Dear Prof. Zadeh, Thanks for your reply. As I understand it, your position is that all of our perceptions are partial, or exist in degrees, and as our experience is entirely based on our perceptions, partiality is a fundamental part of human cognition. Nothing ever fully exemplifies what it is (or what we are calling it), but rather only exemplifies it to some degree, or partially. No one is ever "truly" honest, but rather people are honest (we perceive them as honest) to varying degrees. In fact honesty itself only exists as a sort of continuum, where things are more honest and less honest. Knowledge is based on perception, and perception is always partial.
It seems to me that this view underplays the role of judgement in human congnition. One could argue that people are naturally _classifiers_, and that their natural cognitive response to perception is to categorize it. One never has a perception that someone is 0.1 tall on a scale of 0 to 1. We have perceptions of the person being tall or short in particular instances when we became conscious of the person's height because it was an issue in the situation. The person was too tall or too short for something and they were classified as tall or short in that instance. My total perception of the degree of tallness of the person is an average of these different classifications at different times, but ultimately it is based on classifications and judgements, of actual applications of concepts rather than the experience of degrees of them. Perception of degree follows perception of existence. Likewise with honesty, if you asked me to gauge a person's honesty, and I know something about them but have no preconception of their honesty based on personal experience with them, then I might consider various moral dilemma-type situations and try to predict whether the person would act honestly or not. In this case, I am assigning a likelihood to the person doing the honest thing in each case, and my final judgement of the degree of honesty is based on the average of those considerations weighted by the gravity of the particular situations. I don't perceive degrees of honesty. I perceive particular instances, which I classify as honest or dishonest. Macroscopically I determine a degree of honesty based on the microscopic instances of bivalent decisions, or the application of a concept or not. I think it is interesting to consider the quantum mechanical model. Previously, a continuum of matter and energy seemed self-evident, but it turns out that things acually exist in discrete states (or we can only perceive them as such), and there is a sharp jump from one state to the next, not a smooth continuous transition. However, the most useful model for describing the state of things with incomplete knowledge is in terms of a _distribution_ (wave equation). We imagine things "existing" as distributions prior to observation, and their future being conditioned on what was observed. But what is primary is the thing that happened, and this is all we need to make metaphysical reference to. The rest is a model that aids in the prediction of what will happen in observation. Actually, I don't want to argue _against_ partiality and degree. I believe your ideas concerning partiality and your work on partial knowledge and reasoning under uncertainty are valuable and useful, as is obvious from their impact on science. I only take issue with the emphasis on partiality and degree almost to the exclusion of discrete categorization in epistemics. You argue that perception is fundamentally continuous and that the discrete states that we think we observe are really only points in a more general continuum of perception, in short, that perception is prior to cognition. I believe that we are only aware of perception to the extent that it has been cognized, and that cognition is more fundamentally characterized by discrete classifications and decisions, with perception of degree being secondary, i.e. cognition is prior to perception. Kind regards, Jason - - -----Original Message----- From: Lotfi A. Zadeh [mailto:[EMAIL PROTECTED] Sent: Tuesday, February 03, 2004 6:47 PM To: UAI Cc: Lotfi A. Zadeh; Peter Tillers; Jason Palmer; Paul Snow Subject: Re: [UAI] causal_vs_functional models Dear Jason: <!--[if !supportEmptyParas]--> <!--[endif]--> Thank you or the comment. However, your perception of the relationship between standard probability theory, call it PT, and fuzzy logic, FL, is in need of discussion. The principal difference between PT and FL is this: In PT, only certainty is a matter of degree. In FL, everything, including certainty, is-or is allowed to be-a matter of degree. However, PT can be generalized to perception-based probability theory, PTp. (See "Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities," Journal of Statistical Planning and Inference, Vol. 105, 233-264, 2002, Downloadable at: http://www-bisc.cs.berkeley.edu/BISCProgram/default.htm under Sponsors/Project Titles.) In PTp, as in FL, everything is-or is allowed to be-a matter of degree. This includes such basic concepts as randomness, independence, stationarity, etc. In PTp, as in FL, bivalence is abandoned. Let me be more specific. A concept which has a position of centrality in human cognition is that of partiality. We have partial knowledge, partial understanding, partial belief, partial doubt, partial solution, partial ability, partial control, partial membership, etc. Among the many kinds of partiality, there are three that stand out in importance: partiality of truth (verity), partiality of likelihood (probability) and partiality of possibility. What is not realized to the extent that it should, is that these concepts are distinct. To clarify, let me add a few examples to those given in earlier messages. First, let me focus on the difference between partiality of truth and partiality of likelihood. I know Robert very well. Someone is asking me: On the scale from 0 to 1, how would you rate Robert's honesty? My answer may be, say, about 0.9. There is no randomness and no uncertainty. Thus, "about 0.9" may be interpreted as my perception of the truth value of the proposition "Robert is honest," or, equivalently, as my perception of the grade of membership of Robert in the fuzzy set of honest men. My perception is subjective, context-dependent and imprecise. This, in a nutshell, is how humans assess degrees of truth. We have been doing this for years when we filled out survey forms with questions such as: How would you rate quality of service: excellent, good, fair, poor? What should be stressed is that there is nothing that is probabilistic in these examples. The same applies to Peter's questions: Is a wheelchair a vehicle? Is a motorized wheelchair a motorized vehicle? What I said above relates to Paul's question about partial truth. Now let us consider another scenario. I am acquainted with Robert but do not know him well. Someone is asking me: On the scale from 0 to 1, how would you assess the likelihood that Robert is honest? My answer may be: about 0.9. In this instance, "about 0.9" is my subjective probability that Robert is honest, with the understanding that honesty is treated as a bivalent attribute. For humans, assessment of truth is intrinsically much easier than assessment of likelihood. Note that likelihood and certainty are closely related but are not identical. Both truth (verity) and probability are subjective. The widely accepted thesis that subjective probabilities are definable via betting behavior, is indefensible because betting behavior is influenced by many factors other than probability. What about partiality of possibility? Here is a simple example drawn for my 1978 paper, "Fuzzy Sets as a Basis for a Theory of Possibility," (Fuzzy Sets and Systems, 1, 3-28). (For an up-to-date in depth discussion see the special issue of Artificial Intelligence on, "Fuzzy Set and Possibility Theory-Based Methods in Artificial Intelligence" Elsevier, Vol. 148, Issues 1-2, Pages 1-424, 2003, edited by: D. Dubois and H. Prade.) What is the possibility that Hans may eat n eggs for breakfast? For n=5, say, it may be about 0.3, on some scale of ease of attainment, and for n=1, it will be 1. Note that there is nothing that is probabilistic. On the other hand, the probability that Hans may have one egg for breakfast may be about 0.1, and the probability that he may have more than two eggs for breakfast is zero. In bivalent logic, in modal logic and, more generally, in mathematics, possibility is bivalent. Thus, when I stipulate that a variable, X, takes values in a set, A, what I am defining is the set of possible values of X, or equivalently, its bivalent possibility distribution. More generally, possibility may be epistemic, that is, defined by constraints induced by knowledge. As an illustration, the proposition X is A, where A is a fuzzy set, equates A to the possibility distribution of X. It is of some help to view partiality as a dimension. In this sense, PT is one dimensional. FL is three dimensional. Natural languages are three dimensional in the sense that, in general, propositions drawn from a natural language, NL, involve partial truth and/or partial likelihood and/or partial possibility. The mismatch between dimensionalities of PT and NL is the reason why there are no means in PT for understanding propositions drawn from NL. <!--[if !supportEmptyParas]--> <!--[endif]--><!--[if !supportEmptyParas]--> <!--[endif]-->Dear Paul: <!--[if !supportEmptyParas]--> <!--[endif]--> Thank you for the comment. You refer to solutions to my test problems. Actually, no acceptable solutions have been put forward. There is a basic reason why my problems cannot be addressed through the use of PT. What is absent in PT is a means of counting the number of elements in a fuzzy set, that is, the concept of cardinality of a fuzzy set. Suppose that I am in a room and am asked, "How many tall men are in this room?" with the understanding that tallness is a matter of degree. Note that in this context there is no randomness and no uncertainty. Can you point to a discussion of this basic issue in a standard text on probability theory? Without addressing the issue of cardinality, you cannot define the meaning of propositions of the form Q A's are B's, e.g., most Swedes are tall. Manipulation of partial truths, partial likelihoods and partial possibilities calls for different calculi and different conceptual structures. To try to fit everything into the conceptual structure of probability theory is unnatural and counterproductive. Simple problems in one realm become complex problems in another realm. It is a little like trying to eat soup with a fork. Try solving a system of linear equations in which coefficients are random variables. In perception-based probability theory, PTp, a default assumption is that information is granular and is defined by what are called generalized constraints. Special cases of generalized constraints are veristic constraints, probabilistic constraints and possibilistic constraints. Furthermore, a wide variety of combinations of these constraints are allowed. In this setting, probabilistic constraints, which are the province of standard probability theory, are a special case. The much more general framework of PTp is needed to deal with perception-based information described in a natural language. This is what my test problems are intended to demonstrate. Here is an additional example. I am in a hotel and see a sign saying, "Checkout time is 1 pm." What does it mean? It is not possible to come up with a realistic answer to this question if you choose to stay within the conceptual structure of PT. Viewed in a historical perspective, it is amazing that the issue of partiality of truth-in the context of probability theory-has not been raised-at least to my knowledge-long before. What we see is that, in large measure, practitioners of probability theory are satisfied with the status quo. But we have to remember that scientific progress is driven by a questioning of dogmas, traditions and conventional wisdom. <!--[if !supportEmptyParas]--> <!--[endif]--> Regards to all, <!--[if !supportEmptyParas]--> <!--[endif]--> Lotfi <!--[if !supportEmptyParas]--> <!--[endif]-->P.S. Personal note. Sometimes I get the impression that some participants in our discussions view me as an opponent of probability >theory. In reality, probability theory has always played, and is continuing to play, a major role in my work. My first published paper was entitled, "Probability Criterion for the Design of Servomechanisms." (Journal of Applied Physics, 1949.) A paper published a year later was entitled, "An Extension of Wiener's Theory of Prediction," Journal of Applied Physics, 1950. Many others followed. A recent paper is, "Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities," (Journal of Statistical Planning and Inference, 2002.) A note scheduled for publication in the Journal of the American Statistical Association is entitled, "Probability Theory and Fuzzy Logic-A Radical View." In summary, I am not an opponent of probability theory, nor do I view fuzzy logic as an alternative to probability theory. What I do see-and what is unrecognized and denied-is that standard probability theory, PT, has fundamental limitations which are rooted in the failure of PT to address the issues of partiality of truth and partiality of possibility. These limitations can be removed by generalization of PT, leading to perception-based probability theory, PTp. A realm in which partiality of truth is ubiquitous-and yet not a center of attention-is that of law and legal reasoning. Do any approaches to formalization of legal reasoning address the issue of partiality of truth? - - -- 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) [EMAIL PROTECTED] Tel.(office): (510) 642-4959 Fax (office): (510) 642-1712 - ------- End of Unsent Draft
