BISC: Zadeh/ BISC Seminar, Feb. 8, 2002

From: Masoud Nikravesh (nikravesh@eecs.berkeley.edu)
Date: Fri Jan 25 2002 - 02:04:28 MET

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    Berkeley Initiative in Soft Computing (BISC)
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    A Prototype-Centered Approach to
    Adding Deduction Capability to Search Engines -- The Concept of Protoform

    BISC Seminar
    Lotfi A. Zadeh
    EECS-CS Division
    University of California-Berkeley
    Feb. 8, 2002
    320 Soda Hall
    4:00-5:30 p.m.

    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: "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." A fuzzy rule may be a crisp assertion about fuzzy sets or a
    fuzzy assertion about crisp sets or a fuzzy assertion about fuzzy sets.

    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^^2," whose
    consequent matches the query, with ?Q instantiated to Q^.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^0.5 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 (British Telecom-BT) Senior 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/ -------------------------------------------------------------------- If you ever want to remove yourself from this mailing list, you can send mail to <Majordomo@EECS.Berkeley.EDU> with the following command in the body of your email message: unsubscribe bisc-group or from another account, unsubscribe bisc-group <your_email_adress>

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