A family of grammars for Voynichese

[Mauro]

I have no clue on how to solve the problem of ‘consistency’. Yeah, I could put logarithms or exponents or anything else into the formula until it ‘behaves’, but those would all be ad-hoc fixes: that is to say, a probably useless/futile exercise.  What would be needed is a formula which can be justified rationally, on basic principles (it might also use different ‘X’ variables, of course), but I fear that’s well beyond my math skills.
Should anyone be interested in this obscure problem: any ideas? Remarks? Maybe just settle for F1 score and grammars binned somehow by coverage? But in that case, how the binning should be done, without risking to introduce a personal bias? Thank you for any comments/answers!

I still have very poor grasp of what question would these grammars address, so I definitely have no answer. But maybe if we try with a simple example, where it's possible to enumerate all slot grammars and identify which one of them looks more useful and why, then we can at least qualitatively identify what we are looking for and start talking about numeric metrics. Also this short exercise will let me check whether my understanding of your approach is correct, if you don't mind spending a minute on it.

First let's consider two grammars that have the same set of metrics: coverage, efficiency and the number of elements, and try to see whether we can say that one is better than the other (again, I have no answer to this).

Suppose we have the following set of words: AB, ABC, BC, AC, BA, BAB. Let's say, I'm trying to analyze it using a slot grammar. The degenerate grammars that you mentioned are [A|B|C|∅] [A|B|C|∅] [A|B|C|∅] (any letter in each slot), or [AB|ABC|BC|AC|BA|BAB] (all words in a single slot, 6 elements in 1 slot). These are not interesting, they won't tell us anything. There are not that many non-trivial slot grammars that we can have for this text.

Perfect, you got it right.

Let's compare two grammars that, if I get it right, have the same statistics when it comes to coverage, efficiency and the number of elements:

[B|∅][AB|B|A][C|∅], this one can produce 12 strings: BABC, BAB, BBC, BB, BAC, BA, ABC, AB, BC, B, AC, A, covers the whole text and has 7 elements in 3 slots.

[BA|A|B][A|B|BC|C], this one can produce 12 strings as well: BAA, BAB, BABC, BAC, AA, AB, ABC, AC, BA, BB, BBC, BC, it covers the whole text and has the same stats as above, but with 7 elements in 2 slots

Is any one of these grammars better than the other in any way?

The example is right. In this case I would say those two grammars are equivalent in all respects (the number of slots I think is irrelevant).

Are they better than the trivial 6 elements in 1 slot grammar?

Sure they are, they are not trivial, they actually say something about the structure of words AB, ABC etc., using less information.

 and if so, what exactly is their advantage when it comes to the analysis of the text? I have troubles understanding this. Yes, intuitively these grammars seem “interesting”, they have many different elements, and one could try to guess some interactions, but I still have no idea how they can be practically used to analyze text properties quantitatively and so how to evaluate their usefulness.

[Edit]: I just realized, that my main point got diluted in the text, so I'll try to reiterate: as far as I understand, we can only have a satisfactory quantitative metric for the quality of a grammar if it's tied to some quantitative task wrt the text. If we identify this task, then we can try to work backwards from it to the properties of grammars and find a grammar that would solve this task better. However, I'm still in the woods when it comes to understanding the simple question of what this task is exactly ¯\_(ツ)_/¯

Ah that's the good question. I'll try to be as schematic as possible:

- The VMS has a word structure which is remarkable and unheard of.
- So it's very probable the word structure has something to do with the method used to write it (be it a meaningful or meaningless text, does not matter).
- So getting a better grab on this structure should be of help in studying VMS (and many people have tried to do this since, I don't know exactly, the 60s?). Will this be enough? I very much doubt it, but who knows
- It's very difficult to say if a grammar is 'good'. But having a reliable method to rank them according to some factor would help.

Once one has settled on a grammar the task could be "imagine what the word structure could encode and how, then try demonstrate it does". Very, very difficult. Btw I tried again to try to 'decode' Voynich as a Latin syllabary (by trying to fit the more common Voynich words to the most common Latin ones). Nada de nada, it does not work at all. But that was just one possibility, the problem is there are too many of them