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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:[...] that's the direction where I think the solution lies: iteratively uniting two predicates into one, with a method for indicating which argument-places merge into a single argument-place, ideally without having lexicosyntactically *explicit* variables filling argument-places. E.g. F(a,b) and G(c,d) merge into a compound predicate H(a,b=c,d). (My own unpublished solutiontakes this approach, with an inflectional machinery for encoding how two argument lists (e.g.<a, b> & <c, d>) merge into one (e.g.<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. This number grows pretty fast with n, http://en.wikipedia.org/wiki/Bell_numbers but I guess you must have some way of compositionally creating the inflections so they are manageable,
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. 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. That must be an easyish formula to find for somebody with more maths nous than me. And yes, the inflections are compositional. --And.