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I was watching some lectures by Prof. Pfenning on Proof Theory. Between 5:30 and 15:00, he gave a list for some different kinds of judgments along with their calculus and computation phenomena that they can represent or model. I am looking for a more comprehensive list. I would like to compare and know the advantages and disadvantages of choosing some kind of logic/calculus to represent some kind of a computational phenomenon. Which field is focusing more on such comparisons and where to start?

For example, linear lambda calculus vs pi calculus for concurrent programming. Note that I am not interested in this particular example but just to get my question across. What other mathematical logics/calculi do we have and for what type of computations?

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  • $\begingroup$ No, I am not going to stare at this 37' video. $\endgroup$
    – user16034
    Commented Feb 6, 2023 at 11:22
  • $\begingroup$ @YvesDaoust I have specific the moment when this was mentioned in the video. Although, I think the question is already clear without the examples in the video. $\endgroup$
    – geeko
    Commented Feb 7, 2023 at 10:41
  • $\begingroup$ Crystal clear... $\endgroup$
    – user16034
    Commented Feb 7, 2023 at 11:23
  • $\begingroup$ @YvesDaoust Your attitude is too... which is more important than what you know ;) $\endgroup$
    – geeko
    Commented Feb 7, 2023 at 14:12

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