Return-Path: Received: from SEGATE.SUNET.SE by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #1) id m0tI3k9-0000ZUC; Wed, 22 Nov 95 03:12 EET Message-Id: Received: from listmail.sunet.se by SEGATE.SUNET.SE (LSMTP for OpenVMS v1.0a) with SMTP id 80B07D4B ; Wed, 22 Nov 1995 2:12:57 +0100 Date: Tue, 21 Nov 1995 19:10:44 -0600 Reply-To: "Steven M. Belknap" Sender: Lojban list From: "Steven M. Belknap" Subject: fuzzy truth To: Veijo Vilva Content-Length: 5081 Lines: 116 I would still like to be able to say something like: The food at Le Francais in Wheeling Illinois is 8ish on a 0 to 9 scale. It is possible that there is some easy way to do this already in lojban, although I haven't seen any posts that quite get at what I want to do. As I've written before, I believe this issue of fuzziness is important because it is closer to how most people actually think about the world. Often people are forced into an Aristotlean straitjacket which does not correspond to what they mean. For example, using the legal setting: "Did you or did you not see the defendant defenestrate the errant politician?" Now, perhaps I saw some shadows which on a 0 to 7 scale I am 4ish certain corresponded to the defendant and the errant politician, and suppose I saw these shadows perform the alledged defenestration to certainty 3ish on a 0 to 4 scale. If I attempt to answer this question yes/no, I will be dissatisfied with my answer. If I equivocate, I will be accused by the obnoxious lawyer that I am equivocating, and he will attempt to force me into a falsely dichotomous Aristotlean universe of reply. It would be nice if fuzzy replies would elegantly, compactly allow for this sort of thing. There have been several objections: 1. People don't think this way. This is the way computers handle fuzziness. The use of numbers in my examples is not meant to imply exactness-these numbers are fuzzy. One example I see in my medical practice is when I ask a patient to describe the severity of pain. "How bad does it hurt?" "Well, doc, its about a 3 on a 1 to 10 scale." My patient does not mean its *exactly* 3. He is using a fuzzy concept. Several years ago we did a study where we evaluated the degree of euphoria experienced by an addict after a cocaine injection. For this purpose we used a visual analogue scale, in which the subject drew a dot on a fixed line corresponding to the intensity of euphoria, where the leftmost position corresponded to "not at all" and the right most corresponded to "Most euphoric possible." Despite the obvious subjectiveness of this, addicts mapped out a sequence of points over time describing a smooth curve that could be modeled with a pharmacokinetic/pharmacodynamic model based on cocaine concentration in the blood and acute tolerance, which resulted eventually in a publication to this effect. We showed that the degree of euphoria wears off faster than the cardiac effects, which may explain why addicts redose with cocaine before they recover completely and thus inadvertently kill themselves. People *do* think this way, or perhaps more accurately, people *can* think this way. 2. We can handle this with a sequence of je' things, as suggested by xorxes: je'ucai je'u(sai) je'uru'e je'ucu'i je'unairu'e je'unai(sai) je'unaicai There are two problems with these types of schemes: First, the granularity is fixed. If I want to use a 3 point fuzzy scale (yes, maybe, no) for reasons of being purposely less precise than a 5 point fuzzy scale, (yes, probably, maybe, possibly, no) then I can't get across the intentional choice of greater granularity of my reply with the je' schemes. Second, there is no specification of ordinality. I think ordinality is quite useful, as it seems important in expressing fuzziness. Je'uru'e and the other je' things are not obviously distributed in an even way along the truth scale. 3. You can actually say what you mean in lojban quite exactly by stating the whole thing in mathematical terms. I want to include ordinality, fuzziness, and granularity in my fuzzy statements. Expressing all three concepts with the lojban constructs I know is longwinded, unwieldy, and probably incomprehensible. I doubt that such constructions would be used very often. Because lojban is based on the predicate calculus, logic, and careful attention to semantics, I think lojban is potentially vulnerable to this problem of one speaker forcing false dichotomies on other speakers, and that a rich fuzzy logic mechanism is required. I remember discussing this with lojbab when I visited him several months ago, and I came away from our discussion convinced that this would not require any sort of major or even minor change in the language. Maybe using inexact numbers would be a start: li piso'u to li piro The closest gismu for fuzzy would seem to be x1 is a/the hair/| [body-part] of x2 at body location x3 Although seems to be referring to animals (or perhaps the leftover pizza in the back of my refrigerator), couldn't it also be used for the idea of fuzzy sets or fuzzy logic? This would mean a change in the 3 position, as body location is not analogous to body location. Perhaps there could be a better 2 position as well. If this is unsatisfactory, how about a lujvo or le'avla for fuzzy? la stivn Steven M. Belknap, M.D. Assistant Professor of Clinical Pharmacology and Medicine University of Illinois College of Medicine at Peoria email: sbelknap@uic.edu Voice: 309/671-3403 Fax: 309/671-8413