Would someone please be kind enough to send along Dr. Mitola's comment? Thank you,
Peter Tillers ----- Original Message ----- From: Lotfi A. Zadeh To: uai@engr.orst.edu Cc: Lotfi A. Zadeh Sent: Monday, July 21, 2008 9:06 PM Subject: [UAI] re: Computation with Imprecise Probabilities--The problem of Vera's age Dear Dr. Mitola: Thank you for your constructive comment and for bringing the works of George Lakoff, Johnson and Rhor, Jackendoff and Tom Ziemke to the attention of the UAI community. I am very familiar with the work of George Lakoff, my good friend, and am familiar with the work of Jackendoff. The issue that you raise-context-dependence of meaning-is of basic importance. In natural languages, meaning is for the most part context-dependent. In synthetic languages, meaning is for the most part context-free. Context-dependence serves an important purpose, namely, reduction in the number of words in the vocabulary. Note that such words as small, near, tall and young are even more context-dependent than the words and phrases cited in your comment. In the examples given in my message, the information set, I, and the question, q, are described in a natural language. To come up with an answer to the question, it is necessary to precisiate the meaning of propositions in I. To illustrate, in the problem of Vera's age, it is necessary to precisiate the meaning of "mother's age at birth of a child is usually between approximately twenty and approximately forty." Precisiation should be cointensive in the sense that the meaning of the result of precisiation should be close to the meaning of the object of precisiation (Zadeh 2008). The issue of cointensive precisiation is not addressed in the literature of cognitive linguistics nor in the literature of computational linguistics. What is needed for this purpose is a fuzzy logic-based approach to precisiation of meaning (Zadeh 2004). In Precisiated Natural Language (PNL) it is the elasticity of meaning rather than the probability of meaning that plays a pivotal role. What this means is that the meaning of words can be stretched, with context governing elasticity. It is this concept that is needed to deal with context-dependence and, more particularly, with computation with imprecise probabilities, e.g., likely and usually, which are described in a natural language. In computation with imprecise probabilities, the first step involves precisiation of the information set, I. Precisiation of I can be carried out in various ways, leading to various models of I. A model, M, of I is associated with two metrics: (a) cointension; and (b) computational complexity. In general, the higher the cointension, the higher the computational complexity is. A good model of I involves a compromise. In the problem of Vera's age, I consists of three propositions. p1: Vera has a daughter in the mid-thirties; p2: Vera has a son in the mid-twenties; and p3(world knowledge): mother's age at the birth of her child is usually between approximately 20 and approximately 40. The simplest and the least cointensive model, M1, is one in which mid-thirties is precisiated as 30; mid-twenties is precisiated as 20; approximately 20 is precisiated as 20; approximately 40 is precisiated as 40; and usually is precisiated as always. In this model, p1 precisiates as: Vera has a 35 year old daughter; p2 precisiates as: Vera has a 25 year old son; and p3 precisiates as mother's age at the birth of her child varies from 20 to 40. Precisiated p1 constrains the age of Vera as the interval [55, 75]. Since p2 is not independent of p1, precisiated p2 constrains the age of Vera as the interval [55, 65]. Conjunction (fusion) of the two constraints leads to the answer: Vera's age lies in the interval [55, 65]. Note that the lower bound is determined by the lower bound in p1 while the upper bound is determined by the upper bound in p2. A higher level of cointension may be achieved by moving from M1 to M2. In M2, various terms such as mid-twenties and mid-thirties are precisiated as intervals, e.g. mid-twenties is precisiated as [24, 26], with usually precisiated as always. Elementary interval analysis suffices for computation of Vera's age. A significantly higher level of cointension may be achieved with M3. In M3, various terms are precisiated as fuzzy intervals and, more particularly, as fuzzy intervals with trapezoidal membership functions, or tp-sets for short, with usually precisiated as always. For this model, to compute Vera's age what is needed is fuzzy arithmetic. The best model is M4. M4 differs from M3 in that usually is precisiated as a fuzzy probability represented as a tp-set. To compute Vera's age what is needed is the machinery of the Generalized Theory of Uncertainty (Zadeh 2006). Should you be interested, I will be pleased to send you, and anyone else who is interested, a detailed solution. In relation to M4, Bayesian models are less cointensive and more computationally complex. The reason is rooted in the fact that imprecision in natural languages stems from the elasticity of meaning rather than the probability of meaning. In summary, when the information set, I, is described in a natural language, the answer to a question depends on the model that is used to precisiate I. To achieve a high degree of cointension, what is needed is a combination of fuzzy logic and probability theory. By itself, probability theory is not sufficient. Warm regards to all, Lotfi -- Lotfi A. Zadeh Professor in the Graduate School Director, Berkeley Initiative in Soft Computing (BISC) ------------------------------------------------------------------------------ _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
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