Joe Pfeiffer <pfeiffer@cs.nmsu.edu> wrote in message news:<1blml3okx3.fsf@cs.nmsu.edu>...> (ah, I found the response on Google....)
I'm having the same sort of problem. Oh, well...>> From: S. F. Thomas (sf.thomas@verizon.net) >> Subject: Re: Thomas' Fuzziness and Probability >> Newsgroups: comp.ai.fuzzy, sci.stat.math, sci.stat.edu >> Date: 2001-07-31 10:06:05 PST >> >> I like the term semantic likelihood because it gets to the heart >> of the matter in my view. In a non-calibrational setting, eg. the >> use of the term "tall" by a rape victim in court to describe the >> height of her attacker, it is the calibrational response >> uncertainty in terms purely of language-use, that leads to >> semantic uncertainty about the precise height to which she >> refers. The semantic likelihood function traces out the relative >> possibility of various height-value hypotheses consistent with >> her description of her attacker as "tall". In ordinary discourse >> and comprehension, we don't need to have it spelt out, obviously. >> But is in some sense there. > > I think this is the step I'm having a hard time with. It is > absolutely not intuitive to me that the probability that someone will > be referred to as tall is an accurate description of the extent to > which they are tall...
I suspect it might help for you to go the other way. The witness describes the attacker as "tall". The witness is just another random, supposed competent, speaker of the language. In a calibrational setting, we have traced out, for various height values ranging from, say, 5 ft. to 8 ft. the use of the term "tall" (prob. that the term "tall" would be affirmed as a valid descriptor for the height u) to describe each height value in turn, based on yes/no responses from a random sample of supposed competent speakers of the language. Let u be the variable ranging on this universe of height values, and let mu[TALL](u) denote the probability that a random speaker of the language would use the term "tall" to describe the height value u in the context of men's heights. It is clear that mu[TALL] ranges on the [0,1] interval, and it is easy to imagine that it has a value of 0 at 5ft., increasing to a value close to 1 at 6 ft. and definitely 1 at 6ft6in and above. Now ask what could the witness "mean", in terms of her intended restriction on the unknown height value corresponding now to her unknown attacker. You argue backwards, and apply a weight of relative possibility, or likelihood, for every candidate value u for that unknown height, x, say, equal to mu[TALL](u), for u varying on the relevant domain. Call it semantic likelihood, call it relative possibility, call it membership, call it what you want. But it is precisely because random competent speakers of the language vary in their usage of the term "tall", that there are varying degrees of likelihood/possibility/membership for what the speaker could mean in any non-calibrational setting such as testifying in court. The fact that there is at best some probability that any given speaker would use the term "tall" to refer to any given u, is what leads to the fuzziness in the inferences allowed by the use of the term. And that fuzziness is mapped by what may be called a semantic likelihood function. In this set-up, the "extent to which someone is tall" is deemed to be simply the likelihood that a random, competent speaker of the language would use the term tall to describe the height value for which that someone is an exemplar. I hope that helps. Regards, S. F. Thomas