Alright, syntax. Things are gonna get a bit more… convoluted? Nah, interesting! In principle we’ll see a lot of the same things as in phonology, and that’s kind of the point: phonology and syntax are actually very similar. But syntax isn’t quite as exhibitionist as phonology, it doesn’t show off its subregular complexity in the open for the world to see. So the first thing we’ll need is a suitable representation. Once we have that, it’s pretty much phonology all over again, but now with trees.

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After a brief interlude, let’s get back to locality. This post will largely act as a recap of what has come before and provide a segue from phonology to syntax. That’s also a good time to look at the bigger picture, which goes beyond putting various phenomena in various locality boxes just because we can.

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The previous post covered the essentials of strictly local (SL) and tier-based strictly local (TSL) dependencies over strings. We saw that even though TSL generalizes SL to a relativized notion of locality, it is still a restrictive model in the sense that not every non-local dependency is TSL. In principle that’s a nice thing, but among those non-local dependencies beyond the purview of TSL we also find some robustly attested phenomena like unbounded tone plateauing. Fair enough, but that does not mean that unbounded tone plateauing is entirely non-local.

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Omer has a recent post on listedness. I have a post coming up that expands on my comments there, but it isn’t really fit for consumption without prior knowledge of subregular complexity and how it intersects with the linguistic concept of locality. So I figured I’d first lead in with a series of posts as a primer on some of the core concepts from subregular complexity. I’ll start with phonology — for historical reasons, and because the ideas are much easier to grok there (sorry phonologists, but it’s a playground compared to syntax). That will be followed by some posts on how subregular complexity carries over from phonology to syntax, and then we’ll finally be in a position to expand on Omer’s post. Getting through all of this will take quite a while, but I think it provides an interesting perspective on locality. In particular, we’ll see that the common idea of “strict locality < relativized locality < non-local” is too simplistic.

With all that said, let’s put on our computational hats and get going, starting with phonology. Or to be more specific: phonotactics.

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I promised, and you shall receive: a KISS account of a particular aspect of semantics. Remember, KISS means that the account covers a very narrowly circumscribed phenomenon, makes no attempt to integrate with other theories, and instead aims for being maximal simple and self-contained. And now for the actual problem:

It has been noted before that not every logically conceivable quantifier can be realized by a single “word”. Those are very deliberate scare quotes around word as that isn’t quite the right notion — if it can even be defined. But let’s ignore that for now and focus just on the basic facts. We have every for the universal quantifier \(\forall\), some for the existential quantifier \(\exists\), and no, which corresponds to \(\neg \exists\). English is not an outlier, these three quantifiers are very common across languages. But there seems to be no language with a single word for not all, i.e. \(\neg \forall\). Now why the heck is that? If language is fine with stuffing \(\neg \exists\) into a single word, why not \(\neg \forall\)? Would you be shocked if I told you the answer is monotonicity? Actually, the full answer is monotonicity + subregularity, but one thing at a time.

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