We’re continuing our stroll through the subregular locality zoo, still in the service of ultimately being able to say something about syntax and its interface with PF and LF. We started out with SL as the most restrictive kind of locality. The step to the TSL region corresponds to a relativized notion of locality where it’s not absolute locality that matters, but your position relative to other elements of a specific type. TSL is actually a cluster of different classes, with standard TSL at the very bottom. Depending on what context information the TSL tier projection may take into account, TSL expands to ITSL, OTSL, or IOTSL. While IOTSL has a very liberal notion of locality that can even accommodate insane patterns like nati, it still involves some level of locality. That’s in stark contrast to the strictly piecewise (SP) dependencies of Rogers, Heinz, Bailey, Edlefsen, Vischer, Wellcome, and Wibel (2010), which throw locality out the window.

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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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I just got back from MOL (Mathematics of Language) in Toronto, and much to my own surprise I actually got to talk some more about KISS theories there. As you might recall, my last post tried to made a case for more simple accounts that try to handle only one phenomenon but do so exceedingly well without the burden of machinery that is needed for other phenomena. My post only listed two examples for syntax as I was under the impression that this is a rare approach in linguistics, so I didn’t dig much deeper for examples. But at MOL I saw Yoad Winter give a beautiful KISS account of presupposition projection (here’s the paper version). That’s when it hit me: in semantics, KISS is pretty much the norm!

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Here’s a question I first heard from Hans-Martin Gärtner many years ago. I don’t remember the exact date, but I believe it was in 2009 or 2010. We both happened to be in Berlin, chowing down on some uniquely awful sandwiches. Culinary cruelties notwithstanding the conversation was very enjoyable, and we quickly got to talk about linguistics as a science, at which point Hans-Martin offered the following observation (not verbatim):

It’s strange how linguistic theories completely lack modularity. In other sciences, each phenomenon gets its own theory, and the challenge lies in unifying them.

Back then I didn’t share his sentiment. After all, phonology, morphology, and syntax each have their own theory, and eventually we might try to unify them (an issue that’s very dear to me). But the remark stuck with me, and the more I’ve thought about it in the last few years the more I have to side with Hans-Martin.

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Come and listen to the Vision of the Avengers, who has saved this planet thirty-seven times. Listen to his story of P vs. NP. No, seriously, the following is an excerpt on complexity theory from Tom King’s Vision.

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True to my academic lineage, I’m a big fan of Minimalist grammars (MGs): they are a pretty malleable formalism, their core mechanisms are very easy to grasp on an intuitive level, and they are close enough to current minimalist syntax to allow for interesting computational insights into mainstream syntax. However, I often find that MGs’ charms don’t work that well on my more NLP-oriented colleagues — especially when compared to some very close cousins like TAGs or CCGs. There are very practical reasons for this, of course, but two in particular come to mind right away: the lack of any large MG corpus (and/or automatic ways to generate such corpora) and, relatedly, the lack of efficient, state-of-the-art, probabilistic parsers.

This is why I’m very excited about this upcoming paper by John Torr and co-authors (henceforth TSSC), on a (the first ever?) wide-coverage MG parser. The parser is implemented by smartly adapting the \(A^*\) search strategy developed by Lewis and Steedman (2014) for CCGs to MGs (basically, a CKY chart + a priority queue), and coupling it with a complex neural network supertagger trained on an MG treebank.

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Computational linguists overall agree that morphology, with the exception of reduplication, is regular. Here regular is meant in the sense of formal language theory. For any given natural language, the set of well-formed surface forms is a regular string set, which means that it is recognized by a finite-state automaton, definable in monadic second-order logic, a projection of a strictly 2-local string set, has a right congruence relation of finite index, yada yada yada. There’s a million ways to characterize regularity, but the bottom line is that morphology defines string sets of fairly limited complexity. The mapping from underlying representations to surface forms is also very limited as everything (again modulo reduplication) can be handled by non-deterministic finite-state transducers. It’s a pretty nifty picture, though somewhat loose in my subregular eyes that immediately pick up on all the regular things you don’t find in morphology. Still, it’s a valuable result that provides a rough approximation of what morphology is capable of; a decent starting point for further inquiry. However, there is one empirical argument that is inevitably brought up whenever I talk about the regularity of morphology. It’s like an undead abomination that keeps rising from the grave, and today I’m here to hose it down with holy water.

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In an earlier post I looked at privativity in the domain of feature sets: given a collection of features, what conditions must be met by their extensions in order for these features to qualify as privative. But that post concluded with the observation that looking at the features in isolation might be a case of the dog barking up the wrong tree. Features are rarely of interest on their own, what matters is how they interact with the rest of the grammatical machinery. This is the step from a feature set to a feature system. Naively, one might expect that a privative feature set gives rise to a privative feature system. But that’s not at all the case. The reason for that is easy to explain yet difficult to fix.

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