Re: [UAI] Computation with Imprecise Probabilities--The problem of Vera's age
Dear Professor Scheffler,
I wonder if you think the following attempt to distinguish the plasticity of
words and from uncertainty about the meaning of words makes any sense:
http://tillerstillers.blogspot.com/2008/07/indeterminacy-and-elasticity-of-legal.html
I can say this much with some confidence: in law it seems to make sense to say
-- it has seemed this way to US legal scholars for quite a long time -- that
legal words, or legal concepts, are elastic, sometimes very elastic. Yet
lawyers and legal scholars sometimes (but not always) think they can predict
how (some) elastic words will behave (e.g., how courts under various
circumstances will use {apply} such elastic words and concepts). So in law --
in American law in any event -- it does not violate common (legal) sense for an
informed legal professional to say the following sort of thing: That concept
-- 'possession' -- can mean a lot of things, Mr Jones. But I have good reason
to think that in a 'larceny from the person' case -- that is, in a classic
theft case -- a court will say the victim had possession of the thing allegedly
stolen only if the victim had physical contact with the thing taken and only if
the thing taken was tangible. So, Mr Jones, if you didn't have your fingers
around your hat and your hat was on the ground when David Defendant picked it
up and ran away with it even though he knew it was yours, a court will dismiss
a criminal charge against Defendant of larceny by taking from a person. For
such a charge to lie the victim had to have been in possession of the thing
taken. That's not the way things stand in the case of real property; courts
will readily say you 'possess' real estate even if you are on the moon and your
real property is on the earth. But the owner's physical contact with the thing
taken is necessary to sustain a charge of theft of personal property. Of
course, there are different kinds of theft legally speaking. But, Mr Jones,
none of them apply in this case because etc. Moreover, Mr Jones, I'm very
sorry that David Defendant made use of your copyright after he threatened you
with death if you didn't allow him to do so. But he can't be convicted of
robbery. That's because under our common law a person 'robs' another person
only if the malefactor takes personal tangible property from the possession of
another. Well, as you can see, Mr Jones, perhaps your copyright was your
personal property but it was not tangible property, and it can't fairly be said
-- it won't be said -- that you possessed thhe copyright whose value you have
lost. I wish I could be more helpful, Mr Jones, but that's the way things work
in the State of Whitefish.
Peter Tillers (law teacher and, formerly, pracicing lawyer)
P.S. The sort law of larceny and theft to which I allude is roughly (very
roughly!) the common law that probably prevailed in the US in, say, the year
1900. The law in this area (larceny, theft, robbery etc.) has been dramatically
changed by legislation since 1900. But my anachronistic and possibly
historically-inaccurate example still makes my point, I hope.
- Original Message -
From: Konrad Scheffler [EMAIL PROTECTED]
To: Lotfi A. Zadeh [EMAIL PROTECTED]
Cc: uai@engr.orst.edu
Sent: Wednesday, July 30, 2008 5:42 AM
Subject: Re: [UAI] Computation with Imprecise Probabilities--The problem of
Vera's age
Dear Prof Zadeh,
Perhaps you could elucidate what you mean by cointensive? (I assume this
is explained in detail in your paper, but I also assume that one purpose
of your post here is to convince people that it will be worth investing
the time to read the paper.)
Also, what do you understand under probability? Your distinction between
elasticity of meaning and probability of meaning sounds very similar
to the distinction between the Bayesian and frequentist interpretations of
probability (as I understand elasticity of meaning, the former
encapsulates it while the latter does not - perhaps you can convince me
otherwise).
Regards,
Konrad
Dr Konrad Scheffler
Computer Science Division
Dept of Mathematical Sciences
University of Stellenbosch
+27-21-808-4306
http://www.cs.sun.ac.za/~kscheffler/
On Mon, 21 Jul 2008, Lotfi A. Zadeh wrote:
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
Re: [UAI] Computation with Imprecise Probabilities--The problem of Vera's age
Dear Prof Zadeh, Perhaps you could elucidate what you mean by cointensive? (I assume this is explained in detail in your paper, but I also assume that one purpose of your post here is to convince people that it will be worth investing the time to read the paper.) Also, what do you understand under probability? Your distinction between elasticity of meaning and probability of meaning sounds very similar to the distinction between the Bayesian and frequentist interpretations of probability (as I understand elasticity of meaning, the former encapsulates it while the latter does not - perhaps you can convince me otherwise). Regards, Konrad Dr Konrad Scheffler Computer Science Division Dept of Mathematical Sciences University of Stellenbosch +27-21-808-4306 http://www.cs.sun.ac.za/~kscheffler/ On Mon, 21 Jul 2008, Lotfi A. Zadeh wrote: 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 http://dx.doi.org/10.1016/j.ins.2008.02.012). 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 http://www.aaai.org/ojs/index.php/aimagazine/article/view/1778/1676). 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. p_1 : Vera has a daughter in the mid-thirties; p_2 : Vera has a son in the mid-twenties; and p_3 (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, M_1 , 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, p_1 precisiates as: Vera has a 35 year old daughter; p_2 precisiates as: Vera has a 25 year old son; and p_3 precisiates as mother's age at the birth of her child varies from 20 to 40. Precisiated p_1 constrains the age of Vera as the interval [55, 75]. Since p2 is not independent of p_1 , precisiated p_2 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 p_1 while the upper bound is determined by the upper bound in p_2 . A higher level of cointension may be achieved by moving from M_1 to M_2 . In M_2 , 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
