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I'm sending this reply to Engelang rather than Lojban, since it's not about Lojban. Jorge Llamb�as, On 25/08/2012 20:35:
On Fri, Aug 24, 2012 at 5:34 PM, And Rosta<and.rosta@hidden.email> wrote:Jorge Llamb�as, On 15/08/2012 23:13:On Tue, Aug 14, 2012 at 10:55 PM, And Rosta<and.rosta@hidden.email> wrote:E.g. F(a,b) and G(c,d) merge into a compound predicate H(a,b=c,d).I guess that means you need Bell number B(n) of inflections per connective for predicates that together have n arguments.I don't think it is Bell number, since the Livagian system requires 1--1 correspondences between members of the two sets, whereas Bell number seems to be the number of possible correspondence patterns among members of a set.So you can't have F(a,b) and G(c,d) merge directly into H(a=b=c, d).
That's right. You're always adding a simplex predicate to a previously parsed complex or simplex predicate. If you want to merge arguments of the incoming simplex predicate (i.e. for a reflexive reading), you have to merge them with separate arguments of a predicate analogous to Lojban {du}. Now that I've returned to work on Livagian, tho, I might revisit that decision.
Then the nth Bell number is the number of unary mergers that you need for predicates with n arguments, the binary mergers will be fewer (assuming you can make use the unary mergers first). But presumably you could also do the unary mergers in steps, with only two arguments merging at each step, so for an n argument predicate you only need n(n-1)/2 mergers. Which you could also reduce by combining them with argument shuffling operators.
I'm a bit lost by this. The way it works is that the parsed predicate and the incoming predicate each have an ordered list of arguments. You take the first argument off the incoming list and, starting at the start of the parsed list, work your way through the parsed list until you can merge an item with the current item from the incoming list. Once you've merged it, you then take the next item of the incoming list and continue along the parsed list till you can merge, and so forth. (You can also insert it unmerged into the new joint list, but I am simplifying the description in various ways.)
Each member of each of the two sets may be in correspondence with either exactly one member of the other set or no member of the other set. For reasons I won't go into, there are four different sorts of correspondence. So, each member of each of the two sets is either in exactly one sort of correspondence with either exactly one member of the other set or is in no correspondence with any member of the other set.OK, that's a smaller amount of correspondences than I was thinking of.That must be an easyish formula to find for somebody with more maths nous than me.If my calculations (for a single sort of correspondence) are correct: N(n,m) = Sum from i=1 to min(n,m) of n!m! / i!(n-i)!(m-i)! N(n,1) = n N(n,2) = n(n+1) N(n,3) = n(n^2+2) Probably this number has a name, but I don't know what it is. For four sorts of correspondence, it gets more complicated.
Think of it this way: You have n men and m women, each may enter into monogamous heterosexual marriage or may remain single. How many different marriage patterns are there? In the more complicated system, it's the same but with four different sorts of monogamous heterosexual marriage. I might add that in Livagian, predicate stems can be as little as one segment long, but the inflectional apparatus encoding the argument structure for the predicate is usually unavoidably many segments long (one syllable minimum, maybe two or three syllables typically, thousands of syllables potentially). As a viable easy-to-learn, easy-to-use loglang, Xorban is a better choice than Livagian. --And.