polyadic connectives

["And Rosta" <a.rosta@ntlworld.com>]

There was some recent discussion, instigated by pc, about more-than-binary
connectives. For some, like an extended xor, it's easy to see how to
render them: "exactly one of A, B, C is true". I've got two questions:

1. What connectives make sense when extended to sets of varying size?
(What's the term for what I mean? Commutative functions? Ones where
all arguments are treated alike.)
   * and = all of
   * or  = at least one of
   * extended xor = exactly one of
   * extended iff = all of or none of
   * ... and what else? (apart from negations of these four)

2. Does Lojban have any way of doing "all or none" without resorting to
an explicit disjunction? For example, is there a way of saying "more
than none and less than all", without the conjunction?

--And.