BISC: Lotfi A. Zadeh: BISC Seminar - CAUSALITY IS UNDEFINABLE

From: Masoud Nikravesh (nikravesh@eecs.berkeley.edu)
Date: Tue Jan 16 2001 - 15:19:01 MET

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    Berkeley Initiative in Soft Computing (BISC)
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    CAUSALITY IS UNDEFINABLE

    4:00 - 5:00 pm
    Thursday: Jan 18, 2001
    380 Soda Hall

    Professor Lotfi A. Zadeh

    Causality occupies a position of centrality in human cognition. In particular,
    it plays an essential role in human decision-making by providing a basis for
    choosing that action which is likely to lead to a desired result. There is an
    enormous literature on causality, spanning philosophy, psychology, law,
    statistics, system theory, decision analysis and physics, among others. And yet,
    there does not exist a definition of causality, which satisfies the following
    criteria. My contention is that any attempt to define causality within the
    conceptual structure of classical logic and probability theory has no chance of
    success.

     1. The definition is general in the sense that it is not restricted to a narrow
    class of systems or phenomena.

     2. The definition is precise and unambiguous in the sense that it can be used
    as a basis for logical reasoning and/or computation.

     3. The definition is operational in the sense that given two events A and B,
    the definition can be employed to answer the questions: a) Did or does or will A
    cause B or vice-versa? b) If there is a causal connection between A and B, what
    is its strength?

     4. The definition is consonant with our intuitive perception of causality and
    does not lead to counterintuitive conclusions.

     There are many well-known sources of difficulty in defining or establishing
    causality. Among them there are three that stand out in importance.
     
      1 Chaining. In this case, we have a temporal chain of events, A1, A2,...,
    An-1, An, which terminates on An. To what degree, if any, does Ai(i=1,...,n-1,)
    cause An.? Example.. I am called by a friend. He needs my help and asks me to
    rush to his home. I jump into my car and drive as fast as I can. At an
    intersection, I am hit by another car. I am killed.
    Who caused my death? My friend; I; or the driver of the car that hit me.
     
    2. Confluence (conjunction). In this case, we have a confluence of events,
    A1,...,An, and a resultant event, B. To what degree, if any, did or does Ai
    cause B? Example.. I am a manufacturer of raincoats. I want to increase sales.
    To this end, I increase my advertising budget by 100%. The sales go up 20%. To
    what degree, if any, did the increase in the advertising budget cause the
    increase in sales? In this example, increase in the advertisin budget is just
    one of many events which collectively caused the increase in sales.
     
    3. Covariability (covariation, correlation, co-dependence, statistical
    association). In this case, A and B are variables, and there appears to be a
    deterministic or statistical covariability between A and B. Is this
    covariability a causal relation? More generally, when is a relation a causal
    relation? Differentiation between covariabililty and causality presents a
    difficult problem, especially in the context of data mining.

    Example.. It is generally assumed that aging causes a loss in acuity of hearing.
    However, recent studies have shown that the loss in acuity is caused by
    prolonged exposure to high levels of sound and not by aging per se.
     
    Example.. I fell at home and broke my right leg and left arm. Is there a causal
    connection between breaking my right leg and left arm?
     
    Viewed in a more general setting, definability is associated with a language
    that is used to define a concept, e.g., a natural language or the language of
    first order logic. In what may be called definability hierarchy, the most
    general and hence most expressive definition language is PNL ( Precisiated
    Natural Language ). Basically, PNL is a subset of a natural language, NL, which
    is precisiated through translation into the Generalized Constraint Language
    (GCL). In this context, a concept is undefinable or amorphic, if it is not
    definable through the use of PNL. Examples of amorphic oncepts are those of a
    summary, relevance, rationality, justice, beauty and intelligence.
     
    To say that a concept is undefinable does not mean that it cannot be dealt with
    in effective ways. What it means is that it cannot be dealt with as precisely
    and as rigorously as a concept that is definable in a language within the
    definability hierarchy. Although definability of causality lies beyond the
    expressive power of PNL, PNL is effective in defining or redefining a wide
    variety of non-amorphic concepts. In particular, PNL can be used to redefine
    optimality, Pareto-optimality, Lyapounov stability and statistical independence.
    In general, PNL-based definitions have a much closer rapport with reality than
    conventional, crisp definitions.

    Prof. Lotfi A. Zadeh
    Professor in the Graduate School and Director,
    Berkeley Initiative in Soft Computing (BISC)
    CS Division, Department of EECS
    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
    email: zadeh@cs.berkeley.edu
    http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html

    ----------------------------------------------------------------
    Dr. Masoud NikRavesh
    Research Engineer - BT Senior Research Fellow
    Chair: BISC Special Interest Group on Fuzzy Logic and Internet

    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.cs.berkeley.edu/~nikraves/
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