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*To*: John Cowan <cowan@LOCKE.CCIL.ORG>*Subject*: lu'a*From*: "John E. Clifford" <pcliffje@CRL.COM>*Date*: Thu, 3 Aug 1995 19:54:38 -0700*Reply-To*: "John E. Clifford" <pcliffje@CRL.COM>*Sender*: Lojban list <LOJBAN%CUVMB.BITNET@uga.cc.uga.edu>

lojbab: The lu'a series has two origins. One was as a solution for the multiple connectives problem: how do you for example specify a 4 term XOR - pc found that by the time you got to 4 terms that Lojban's grammar did not generate all possible truth-table combinations without repetition and rearranging. But the tough ones could all be expressed using the form "1 from the set {a,b,c}} and 2 from the set {d,e,f}". Hence lu'a. pc: Boy, that stuff about multiple connectives sounds familiar, though the details escape me now. In particular, I am not sure how lu'a fits in: it creats a set from even a sentential structure and then allows quantification over it? lojbab: Then the others were added as a way to disambiguate conversion among sets, masses and indivudals. I can't remember the archetype of this, but it may have been the multiple interpretations of mi'o, do etc as individuals or masses. pc: That looks like a likely source, although the difference between masses and averages -- and probably the distributive sense -- seem to be generating more problems right now. So the question is what these really do do, keeping both the original solutions and yet making the structures as useful as possible. So far, I have just been following the brief entries from the dictionary (often not the clearest help,alas) and trying to make some sense of xorxes' comments. These are becoming more numerous and more detailed, though still examples rather than principles. For example, > lu'i mu lo plise: a set of exactly five apples. This and similar items seem to be no problem: xorxes' interpretation coincides with the one I hypothesized. mu lo plise gives us five apples distributively and lu'i groups them into a set, a five-membered subset of lo'i plise (here we really are forced to use set talk). The set is presumably definite (or is it specific) even though the members have not been identified. Presumably lu'o mu lo plise would mean the five apples were massifed for both of us. But I suspect that lu'a mu lo plise may be treated differently. Indeed, I am not sure how to treat it, because I do not know what the implicit quantifier on lu'a is, ro or su'o. If it is ro, then I would take the lu'a as being redundant, since mu lo plise already takes all the five apples distributively. If lu'a is su'o lu'a then this would distribute only some of the original five. I am unclear how, in that case, lu'a mu lo plise is related to lo mu lo plise (or even le mu lo plise, which seems a particularly useful notion, if I understand it: the old "a" - "the" game in English, though that has better explanations within logic). But I see that this is clearly not what xorxes has in mind: >> lu'a ci le selcku might make sense, bringing us down to a new set >> (assuming that I was calling more than three things selcku originally). >No, to talk about one of the three books one would say {lo ci le selcku}. >{lu'a ci le selcku}, if it makes any sense, should be a component common >to each of the three books in question. I cannot see how lo ci le selcku means "one of the three books"; it seems literally to mean "some of the three things which are among the books," i.e., " at least one of some three of the books," selecting distributively from a selection already made (but not specified) from the specified books. If there were four originally specified books, there are fourteen arrays of books that might be covered by lo ci le selcku, but only four by "one of the three books" (assuming we could figure out what the three books are). But that gets us no nearer to understanding xorxes' lu'a ci le selcku: whence comes this "component common to each of the three books"? There is nothing about that either in ci le selcku, which is just some three books, or in the notion of the members of a set or component of a mass (neither of which ci le selcku refers to anyhow). >> Massification is a logical operation, not a >> Waring blender. >Of course it is. but you don't need to refer to the mass always in terms >of its components. Consider this: > lei pare plise cu gunma i mi citka re lu'a le gunma > The twelve apples are a mass. I eat two components of the mass. >The second sentence should not say that I eat two masses. To say that >I can simply say {mi citka re le gunma}. The whole point of the lu'a >series is that they work on top of the previous gadri. If they are >going to bypass them then there's no point in having them. As to the point, I suspect that the original use was to make sets, masses and distributions from things that did not quite fit those patterns, that did not start with gadri (mi'o was mentioned). And there is the convenient subsetting routine just explored. I don't quite understand the latest example here: lei pare plise cu gunma is analytic, "the mass of (the) twelve apples is a mass." But the second part is very unclear, even given xorxes reading. le gunma refers to all the masses the speaker has in mind, presumably the one mass of 12 apples. lu'a le gunma is then said to be a component common to all of these, i.e., a component, in this case, of the one mass referred to. Ahah! we are to wander through the la'e/sa'e (old style -- what have they become? the symbol for a referent and the referent of a symbol) complex here. That might be very useful, in fact, if it does not interfere with more fundamental uses. But what then becomes of a case where we DO refer to a mass throughits components: what is lu'a le'i pare plise or, worse, lu'a le pare plise? There does not seem to be any components here, since this phrase does not refer beyond itself. But, in fact, we want to get back to the same apples. I'm not convinced that this is a consistent interpretation, as the one I guessed at is (even if useless -- which I don't think it is). > lu'i re lu'o mu lo plise: a set whose two elements are masses > of five apples each. Presents another set of problems, since presumably re lu'o mu lo plise is not legitimate, masses getting at most fractional quantifers (and those only on idiomatic sufferance). Thus, there is no form to add lu'i to. I suspect that somewhere here we have stepped over from making new descriptions to introducing new predicates. There are, of course, many lu'o mu lo plise, since there are many ways to meet the conditions of mu lo plise, but I think to start talking about this multiplicity, we have to introduce gunma. But then I am still unsure just how this is to work. It does seem to offer some useful devices if they can be made to work consistently, but I need some explanation -- or an enormous number of examples -- before I can begin to be convinced. pc>|83

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