From LOJBAN%CUVMB.BITNET@UGA.CC.UGA.EDU Thu Jun 23 08:58:42 1994 Message-Id: <199406231258.AA02305@nfs1.digex.net> Date: Thu Jun 23 08:58:42 1994 Reply-To: i.alexander.bra0125@oasis.icl.co.uk Sender: Lojban list From: i.alexander.bra0125@oasis.icl.co.uk Subject: TECH: nunsucta sidbo To: lojban@cuvmb.cc.columbia.edu Status: RO Some ideas for identifying focus points, "objects of interest", in abstractions. Option 1: The direct approach I've tried expressing some of these "indirect question"-type phrases without using {kau}. I came up with the idea of using {lu'e} to turn "X" into "a symbol for X", as an approximation to "the identity of X". This seems to work reasonably well for some things mi djuno lu'e le klama be le zarci I know the-symbol-for the-one-I-describe-as-a goer to the store I know who goes to the store (instead of mi djuno ledu'u dakau klama le zarci ) but a lot of other types don't yield so easily. For instance, "how many" questions are awkward. mi djuno ledu'u tu'okau da klama le zarci I know how many went to the store There isn't even an ideal gismu which relates a set to the number of elements it has. The best I could find was mi djuno le te kancu be le'i klama bele zarci Even if we can ignore the suggestion of an agent in {kancu}, this is starting to get clumsy, and quantities are one of the things we need good expressions for. Other uses of {kau} are even more problematical, such as {xy. jikau .ybu}. There may be a way of getting this to work, which would free up {kau} for other things such as the "property of X" construction, but it's not clear at the moment. Option 2: Tweak the status quo Option 2a: More UI tags Scrape up another cmavo or two, and/or invent a pseudo-scale for {kau} (kau-kaucu'i-kaunai, or whatever), to extend the possibilities. The situation I'm fairly sure needs a solution is the quantified property - the property of X which is the number of Y in P(X, Y). So if {kaunai} (ugh!) was used to flag the number which we are interested in, and {kau} as in the abstraction paper for the DA whose property we are describing, we could get something like mi zmadu do le ni dakau citka tu'okaunai plise I exceed you in the number of apples we eat. or mi zmadu do le ni dakaunai prami dekau I exceed you in the number of those who love us. While we're at it, we might want to allocate a LUhE for "the number of elements in the set". Option 2b: {kau} vs. non-{kau} Of course there's always my previous idea of using an un-{kau}-ed variable for the lambda-binding and {kau} for the quantity of interest. I don't see shortage of DA being a real problem - a lot of the time you won't even bother putting one into a property abstraction; and occasionally you'll need lots of them, but we've got subscripts to handle that. Option 3: Extend the prenex/quantifier construction The main mechanism in Lojban for introducing bound variables is the prenex, and the way the variable is quantified in the prenex tells what kind of binding is intended. A (frequently implicit) {su'o} introduces an existentially bound variable, an explicit {ro} introduces a universal binding, an ordinary number introduces an exact numerical binding, and most other situations (e.g. a simple pro-sumti or a description with no explicit quantifier) suggest a mere topicalisation. How about we introduce some quantifiers or pseudo-quantifiers for other kinds of binding, such as lambda-binding or number-of binding. This would be more-or-less conventional, and could potentially be extensible to allow things which we've forgotten to be added later. Time for an example. Just using existing syntax, we can say vei ge'o ly. da zo'u da blanu lambda x: x is-blue vei ni bu da zo'u da plise number-of x: x is-an-apple Ultimately this ends up not too different from option 2, since of course you can move the pseudo-quantified variables out of the prenex and into the bridi, and then throw away the prenex, just as we do with the more conventional quantifications. Of course these are unbearably clumsy for everyday use, so we'd probably try and allocate them a couple of the few remaining cmavo (as PA), but in an emergency you could invent a new quantifier on the spot using the long-winded method. If we use {xa'a} for lambda and {xa'i} for number-of, we get xa'a da blanu lambda x: blue(x) xa'i da plise number-of apples xa'i da prami xa'a de lambda y: number-of x: loves(x, y) What's happened to {du'u}, {ka} and {ni} in all this? I'm not sure - they seem to be mutually redundant, but we might retain them all for convenience. pinka fi ko .e'o mu'o mi'e .i,n.