BISC: A Prototype-Centered Approach to Adding Deduction Capability to Search

From: masoud nikravesh (nikraves@eecs.berkeley.edu)
Date: Sat Dec 22 2001 - 22:32:55 MET

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    The attached abstract "A Prototype-Centered 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 e-mail 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

    --
    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 zadeh@cs.berkeley.edu http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html ==================================

    December 19, 2001

    A Prototype-Centered 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 sigma-summary, 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 PF-equivalent 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 PF-equivalent. The importance of the concepts of protoform and PF-equivalence 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 Q A's are B's and Q (A and B)'s are C's," then "Q Q A's are (B and C)'s,” where Q and Q 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 query-relevant.

    A very simple example of deduction in the prototype-centered 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, where Q is a fuzzy quantifier and B is assumed to represent the meaning of “very B,” with the membership function of B being the square of the membership function of B. Searching DDB, we find the rule “If Q A’s are B then Q A’s are B,” whose consequent matches the query, with ?Q instantiated to Q , 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 Swedes are very tall,” where the membership function of “Most ” is the square root of Most in fuzzy arithmetic.

    The concept of a prototype is intrinsically fuzzy. For this reason, the prototype-centered approach to deduction is based on fuzzy logic and perception-based 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 many-faceted 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 94720-1776; Telephone: 510-642-4959; Fax: 510-642-1712;E-Mail: zadeh@cs.berkeley.edu. Research supported in part by ONR Contract N00014-99-C-0298, NASA Contract NCC2-1006, NASA Grant NAC2-117, ONR Grant N00014-96-1-0556, ONR Grant FDN0014991035, ARO Grant DAAH 04-961-0341 and the BISC Program of UC Berkeley.

    ==========

    With my warm regards and best wishes for the Christmas and New Year.

    Cheers Masoud, Laura, Nikolas Nikravesh

    --- Dr. Masoud Nikravesh BISC Associate Director and Program Administrator

    BTExact (British Telecom-BT) Senior Research Fellow Chairs: BISC-SIG-FLINT,ES, RT Berkeley Initiative in Soft Computing (BISC) Computer Science Division- Department of EECS University of California, Berkeley, CA 94720 Phone: (510) 643-4522; Fax: (510) 642-5775 Email: Nikravesh@cs.berkeley.edu URL: http://www-bisc.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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