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CONLANG  June 2016, Week 2

CONLANG June 2016, Week 2

Subject:

Re: Category theory, PCA, and demotic cuneiform

From:

Alex Fink <[log in to unmask]>

Reply-To:

Constructed Languages List <[log in to unmask]>

Date:

Tue, 14 Jun 2016 16:01:47 -0400

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (30 lines)

Potentially others on the list will find this interesting anyhow.

On Tue, 14 Jun 2016 11:42:27 +1000, Siva Kalyan <[log in to unmask]> wrote:

>Re your projects (which I’m always excited by):

Aww, thanks.

>1. Was Unlws in any way inspired by category theory? (And is there a category-theoretic formalism for it?) It definitely looks similar to the notion of an “olog” (or “ontology log”) as presented in David Spivak’s “Category Theory for the Sciences” (see https://en.wikipedia.org/wiki/Olog). (Or maybe I’m just seeing category theory everywhere because I’m currently trying to learn it—just starting to struggle with Yoneda's Lemma.)

Good question.  From what I've just read at your Wikipedia link, Unlws is unlike an olog.  In an olog morphisms have predicates on them and vertices refer to objects in the world; in the "modelly" part of Unlws (after And), vertices have predicates on them and edges impose coreference.

But there is category theory everywhere, and Unlws is surely no exception.  It could probably be nicely related to a framework I've seen used in computational attempts to handle semantics which is set in a monoidal category (actually I think researchers in this area use richer formalism, e.g. trying to capture something about syntax with a pregroup, but I haven't completely absorbed it).  Using @ for tensor product, and B for some object, a predicate is a morphism 1 -> B @ ... @ B, with one tensor factor for each operand; coreference is the trace B @ B -> 1 (or maybe they actually use B^* instead of B in some places to make things more natural).  The natural language processing game here is to make B a vector space and try to learn tensor representations for different predicates by principal component analysis on a cooccurrence matrix for the words in your text corpus etc.

>2. Is there a description of how your current phonology generator works? Also, for procedurally generating a grammatical description, I recently had the idea of doing PCA on a typological database of binary features, then taking a random point in feature space and projecting it onto the subspace found by the PCA (and then rounding all fractional feature values or something). I have in fact done such a PCA (with a database much bigger than WALS), and could share it with you if you’re interested.

Current as in Gleb, or current as in the work in progress?

I'm glad that someone is taking an approach like that PCA one.  It's the conceptually correct way to attain a shallow sort of statistical naturalism.  But it is shallow, since typological feature comparison can only be shallow: as far as I can tell, it doesn't particularly help at generating the actual structure of the language, only a few of its consequences.  I do want to generate structure.

I'm also curious about what database you've used.

>3. I notice that for your cuneiform English orthography, you’ve been using the classical Sumerian shapes. For your “demotic cuneiform", you’d probably want to use the simplified Neo-Assyrian style, as seen in fonts such as Assurbanipal (http://www.hethport.uni-wuerzburg.de/cuneifont/download/Assurbanipal.zip).

Wha?  You notice?  I haven't documented it yet!  Actually I did start from the Neo-Assyrian ductus, both for the historical reasons you have in mind and because the much reduced variety of sign shapes make the graphical evolution much simpler to carry out.  My main reference has been the font of Ellermeier and Studt, presented at <www.sumerisches-glossar.de/download/SignListNeoAssyrian.pdf>.

... oh, I know what you're talking about.  In one of my earlier musings I was using Unicode's cuneiform range.  Unicode unifies all the different chronological periods of cuneiform, so the one you're seeing there is determined by the font yòu happen to have installed.  I should probably take that page down; it's out of date wrt the way I write English.

Alex

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