As you might know, I love reanalyzing linguistic phenomena in terms of monotonicity (see this earlier post, my JLM paper, and this NELS paper by my student Sophie Moradi). I’m now in the middle of writing another paper on this topic, and it currently includes a section on freezing effects. You see, freezing effects are obviously just bog-standard monotonicity, and I’m shocked that nobody else has pointed that out before. But perhaps the reason nobody’s pointed that out before is simple: my understanding of freezing effects does not match the facts. In the middle of writing the paper, I realized that I don’t know just how much freezing effects limit movement. So I figured I’d reveal my ignorance to the world and hopefully crowd source some sorely needed insight.

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Sometimes students get hung up on the difference between substring and subsequence. But the works of Edgar Rice Burroughs have given me an idea for an exercise that might just be silly enough to permanently edge itself into students’ memory.

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Omer has a great post on gradience in syntax. I left a comment there that briefly touches on why gradience isn’t really that big of a deal thanks to monoids and semirings. But in a vacuum that remark might not make a lot of sense, so here’s some more background.

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Outdex posts can be a dull affair, always obsessed with language and computation (it’s the official blog motto, you know). Today, I will deviate from this with a post that’s obsessed with, wait for it, computation and language. Big difference. Our juicy topic will be regular expressions. And don’t you worry, we’ll get to the “and language” part.

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Last time I gave you a piece of my mind when it comes to the Kuratowski definition of pairs and ordered sets, and why we should stay away from it in linguistics. The thing is, that was a conceptual argument, and those tend to fall flat with most researchers. Just like most mathematicians weren’t particularly fazed by Gödel’s incompleteness results because it didn’t impact their daily work, the average researcher doesn’t care about some impurities in their approach as long as it gets the job done. So this post will discuss a concrete case where a good linguistic insight got buried under mathematical rubble.

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As some of you might know, my dissertation starts with a quote from My Little Pony. By Applejack, to be precise, the only pony that I could see myself have a beer with (and I don’t even like beer). You can watch the full clip, but here’s the line that I quoted:

Don’t you use your fancy mathematics to muddy the issue.

Truer words have never been spoken. In light of my obvious mathematical inclinations this might come as a surprise for some of you, but I don’t like using math just for the sake of math. Mathematical formalization is only worth it if it provides novel insights.

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Bill Idsardi brought this to my attention. Enjoy your reading!

Star-Free Regular Languages and Logic

on the Gödel’s Lost Letter and P=NP blog.

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Here’s another quick follow-up to the unboundedness argument. As you might recall, that post discussed a very simple model of syntax whose only task it was to adjudicate the well-formedness of a small number of strings. Even for such a limited task, and with such a simple model, it quickly became clear that we need a more modular approach to succinctly capture the facts and state important generalizations. But once we had this more modular perspective, it no longer mattered whether syntax is actually unbounded. Assuming unboundedness, denying unboundedness, it doesn’t matter because the overall nature of the approach does not hinge on whether we incorporate an upper bound on anything. Well, something very similar also happens with another aspect of syntax that is beyond doubt in some communities and highly contentious in others: syntactic trees.

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Ignas Rudaitis left a comment under my unboundedness post that touches on an important issue: the interaction of unboundedness and the poverty of the stimulus (POS). My reply there had to be on the short side, so I figured I’d fill in the gaps with a short follow-up post.

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Jon’s post on the overappreciated Marr argument reminded me that it’s been a while since the last entry in the Underappreciated arguments series. And seeing how the competence-performance distinction showed up in the comments section of my post about why semantics should be like parsing, this might be a good time to talk one of the central tenets of this distinction: unboundedness. Unboundedness, and the corollary that natural languages are infinite, is one of the first things that we teach students in a linguistics intro, and it is one of the first things that psychologists and other non-linguists will object to. But the dirty secret is that nothing really hinges on it.

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