn
together by indistinguishability, similarity, proximity and
functionality. The problem with theories based on Aristotelian logic
and probability theory is that they do not have the capability to deal
with f-granular propositions drawn from a natural language. The
importance of computing with words derives from the fact that it does
provide this capability.
A key concept in computing with words is that of Precisiated
Natural Language (PNL). Basically, PNL is a subset of a natural
language, NL, which consists of propositions which are precisiable
through translation into what is called the Generalized Constraint
Language, GCL. PNL serves an important function as a definition
language ,with the language of fuzzy if-then rules being a sublanguage
Computing with words provides a basis for an important
generalization of probability theory -- from standard probability
theory, PT, to perception-based probability theory, PTp. Separately and
in combination, computing with words and perception-based theory of
probabilistic reasoning open the door to solution of problems which lie
beyond the critical threshold. This is the principal rationale for the
positive thesis of the Intractability Principle.
* Professor in the Graduate School and director, Berkeley Initiative in
Soft Computing (BISC), Computer Science Division and the Electronics
Research Laboratory, Department of EECS, University of California,
Berkeley, CA 94720-l776; Telephone: 5l0-642-4959; Fax: 5l0-642-l7l2;
E-mail: firstname.lastname@example.org. Researh supported in part by ONR
Contract N000l4-99-C-0298, NASA Contract NCC2-l006, NASA Grant NAC2-ll7,
ONR Grant NOOOl4-96-l-0556, ONR Grant FDNOOl499l035, ARO Grand DAAH
04-96l-034l and the BISC Program of UC Berkeley.
-- Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC)
Address: Computer Science Division 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, (510) 526-5181 email@example.com http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html
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