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    • CommentRowNumber1.
    • CommentAuthoralexis.toumi
    • CommentTimeAug 29th 2019

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthoralexis.toumi
    • CommentTimeAug 29th 2019
    I noticed the nlab did not have a dedicated page for pregroup grammars.
    I'm starting to write down some notes, trying to connect them with what was already there on categorial grammars and linguistics in general.
    • CommentRowNumber3.
    • CommentAuthoralexis.toumi
    • CommentTimeAug 29th 2019

    removing capital letter

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 29th 2019

    It should be pointed out (somewhere, sometime) the relationship between pregroups and residuated lattices, which appears in much older work of Lambek dating back at least to the 60’s. This work of Lambek was all of a piece, connecting module theory to proof theory to linguistics. I would like to add some of this history at some point.

    • CommentRowNumber5.
    • CommentAuthoralexis.toumi
    • CommentTimeAug 30th 2019
    Great suggestion! I don't know so much of the historical details, apart from the original paper from Lambek, The Mathematics of Sentence Structure (1958). There should definitely be a page for the Lambek calculus, residuated monoids and their categorification to biclosed monoidal categories. Some of the details are in Coecke et al, Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus (2013).
    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeSep 2nd 2019
    I would like to know where did this sentence come from: "A sequence of words is grammatical whenever there exists a string diagram going from the sequence of words to the sentence type.", and if there are any references and research on the use of string diagrams to model natural languages, or, more specifically, to describe context-free grammars. I am interested in the use of pregroup grammars and Lambek's research on the development of visual programming languages. Zorkedon
    • CommentRowNumber7.
    • CommentAuthoratmacen
    • CommentTimeSep 4th 2019

    Re #6: This blog post is saying something very similar, using a monoidal category for sentence derivations. “That is, a string uV u \in V^\star is grammatical whenever there exists an arrow from the start symbol ss to uu in 𝒞 R\mathcal{C}_R.” Morphisms in monoidal categories can be notated using string diagrams.

    • CommentRowNumber8.
    • CommentAuthoralexis.toumi
    • CommentTimeSep 4th 2019
    The use of string diagrams to model natural language has become folklore in the DisCoCat (categorical compositional distributional) community, see e.g. Coecke et al. (2010) https://arxiv.org/abs/1003.4394
    As far as I'm aware there isn't any reference which spells out the details fully, which is part of the reason why I started this page, as well as the one on context-free grammars.
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