My Dear Colleagues, Violating my short-lived vow of silence -- and perhaps proving that it _is_ possible to speak when one has nothing to say -- I forward the below message -- at Professor Zadeh's request -- to the members of this list.
Sincerely, P tillers ***** � -----Original Message----- From: Peter Tillers [mailto:[EMAIL PROTECTED] Sent: Wednesday, November 12, 2003 12:18 PM To: [EMAIL PROTECTED] Subject: Re: RE:[UAI]causal_vs_functional models? Dear Lotfi, I am now fully persuaded -- i.e., you have fully persuaded me -- that legal reasoning (about so-called "hard cases") -- that reasoning about the scope or reach of legal norms typically involves partial truth. Thank you _very_ much for your clarifications. I hope that some junior legal scholar picks up this theme. I think it would be very helpful, it would be very important, to have an elaboration of the thesis that we should be talking, some or much of the time, not (just) about the probability that some system is a system of legal rules, but instead (also) about the notion that different systems of social control can have partial and varying "amounts" of "law." (Such an argument would be one level above the thesis that particular elements -- e.g., roller skates -- can have partial "amounts" of classifications -- or sets of things -- in legal rules -- such as the set or class "motor vehicles." [This problem was made famous by Lon L. Fuller: Does riding on roller skates in the park violate an ordinance against using a motor vehicle in the park.]) Best wishes, Peter > > From: "Lotfi A. Zadeh" <[EMAIL PROTECTED]> > Date: 2003/11/11 Tue AM 04:13:10 EST > To: Peter Tillers <[EMAIL PROTECTED]>, [EMAIL PROTECTED] > CC: Lotfi Zadeh <[EMAIL PROTECTED]> > Subject: RE:[UAI]causal_vs_functional models? > > Dear Peter: > > Thank you for not following Wittgenstein's advice in your > message :" That about which one cannot talk, one should remain silent > about." With characteristic humility and insight, you touch upon > issues which play basic roles in law and legal reasoning. Looking from > the outside, to clarify these issues it is necessary to differentiate > between partiality of truth and partiality of certainty. The problem > with the concept of factuality is that it may involve a mixture of the two. > > A simple example which clarifies the difference is one that > I used before. If Robert is half- German and half- French, and I say > that Robert is German, then what I say is half-true, with no uncertainty > involved. On the other hand, if I am not sure whether Robert is German > or not German, then the probability that he is German may be 0.5. In > the first case, we have partial truth and no uncertainty ,while in the > second case we have partial certainty of full truth. > > In the realm of law and legal reasoning, most assertions are > both partially true and partially certain. > > In bivalent logic and bivalent- logic-based probability > theory, partiality of truth is not addressed. This is the reason why, > in my view, bivalent logic and bivalent- logic - based probability > theory do not provide adequate tools for formalization of legal > reasoning. In this sense, Ron Allen is right. > > Probability theory has been in existence for over two > centuries. What is amazing is that in the enormous literature of > probability theory the fact that probability theory does not address > partiality of truth has not been articulated. Perhaps the reason for > benign neglect is that there was no machinery for this purpose. Fuzzy > logic provides this machinery because in fuzzy logic, truth, certainty > and everything else are, or are allowed to be, a matter of degree. > > Perceptions play a pivotal role in law and reasoning. Much > of legal reasoning is perception-based. Perceptions are intrinsically > imprecise. Can standard probability theory, call it PT, operate on > perception-based information? > > Following are a few simple test problems.It is understood > that imprecise terms such as most, tall, etc. require precisiation in > one form or another. > > l. The tall Swedes problem: Most Swedes are tall. What is > the average height of Swedes? > > 2. Usually it is not very cold ,and usually it is not very > hot in Berkeley. What is the average temperature in Berkeley? > > 3. The Robert example: Usually Robert returns from work at > about 6 pm. What is the probability that Robert is home at about 6 :l5 pm? > > 4. The balls- in- box problem: A box contains about 20 > black and white balls. Most are black. There are several times as many > black balls as white balls. What is the probability that a ball drawn at > random is white? > > In probability community it is an article of unquestioned > faith that standard probability theory is adequate for dealing with all > problems involving uncertainty and imprecision.What is unrecognized is > that, unfortunately, this is far from being true. However, probability > theory can be generalized, making it capable of dealing with both > partiality of certainty and partiality of truth. The generalized > probability theory, which I call perception-based probability theory, > PTp, is outlined in the paper cited in my message of ll/l0/03. The > correct title is "Toward a Perception-based Theory of Probabilistic > Reasoning with Imprecise Probabilities." > > Thank you for contributing so importantly to a > clarification of basic issues in the realm of law and legal reasoning. > Actually, these issues play pivotal roles not just in law and legal > reasoning but, more generally, wherever partiality of truth and > partiality of certainty are important factors, as they are in the > conception, design and utilization of intelligent systems. > > Warm regards. > > Sincerely, > > Lotfi > > -- > Lotfi A. Zadeh > Professor in the Graduate School, Computer Science Division > Department of Electrical Engineering and Computer Sciences > University of California > Berkeley, CA 94720 -1776 > Director, Berkeley Initiative in Soft Computing (BISC) > >
