Yaguello is always a problem for conlangers, but she does tend to focus on philosophic languages, which are a bit more neurotic than most (though a case can be made about loglans). The conlangs with purposes like PoohBahing a story (but the ones for which stories are created may be a different case) and the one created purely as aesthetic objects are easier to accept, as are the one that purport to be intended to test some hypothesis of some sort (often, but not always, linguistic or at least social scientific -- which is to science what social disease is health). Bliss was probably demonstrably loony -- of a rather nasty sort -- but his language is not really all that bad, Weilgart is a better case for a loony language, except for the tradition of philosophic languages (I don't think he really believed he got it from a space man, it was just a good contemporary trope).
Mathematics is a branch of Logic (see Principia Mathematica). But the 'pilin' problem keeps popping up -- maybe some new word will come along to help it.
EBNFs for natural languages are very hard to do, as are any sort of formal grammars, but they can be done (I forget what the outer limit of BNFs is in the spectrum of grammars, but I think it can be extended to cover most of the possibilities). In any case, most conlangs have relatively straightforward EBNFs. Loglans maybe special in that they have actually worked out EBNFs and the other grammars and tend to stick with the results.
Thanks for POP. I have to check its procedures a bit, since it seems to hedge a bit on the most general principle (that is, it uses semantic and pragmatic data to identify words, which is OK in practice but screws up the grammar).