## Friday, October 28, 2011

### Fuzzy Logic & Causality

Dear Members of the BISC [Berkeley Initiative in Soft Computing] Group:

Few concepts are as pervasive as the concept of causality. Causality has a position of centrality in medicine and legal reasoning. Causality is pervasive in everyday reasoning and decision-making. But what is widely unrecognized is that in the enormous literature of causality what cannot be found are theories which work in real-world settings--settings in which information is uncertain, imprecise, incomplete or partially true. If you know of a working theory developed by yourself or others, please bring it to my attention. I will admit that I am wrong if you are right.

All theories of causality founder on the rocks of multicausality. The problem is that in real-world settings multicausality is the norm rather than exception. I find it helpful to talk about multicausality in the context of a prototypical example which I call the Raincoats Problem, or RP for short. I am a manufacturer of raincoats. I would like to increase my sales. To this end I increase the advertising budget by 20%. Six months later sales have risen by 10%. Was the increase in sales caused by the increase in the advertising budget? Can a theory of causality come up with an answer to this simple question? This is the litmus test. What is the problem? The problem is that the increase in sales may have been caused by a variety of causants other than the increase in the advertising budget--causants such as rainy weather, improvement in economic conditions, lowering price of raincoats, etc. Some of the causants may be known and some not. Given this setting, the question should be restated as: To what degree was the increase in sales caused by the increase in the advertising budget? It is this question that cannot be answered by existing theories. In existing theories, causality is not a matter of degree--as it should be. What should be underscored is that the degree of strength of causality is not the same as the probability of causality. What is the meaning of: The probability that the increase in sales was caused by the increase in the advertising budget, is 0.8?

In the case of RP, a theory of causality should suggest a procedure for assessing the degree to which the increase in sales was caused by the increase in the advertising budget. One such procedure may involve interviewing all purchasers of my raincoats, to identify in each case what led to the purchase of a raincoat? The problem is that no such procedure can be devised. The problem becomes more apparent when the advertising budget is increased by 20% but the sales declined by 10%. Consider the question: Was the 10% decline in sales caused by a 20% increase in the advertising budget? How should it be interpreted? Can an existing theory of causality deal with this question?

As an underlying issue, causality plays an important role in political debates. Was the financial crisis caused by Wall Street? To improve the economy, the Federal Reserve lowered the interest rate from 1% to 0.8%. Six months later, the economic activity rose by 5%. Was the increase in economic activity caused by lowering the interest rate? Will a particular initiative cause a decrease in unemployment? Is Obama's stimulus program a success or failure? What lessons can be drawn from RP to answer such questions?

A sobering thought is that no theory of causality can answer such questions. Is Obama's stimulus program a success or failure? Republicans argue that it is a failure because the unemployment rate remains above 9%. The democrats can argue, counterfactually, that it is a success because without the stimulus the unemployment rate would be over 12%. The problem is that counterfactual arguments are much less convincing than factual arguments. Nevertheless, the fact remains that in the instance of political debates, most causality assertions can neither be proved nor disproved. It would be much more realistic to accept that basically causality is a matter of degree. Once this is accepted, debates will become less polarized. A fundamental conclusion is that in realistic theories of causality, causality should be a matter of degree. To put it another way, realistic theories of causality should necessarily be based on fuzzy logic. Having said that, a word of caution is in order. Introduction of degrees into theories of causality is an undertaking which is far from simple to formalize. Comments are welcome.

Regards to all,

Lotfi

```--
Director, Berkeley Initiative in Soft Computing (BISC)

729 Soda Hall #1776
Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720-1776