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nLab > Latest Changes: differential linear logic

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1 to 13 of 13

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2021

    a stub, for the moment just so as to make links work at differential category

    v1, current

    • CommentRowNumber2.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 26th 2022

    I start thinking to this page. Just a few words and section titles that I’m going to complete.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 26th 2022

    What are the formulas used in DiLL.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 26th 2022

    More explanations

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 26th 2022

    I’ve started categorical semantics.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 8th 2022
    • (edited Aug 8th 2022)

    Page under construction. I’ve just added how to differentiate a proof but I haven’t written what comes before.

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 8th 2022

    Currently the entry says:

    The intuitive understanding of linear logic is difficult to extend to differential linear logic.

    Is that so? Isn’t the intended semantics in differential categories the intuition – in fact the motivation – behind differential linear logic?

    (Maybe it feels like this is a “semantical” and not a “logical” intuition – but to trilogicians, there is no such distinction. ;-)

    • CommentRowNumber8.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 8th 2022
    • (edited Aug 8th 2022)

    Yes, you’re right! This is fine for a trilogician. But it’s difficult to make concrete reasoning in differential linear logic, like the “Menu de Lafont” which explains linear logic in terms of the process of eating in a restaurant! You really need to become a trilogician when you go from linear logic to differential linear logic.

    I’m going to add your remark.

    • CommentRowNumber9.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 8th 2022

    Worked on the page.

    Including some improvment of the idea section.

    diff, v6, current

    • CommentRowNumber10.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 8th 2022

    Written all the inference rules…

    diff, v6, current

    • CommentRowNumber11.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 8th 2022

    Added an explanation of the meaning of the cut-elimination and the relation with commuting diagrams in categorical semantics.

    diff, v6, current

  12. fixed minor grammatical typos

    Wilf Offord

    diff, v9, current

  13. The manual redirect is no longer needed

    Empress of Light

    diff, v10, current

1 to 13 of 13

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