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Linguistics Using Category Theory (2018)

golem.ph.utexas.edu

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Re: Linguistics Using Category Theory (2018)

#21

Post by crimsonalucard »

igravious wrote: post #11
crimsonalucard wrote: post #2

I'm starting to study category theory and I'm realizing if there exists a formal theory around 'design' and 'abstraction' category theory is it. I could be wrong though. What do you guys think?

Not to be glib; it depends what you mean by 'design' and 'abstraction', doesn't it?

The design and abstraction of systems.

So usually we "design" one possible system out of many to solve a problem in a solution space we do not completely understand.

Once a formal axiomatic theory is in place it could very well become "deriving" the best system to solve a problem in a solution space we completely understand.

Of course it's likely not that simple and likely there is no singular "best" solution but a theory, in my opinion, would quantify all possible tradeoffs between a subset of "best" solutions out of all possible solutions.

Category theory seems to be the closest thing to such a theory I have found. I'm a beginner in learning this stuff though. So far I'm guessing that it's more than likely that there are no algorithms within category theory that can be used to optimize systems or even derive one... but it is the closest thing to such a theory that I have uncovered? My question in the initial post was asking whether or not anyone has found anything better....

Some posters have remarked that the movement of category theory into engineering (a field which is largely involved with designing solutions more-so than deriving solutions) is starting to happen.

Re: Linguistics Using Category Theory (2018)

#22

Post by crimsonalucard »

notfashion wrote: post #5
codekilla wrote: post #4

Earlier quoted context omitted.

Jean-Pierre Marquis, in his contribution to the volume "What is Category Theory", wrote: 'Category theory is the Architectronic of Concepts'. I think this is the best way I have heard it put.

Here's the quote: "Once category theory was developed and used, in particular when the central theoretical role played by adjoint functors was understood, a fascinating process of reversal of perspective, a gestalt switch, took place: what was seem as a useful tool in organizing and guiding mathematical thought became a theoretical framework that revealed the basic or fundamental principles underlying mathematical co…

Is there anything more fundamental than mathematics though? If category theory represents the mathematical aspect of design and mathematics is fundamental to the universe then perhaps category theory is a fundamental theory of design.

There's got to be counter-examples of good system design where category cannot be applied.

Re: Linguistics Using Category Theory (2018)

#23

Post by rgoulter »

willis936 wrote: post #6

Even if a mathematical definition of a sandwich is presented, it is very unlikely to have majority support in localities of any size (down to two individuals).

In your particular example, I like the cube rule (e.g. to answer 'is a hotdog a sandwich?')

EDIT: http://cuberule.com/

Re: Linguistics Using Category Theory (2018)

#25

Post by proc0 »

crimsonalucard wrote: post #2

I'm starting to study category theory and I'm realizing if there exists a formal theory around 'design' and 'abstraction' category theory is it. I could be wrong though. What do you guys think?

If we define abstraction as hiding the unnecessary in order to reveal the essentials, and we take it to an extreme such that we reduce everything to a point and only talk about relationships of the point, then yes I completely agree. CT is the math of abstraction, from which I think composition arises (since you cannot look inside an object).

Re: Linguistics Using Category Theory (2018)

#26

Post by codekilla »

notfashion wrote: post #5
codekilla wrote: post #4

Earlier quoted context omitted.

Jean-Pierre Marquis, in his contribution to the volume "What is Category Theory", wrote: 'Category theory is the Architectronic of Concepts'. I think this is the best way I have heard it put.

Here's the quote: "Once category theory was developed and used, in particular when the central theoretical role played by adjoint functors was understood, a fascinating process of reversal of perspective, a gestalt switch, took place: what was seem as a useful tool in organizing and guiding mathematical thought became a theoretical framework that revealed the basic or fundamental principles underlying mathematical co…

No, in the article I'm referencing he goes further, to concepts. It's here: https://www.amazon.com/What-Category-Theory-Giandomenico-Sic...

I had confused in my mind -tectonic with a phrase from another book I admire: https://www.amazon.com/Between-Two-Ages-Americas-Technetroni.... I guess that's what I get for not double-checking; and you get a random book link :)

Re: Linguistics Using Category Theory (2018)

#27

Post by fapjacks »

codekilla wrote: post #26
notfashion wrote: post #5

Earlier quoted context omitted.

Here's the quote: "Once category theory was developed and used, in particular when the central theoretical role played by adjoint functors was understood, a fascinating process of reversal of perspective, a gestalt switch, took place: what was seem as a useful tool in organizing and guiding mathematical thought became a theoretical framework that revealed the basic or fundamental principles underlying mathematical co…

No, in the article I'm referencing he goes further, to concepts. It's here: https://www.amazon.com/What-Category-Theory-Giandomenico-Sic... I had confused in my mind -tectonic with a phrase from another book I admire: https://www.amazon.com/Between-Two-Ages-Americas-Technetroni... . I guess that's what I get for not double-checking; and you get a random book link :)

However thanks for not using referral/affiliate links. :)

Re: Linguistics Using Category Theory (2018)

#28

Post by YeGoblynQueenne »

notfashion wrote: post #15
YeGoblynQueenne wrote: post #14

Earlier quoted context omitted.

>> -tectonic (from the Greek for carpenter) "Tecton" ("τέκτων") is probably best translated as "mason". It has the connotation of a builder who works with stone, so a stone-mason. It is also the more official name of freemasons (colloquially known as "μασώνοι", a Greek transliteration of "masons"). Grammatically, "τέκτων" is the gerund of the verb "τίκτω", meaning "to give birth". So a more literal interpretation is…

Hmmm, I have a strange sense of deja vu in replying to this comment. There is https://en.wikipedia.org/wiki/Tekt%C5%8Dn which broadly supports your first paragraph. On the other hand, in architecture, tectonics is usually contrasted with stereotomics. Tectonics is concerned with framing, stereotomy with compressive masses. The former is paradigmatically a branch of carpentry, the latter part of stone-masonry. This is…

Re the deja-vu. Maybe I have made the same comment on "τέκτων" before. Sorry, I can't remember. I write way too much on HN.

The wikipedia page you link favours the "wood-worker" translation, so you are probably right and I'm wrong, but I have to say that Greek _is_ my language and "τέκτων" just doesn't sound anything like "wood-worker" to me. It's probably just my modern ears. Thanks for correcting me and apologies for opining on something I don't understand that well after all (the etymology of the word).

Re: Linguistics Using Category Theory (2018)

#29

Post by jesuslop »

WaxProlix wrote: post #18

Chris Barker of NYU does a lot of category theory and linguistics work. I remember a colloquium or two which did good work in talking about modeling certain semantic structures in monad terms. I remember it because at the time I liked the idea of keeping a monadically updated 'context' node (at or above C) in an otherwise fairly orthodox Chomskyan x-bar framework to start modeling the syntax-semantics interface, but…

That colloquium looked nice, I assume no slides are available? Barker is anouncing another seminar on deep learning and semantics, that looks intriguing from the attached public materials. I think that compsci furnishes ideas from formal language parsing that can be toy models of fragments of natural languages, Montague made a case in favour of formalizability. Wadler investigated monadic parsing and this can be an entry point for what is happening in linguistics. I have as reference arXiv:cs/0205026v1

added: on Barker seminar day 4 I see CCG derivations that are a close formalism of pregroup grammars used in the original post, nice to see this concurrently with nnets talk.

Re: Linguistics Using Category Theory (2018)

#30

Post by willis936 »

rgoulter wrote: post #23
willis936 wrote: post #6

Even if a mathematical definition of a sandwich is presented, it is very unlikely to have majority support in localities of any size (down to two individuals).

In your particular example, I like the cube rule (e.g. to answer 'is a hotdog a sandwich?') EDIT: http://cuberule.com/

Then subs are tacos and not sandwiches? I would disagree.

The definition I like for sandwich is “A set of materials in the configuration ABA, mated along their longest side”. It holds up in contexts outside of food, that the word “sandwich” is sometimes used in, and is valid in dimensionalities other than 3.

The sub issue remains though. Semantically, it could be argued that subs are sandwiches that have not had their end fully cut.

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