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Berkeley Initiative in Soft Computing (BISC)
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The attached abstract "A PrototypeCentered Approach to Adding Deduction
Capability to Search Engines  The Concept of Protoform" is for your
information and comments, if any.
Should you like your comment to be ported to the BISC mailing list,
please email it to Dr. Nikravesh <nikravesh@cs.berkeley.edu> with cc to
me.
With my warm regards and best wishes for the New Year
Cheers
Lotfi Zadeh
=====================
December 19, 2001
A PrototypeCentered Approach to Adding Deduction
Capability to Search Engines  The Concept of Protoform
Lotfi A.
Zadeh *
Abstract
Existing search engines have many remarkable capabilities. But
what is not among them is the deduction capability  the capability to
answer a query by drawing on information which resides in various parts
of the knowledge base or is augmented by the user.
Limited progress toward a realization of deduction capability is
achievable through application of methods based on bivalent logic and
standard probability theory. But to move beyond the reach of standard
methods it is necessary to change direction. In the approach which is
outlined, a concept which plays a pivotal role is that of a prototype 
a concept which has a position of centrality in human reasoning,
recognition, search and decision processes.
Informally, a prototype may be defined as a sigmasummary, that is,
a summary of summaries. With this definition as the point of departure,
a prototypical form, or protoform, for short, is defined as an
abstracted prototype. As a simple example, the protoform of the
proposition "Most Swedes are tall" is "QA's are B's," where Q is a fuzzy
quantifier, and A and B are labels of fuzzy sets.
Abstraction has levels, just as summarization does. For example,
in the case of "Most Swedes are tall," successive abstracted forms are
"Most A's are tall," "Most A's are B's" and "QA's are B's."
At a specified level of abstraction, propositions are
PFequivalent if they have identical protoforms. For example,
propositions "Usually Robert returns from work at about 6 pm" and "In
winter, the average daily temperature in Berkeley is usually about
fifteen degrees centigrade," are PFequivalent. The importance of the
concepts of protoform and PFequivalence derives in large measure from
the fact that they serve as a basis for knowledge compression.
A knowledge base is assumed to consist of a factual database, FDB,
and a deduction database, DDB. In both FDB and DDB, knowledge is
assumed to fall into two categories: (a) crisp and (b) fuzzy. Examples
of crisp items of knowledge in FDB might be: “The height of the Eiffel
tower is 324m” and “Paris is the capital of France.” Examples of fuzzy
items might be “Most Swedes are tall,” and “California has a temperate
climate.” Similarly, in DDB, an example of a crisp rule might be “If A
and B are crisp convex sets, then their intersection is a crisp convex
set.” An example of a fuzzy rule might be “If A and B are fuzzy convex
sets, then their intersection is a fuzzy convex set.”
The deduction database is assumed to consist of a logical database
and a computational database, with the rules of deduction having the
structure of protoforms. An example of a computational rule is "If Q1
A's are B's and Q2 (A and B)'s are C's," then "Q1 Q2 A's are (B and
C)'s,” where Q1 and Q2 are fuzzy quantifiers, and A, B and C are labels
of fuzzy sets. The number of rules in the computational database is
assumed to be very large in order to allow a chaining of rules that may
be queryrelevant.
A very simple example of deduction in the prototypecentered
approach—an example which involves string matching but no chaining  is
the following. Suppose that a query is “How many Swedes are very tall?”
A protoform of this query is: ?Q A’s are B**2, where Q is a fuzzy
quantifier and B**2 is assumed to represent the meaning of “very B,”
with the membership function of B**2 being the square of the membership
function of B. Searching DDB, we find the rule “If Q A’s are B then
Q**0.5 A’s are B,” whose consequent matches the query, with ?Q
instantiated to Q**0.5, A to “Swedes” and B to “tall.” Furthermore, in
FDB, we find the fact “Most Swedes are tall,” which matches the
antecedent of the rule, with Q instantiated to “Most.” A to “Swedes” and
B to “tall.” Consequently, the answer to the query is “Most**0.50 Swedes
are very tall,” where the membership function of “Most**0.5” is the
square root of Most in fuzzy arithmetic.
The concept of a prototype is intrinsically fuzzy. For this
reason, the prototypecentered approach to deduction is based on fuzzy
logic and perceptionbased theory of probabilistic reasoning, rather
than on bivalent logic and standard probability theory.
What should be underscored is that the problem of adding deduction
capability to search engines is manyfaceted and complex. It would be
unrealistic to expect rapid progress toward its solution.

* Lotfi A. Zadeh is 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 947201776; Telephone: 5106424959; Fax:
5106421712;EMail: zadeh@cs.berkeley.edu. Research supported in part
by ONR Contract N0001499C0298, NASA Contract NCC21006, NASA Grant
NAC2117, ONR Grant N000149610556, ONR Grant FDN0014991035, ARO Grant
DAAH 049610341 and the BISC Program of UC Berkeley.
 Dr. Masoud Nikravesh BISC Associate Director and Program AdministratorBTExact Technologies (British TelecomBT) Senior Research Fellow Chairs: BISCSIGFLINT,ES, RT Berkeley Initiative in Soft Computing (BISC) Computer Science Division Department of EECS University of California, Berkeley, CA 94720 Phone: (510) 6434522; Fax: (510) 6425775 Email: Nikravesh@cs.berkeley.edu URL: http://wwwbisc.cs.berkeley.edu/
Staff Scientist Lawrence Berkeley National Lab, Imaging and Collaborative Computing Group Email: Masoud@media.lbl URL: http://vision.lbl.gov/
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