A family of grammars for Voynichese

[Mauro]

I think you can find all the answers in my post #14. For an example of how functional element could be identified, see the note in small characters at the end of the point "It's a sillabary".

It's exactly the analysis in post #14 that I have troubles understanding. I still have a very poor comprehension of how a grammar relates to potential features of the text. If I understand this correctly, any list of words can be approximated (?) via any of multiple grammars incompatible between themselves (in a sense that they can generate quite different sets of strings). As far as I can see, almost all proposed grammars generate vastly larger number of word types than those that are actually contained in the manuscript. In this case, I suppose, if it's possible to compute the overlap between all the strings predicted by grammar A and all the strings predicted by grammar B, this overlap would probably represent a very tiny fraction of both spaces. Does this mean that either grammar is likely a very poor model of the underlying text?

[Edit] My understanding of using grammars for Voynichese originally was that they are just to show that there is some structure to the words. For this grammars serve as a good tool. However, unless there is a very tight grammar that, say, covers 95% of the text and only produces less than 10x the number of known words types....

Your remarks are all true and the question you pose is very interesting: I don't have a definitive answer, as post #14 made clear (I'd wish I do!), but I can try to explain how I see it (I'll use an example, because a general explanation would be terribly convoluted). Let me re-work the 'syllabary hypothesis' for my example, I hope it will be enough (and the example does not at all implies I want to propose it as a possible actual solution!).

Say I want to encode the sentence "Voynich manuscript is a hard problem" as a sillabary, so I get "Voy-nich ma-nu-script is a hard pro-blem". Then I devise a weird method for it, for instance I decide to encode VC/CV syllables as I briefly sketched in post #14 (the part you copied). What I did in effect is to define a 'grammar':

SLOT1: the consonant, encoded, say, with the cipher glyphs "ld", "lk", "l", "r", "s" etc. (let's say 16 symbols)
SLOT2: the first vowel, encoded, say, with "a", "ai", "aii", "oi" etc. (let's say 8 symbols)
SLOT3: the last vowel, encoded (because I'm weird) in a different way than before, say "m", "n", "s", "l" etc. (let's say 16 more symbols, they can overlap those of SLOT1)

This grammar will generate 16*8*16 = 2048 different word types.
But in "Voynich manuscript is a hard problem" there are just two CV syllables, so of my grammar of 2048 words I will just use two in my encrypted text.

Does the fact that 2048 is much greater than 2 invalidates the grammar? Surely not, because that's the grammar I actually used for the encoding. [By the way, this opens up the cipher for a decryption attack based on frequencies, slot frequencies in this case, which is reason why, of all the possibilities I listed in post #14, the syllabary is the only one which could be reasonably attacked. Just, and see again post #14, it would be very, very, ... , very difficult to do it]. So, to try an attack on a syllabary by using a slot alphabet grammar, the problem is not 'define a grammar with excellent coverage and efficiency' (that would be auspicable, of course!) but rather "define a grammar with excellent coverage and which makes sense (expecially in the context of late Middle Ages technology and culture) and is not trivial", and by "trivial" I mean something like:

SLOT1: every possible symbol
SLOT2: every possible symbol
SLOT3: every possible symbol

Now this kind of trivial grammar has a very low efficiency, so efficiency does indeed help in discarding from consideration the grammars which are little informative, but it cannot be taken as an absolute requirement, at all.

.... I have little understanding of what we can learn by further refining these loose grammars.

As I said in post #14, unfortunately, the probabilities we can find a 'solution' are about zero. They are about zero both with grammars (any kind of them) and without. But I wouldn't say there is nothing to gain in exploring the grammars path: after all, Voynich words obviously have a (weird) structure, which probably has some function in the manuscript (or, in the case it's a meaningless text, it is some consequence of the pseudo-random method used to generate the gibberish) and even just finding a class of grammars where we cannot say exactly which is the right one, but we can be confident that one of them is probably the correct one, would be a step forward.

It may also open up new lines of inquiry, for instance the hypothesis of a syllabary is usually discarded because there are not enough characters to represent syllables, but the LOOP grammar rescues the hypothesis because it gives a way to encode syllables using few characters (now, that syllables can by encoded by using just few characters is by itself a rather trivial conclusion, but the grammar also gives a framework which fits naturally the manuscript, because it also 'explains' its remarkable word structure).