Berkeley Initiative in Soft Computing (BISC)
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
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
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
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