BISC: Zadeh/ A Prototype-Centered Approach to Adding Deduction (Revised)

From: masoud nikravesh (nikraves@eecs.berkeley.edu)
Date: Sat Dec 29 2001 - 14:39:35 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

    =====================
    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 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 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**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 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.

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

    BTExact Technologies (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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