Hi Bob, Thanks for the response. Some later date, I would like to talk more. Yes, its the non-Cartesian-ness of it all that I think I now know how to handle. Very briefly: in the original papers on link-grammar (1991-1993), they explained it by drawing pictures of jigsaw puzzle-pieces. One of the pop-sci reports of your work has a diagram of ... jigsaw puzzle pieces. I slapped my forehead. The current realization is that the "jigsaw pieces" are exactly the same thing as the local sections of a sheaf, and so I am busy data-mining those.
As I just discovered a terrible terrible bug in my code (dropped minus sign) earlier today, a month or two of data collection is wiped out. :-( That's life. Back to work, and slightly less conversation, for me, just right now. --linas On Sun, Jul 9, 2017 at 9:44 PM, Bob Coecke <[email protected]> wrote: > Dear Linas, thanks for including me here. One crucial thing about > language is that it manifestly “non-Cartesian”, and may as well be the > total opposite in the spectrum of compositional structures, if one follows > Lambek in the 2000s. The upshot of this is that it gives language a > leading role in a spectrum of theories across many disciplines where these > "anti-Cartesian” structures rule [ :) ]. I have written a couple of > pedestrian/popular papers about this: > > From quantum foundations via natural language meaning to a theory of > everything > https://arxiv.org/abs/1602.07618 > > An alternative Gospel of structure: order, composition, processes > https://arxiv.org/abs/1307.4038 > > and my recent book with Aleks Kissinger, although in 1st order quantum > theory, provides a framework on compositionally that applies equally well > to language (as we explain in some advanced material sections): > > http://www.cambridge.org/pqp > > > On 10 Jul 2017, at 02:44, Linas Vepstas <[email protected]> wrote: > > > > My answer was too brief. Link-grammar is a kind of CCG, where the > morphisms are are given streamlined, less klunky labels, called "types". A > branch of mathematics called "type theory" explains how types and > categories are dual to each other, and how talking about types often > provides a simpler, deeper insight than talking about categories. But they > are the "same thing" in a certain sense. > > > > More precisely, categories have an "internal hom" functor, and that hom > defines the "internal language" of the category. The most famous example is > that the "internal language" of closed cartesian categories is simply-typed > lambda calculus. This can be seen as a form of Curry-Howard correspondence. > John Baez and Bob Coecke have written extensively on this topic; before > them was Lambeck and many others. > > > > Roughly speaking, types describe how morphisms can be composed; they > describe allowed combinations. > > > > I think I wrote previously about how I believe that we can beat other > research: by using what are called "sections of a sheaf" in mathematics, > and are called "disjuncts" in link grammar. Here's why: > > > > Pretty much all work on meaning uses vector spaces (e.g. word2vec, and > so on) and vector spaces are a certain kind of category with a certain kind > of internal language, that we know, a priori, is not quite right for the > categories that describe language. To overcome this limitation, I believe > that by using sections of a sheaf (i.e. link-grammar disjuncts) we can > locally "glue together" the necessary semantic space, in the correct shape, > instead of assuming that it is flat, which is what vector spaces do. > > > > Of course, I am just throwing around big words here. The actual work is > harder, and I just spent the last month creating a dataset which turns out > to have a deep, maybe fatal flaw. Its a lot of work to take a small step. > > > > --linas > > > > > > On Sun, Jul 9, 2017 at 1:23 PM, Linas Vepstas <[email protected]> > wrote: > > Link Grammar is a certain kind of CCG. -- linas > > > > On Sun, Jul 9, 2017 at 6:15 AM, Alex <[email protected]> wrote: > > Probably offtopic - while I am reading about OpenCog community efforts > in NLP, I am quite suspicious about statistical methods. I think that the > only meaningful approach to the NLP ir the combinatory categorial grammars > (Lambek calculus, Montague semantics) and this effort tries to translate > natural language sentences into logical expressions - lambda calculus > expressions. So - if there is connection between Schema as a language of > lambda calculus, then CCGs are the way of translating NL sentences directly > into Scheme structures. Besides CCGs approach uses white box approach and > understanding for the semantics of natural language, these semantical > knowledge can also be encoded as the Scheme/OpenCog structures and can be > learned of enhanced by time. > > > > Of course, raw statistical approach in the end can give the same > results, but structured approach can be more feasible. Besides - > statistical approach yields results that are worth all or nothing. But CCG > approach yields results that are improving step by step and such improving > understanding reflects the human approach to the world and language - > humans progresively learns language, its syntax and semantics. I we have > the slightest doubts about existence of the perfect understanding of the > language then we should also must have doubts about efficiency of the > statistical approach. > > > > -- > > You received this message because you are subscribed to the Google > Groups "opencog" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To post to this group, send email to [email protected]. > > Visit this group at https://groups.google.com/group/opencog. > > To view this discussion on the web visit https://groups.google.com/d/ > msgid/opencog/393b88c8-aadd-456c-bd84-eaac92b55fd8%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. > > > > > > -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. 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