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A Brief Comment upon Gibson(2026a) and Some Other Reflections

1. Primary Comment on Gibson(2026a) Gibson(2026a) argues that dependency grammar (DG) is "the simplest theory of Grammar", and the author's later response to Fujita(2026) ends with the same conclusion.  As many have made the point, the SS-styled PSG has long been discarded by generative linguistics (I use this term instead of the term "Chomskyan generative lingusitics", which is an abomination to me, since if my memory is correct, Chomsky has many times expressed that he's not fond of this personalization, neither do I, there are many people engaging in this rational enquiry) due to its many inadequacies, of which many had already been noticed since Chomsky(1956). The primary reason to reemphasize this point is that I'm not going to spend too much time clarifying the matter concerning these FLT (formal language theory)-related issues. Gibson (2026a) seems to specifically target SS-styled PSG, while a relevant paper cited, Osborne (2018), as evidence s...
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Some Amateur Analysis of the Consequences of the Current AI-math Fever

Disclaimer :  I'm Not a mathematician, merely some guy who's interested in Mathematical linguistics.  Here the term "AI-math fever" refers specifically to the narratives of the form "AI is gonna replace human mathematician", "AI is gonna revolutionize mathematics", "It shall be allowed to use AI (unrestrictedly) to do mathematical researches." etc..   There are at leat three problems along with these narratives:  1. If a mathematical probelm is not solved, we shall first of all ask why it is not solved. It's absolutely absurd to hype over some results without first knowing why the probelm is not solved.  2. That the problems are not solved does not indicate that nobody has been working on the probelms.  It's also well-known that these models are trained on large amounts of data produced by human. H uman mathematicians who are working on the unsolved problems are human.  Thus, the models are trained on (at least some) materials pr...
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Some Sidenotes upon My Tentative Proof of Chomsky(1956)'s Claim concerning FSG.

The Claim : if S has an m -termed dependency set, then at least 2^m   states are necessary for the FSG that generates L. Here is The proof . It's proven based on the Myhill-Nerode Theorem .  I'm working on this simply because:  It's a crucial point in understanding the whole motivation of the development of transformational grammar.  Simply put, for a FSL contains m dependencies, the FSG that could generate it would need at least 2^m such states.  In other words, a FSG with 2^m states could at most generate a FSL with m dependencies.  More generally,  for any finite state grammar, the language it generates shall contain finite number of dependencies. Natural language Grammar, however, has no such upper bound.  It is for this reason that natural language could not be adequately described by the type of FSG defined in Chomsky(1956).  My interactions with people in the field (of linguistics) informed me that there is systematic ignorance of the ...
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Some thoughts on classic optimality theory (Prince & Smolensky 1993/2004)

[This is a term paper of mine, I'm not that familar with OT, thus I cannot guarantee that similar proposals had not been made before , comments are welcome .] Basic structure of classic optimality theory   Generation Function : G(input) = {C1, C2,..., Cn}  Evaluation Function :  E({C1, C2, C3,..., Cn}, Con) = Ck (1<=k<=n);                                        Ck = <In_k , G(in_k)>, In_k is the kth input, 1<=k<=n         To be more precise, G-function could be considered as a function of the form P(g(x), x), in which x is input, g is a generation function that generates an infinite number of outputs,  and P is a pairing function which generates an order pair called candidate, in which an input is paired with its corresponding output. The G-function thus generates an infinite number of candidates, which are inputs to the E-function...
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