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1. • CommentRowNumber1.
   • CommentAuthortomr
   • CommentTimeApr 21st 2019
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   Author: tomr
   Format: MarkdownItexAs far as I understand - then each institution is designed for some logic. It has two categories - one for syntax (whose objects are signatures) and one for models, effectively - each pair of objects in those categories describe one theory for the logic of this institution. My question is: are there efforts to construct category of institutions - whose objects would be some logic? I am beginning to read https://academic.oup.com/logcom/article-abstract/27/6/1753/2687725 and the logical framework mentioned in this articles, seems to be the step in this direction, but this article is somehow detached from the other papers in institutional model theory, so, some comments would be welcome. Applications sometimes require to construct logic with some peculiar properties, e.g. field of normative reasoning and deontic logics is in search of paradox-free (purely philosophical notion, axiomatic level) deontic logic. So - maybe one can construct category of institutions and then find some universal property, some distinct object which would be the sought after deontic logic with excellent properties?

   As far as I understand - then each institution is designed for some logic. It has two categories - one for syntax (whose objects are signatures) and one for models, effectively - each pair of objects in those categories describe one theory for the logic of this institution.

   My question is: are there efforts to construct category of institutions - whose objects would be some logic?

   I am beginning to read https://academic.oup.com/logcom/article-abstract/27/6/1753/2687725 and the logical framework mentioned in this articles, seems to be the step in this direction, but this article is somehow detached from the other papers in institutional model theory, so, some comments would be welcome.

   Applications sometimes require to construct logic with some peculiar properties, e.g. field of normative reasoning and deontic logics is in search of paradox-free (purely philosophical notion, axiomatic level) deontic logic. So - maybe one can construct category of institutions and then find some universal property, some distinct object which would be the sought after deontic logic with excellent properties?

2. • CommentRowNumber2.
   • CommentAuthorThomas Holder
   • CommentTimeApr 23rd 2019
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   Author: Thomas Holder
   Format: MarkdownItexInstitutions organize into a 2-category - this discussed a bit in Diaconescu's monograph or his paper on "Grothendieck institutions" (see at [[institution]] for the exact references). The monograph has also some discussion of the institution for modal logic under which I suppose deontic logic would be subsumed. Though not expert in institutions I doubt it that one can crank out a specific deontic logic by abstract nonsense even among the subinstitutions for modal logic. Another perspective on paradoxes in deontic logic might be to study them via [[adjoint modality|adjoint modalities]] and the calculus of [[Aufhebung]].

   Institutions organize into a 2-category - this discussed a bit in Diaconescu’s monograph or his paper on “Grothendieck institutions” (see at institution for the exact references). The monograph has also some discussion of the institution for modal logic under which I suppose deontic logic would be subsumed.

   Though not expert in institutions I doubt it that one can crank out a specific deontic logic by abstract nonsense even among the subinstitutions for modal logic. Another perspective on paradoxes in deontic logic might be to study them via adjoint modalities and the calculus of Aufhebung.