Linas, Nil, etc. -- This variation of type theory
http://www.dcs.kcl.ac.uk/staff/lappin/papers/cdll_lilt15.pdf seems like it may be right for PLN and OpenCog ... basically, dependent type theory with records (persistent memory) and probabilities ... If we view PLN as having this sort of semantics, then RelEx+R2L is viewed as enacting a morphism from: -- link grammar, which is apparently equivalent to pregroup grammar, which is a nonsymmetric cartesian closed category to -- lambda calculus endowed with the probabilistic TTR type system, which is a locally cartesian closed category https://ncatlab.org/nlab/show/relation+between+type+theory+and+category+theory#DependentTypeTheory For the value of dependent types in natural language semantics, see e.g. http://www.slideshare.net/kaleidotheater/hakodate2015-julyslide?qid=85e8a7fc-f073-4ded-a2c8-9622e89fd07d&v=&b=&from_search=1 (the examples regarding anaphora in the above are quite clear) https://ncatlab.org/nlab/show/dependent+type+theoretic+methods+in+natural+language+semantics This paper http://www.slideshare.net/DimitriosKartsaklis1/tensorbased-models-of-natural-language-semantics?qid=fd4cc5b3-a548-46a7-b929-da8246e6c530&v=&b=&from_search=2 on the other hand, seems mathematically sound but conceptually wrong in its linguistic interpretation. It constructs a nice morphism from pregroup grammars (closed cartesian categories) to categories defined over vector spaces -- where the vector spaces are taken to represent co-occurence vectors and such, indicating word semantics.... The morphism is nice... however, the idea that semantics consists of numerical vectors is silly ... semantics is much richer than that If we view grammar as link-grammar/pregroup-grammar/asymmetric-CCC ... we should view semantics as {probabilistic TTR / locally compact closed CCC *plus* numerical-vectors/linear-algebra} I.e. semantics has a distributional aspect AND ALSO a more explicitly logical aspect Trying to push all of semantics into distributional word vectors, leads them into insane complexities like modeling determiners using Frobenius algebras... which is IMO just not sensiblen ... it's trying to achieve a certain sort of mathematical simplicity that does not reflect the kind of simplicity seen in natural systems like natural language... Instead I would say RelEx+R2L+ECAN (on language) + word-frequency-analysis can be viewed as enacting a morphism from: -- link grammar, which is apparently equivalent to pregroup grammar, which is a nonsymmetric cartesian closed category to the product of -- lambda calculus endowed with the probabilistic TTR type system, which is a locally cartesian closed category -- the algebra of finite-dimensional vector spaces This approach accepts fundamental heterogeneity in semantic representation... -- Ben -- Ben Goertzel, PhD http://goertzel.org Super-benevolent super-intelligence is the thought the Global Brain is currently struggling to form... -- 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 opencog+unsubscr...@googlegroups.com. To post to this group, send email to opencog@googlegroups.com. 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/CACYTDBdon6m8Vc8JN8Xt%3Dge3O1iQOPQ-yVL%2BZc%2Bjizt7S7S8%2Bw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
