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In his 1958 paper, The Mathematics of Sentence Structure, Joachim Lambek introduced the Lambek calculus. In modern terms, it could be understood as a syntax for biclosed monoidal categories, and he remarked that it was very similar to a calculus for linear algebra he had worked on with G. D. Findlay -- Calculus of Bimodules (apparently never published).

I am interested in papers applying Lambek-calculus style methods to linear algebra. So far, I have only found Lambek's original paper, and D. Stott Parker's 1997 paper Schur complements obey Lambek's categorial grammar: Another view of Gaussian elimination and LU decomposition.

  1. Does anyone know of an online source for G. D. Findlay and J. Lambek's Calculus of Bimodules? I can't find it.
  2. Can anyone point me to other papers formulating results in linear algebra in terms of the proof theory of categorial logic (and similar systems like linear logic)?
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    $\begingroup$ Completely off topic and unrelated to to this question (which I apologize for) but I believe you may find some interest in this question on rpg.stackexchange: Which Article Helped Get Rid of Technobabble in RPGs?. Unless I'm mistaken you wrote the article in question. $\endgroup$
    – Mr.Mindor
    Commented Mar 21, 2019 at 22:25

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