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    • CommentRowNumber1.
    • CommentAuthorbblfish
    • CommentTimeSep 17th 2018
    • (edited Sep 17th 2018)

    I was just wondering why there was so little on “Institution independent Model Theory” or Absrtact Model Theory in the wiki. I found this short entry for Abstract Model Theory, and a link to yet non existing page on institutions.

    I am trying to use this to see if this can help me extend the semantic Web semantics to modal logic. The reason is that institutions have been used to show the coherence between the different RDF logics - RDFS, OWL, … and so it seems that it should be helpful to go beyond that.

    Some papers on semantic web and institutions are listed below. These are great because the semantic web is quite simple, useful, - and I understand it well - and these show in a practical way how to think about institutions, which would be otherwise much more difficult to get into. Also the basics of Abstract Model theory are quite intuitive

    The last one ties rdf to Contexts and to Institutions.

    The RDF model is actually really simple btw. See the question and answer “What kind of Categorical object is an RDF Model?

    It is nearly self evident from using it that RDF already contains modal logic (see my short example on semweb mailing list), especially as for RDF1.0 xml syntax one can have relations to RDF/XML literals, whose interpretations are of course sets of models, and in RDF1.1 this is made clearer with the notion of DataSets which are sets of graphs. But they have not given a semantics for it… But self evidence does not make for a proof. (and by the way, RDF/XML is really the ugliest syntax existing. Much better to consider N3 which is Tim Berners-Lee’s neat notation for doing logic on the web.

    Btw, as an extra part the discussion on modal logic in RDF is tied up with the notion of context, which may just be another way of thinking of modal logic (I am working to see if there is a difference)

    So because there was little on the wiki on abstract model theory I was wondering if that was not quite thought of as good Category Theory, or if there just had not been time to complete that page. And for Contexts I was wondering if this was the right place to look at. In the book “Institution independent Model Theory” R Diaconescu has a chapter on Kripke frames, but I think we actually need neighborhood semantics, that is not relations between one world and another but between one world and a set of worlds. So that one can represent inconsistent sets of ideas. (which the web really is a big example of)

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 17th 2018

    if there just had not been time to complete that page.

    yes :-)

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeSep 17th 2018

    The answer to your first question is the evident one. No one has written more as yet. Perhaps you could see a way to creat some pages on Institutions etc. as a way to express what you are investigating.

    Remember it says on the Home page:

    The purpose of the nnLab is to provide a public place where people can make notes about stuff. The purpose is not to make polished expositions of material; that is a happy by-product.

    Another happy biproduct is that sometimes people working on their open Lab notes see otherwise hidden links with other peoples ideas. I was interested in the semantic Web at one time but never got in far enough to make any useful progress.

    • CommentRowNumber4.
    • CommentAuthorbblfish
    • CommentTimeSep 17th 2018
    • (edited Sep 17th 2018)

    Thanks David, Tim for you replies.

    I was asking because I could not discount the possibility that Institutions might have gone out of fashion in Category Theory, somehow having been replaced by something better. (Note that as the preceding sentence is one requiring counterfactual modal logic involving a mathematical sentence, it would require a modal logic with impossible worlds to model it)

    I am not yet good enough to contribute to the wiki: indeed I am only just now at the point of being able to read it. When I am closer to completing my thesis (in the next 1.5 years), I’ll feel more confident to contribute. At least I’ll be able to write up a page on RDF and Category Theory, as that is a key part of what I am doing.

    Well I could open the following wiki pages at present:

    • 1 on Category Theory and RDF (perhaps just call it RDF) and list all the key papers I know on that (I think there are 4)
    • one on Contexts and list the papers I mentioned above
    • Modal Logic and Category Theory (I have a number of papers and thesis on the subject) which I could put up.

    That is as much as I can do now. That might spur others to notice some parallels that I could explore. And with time I could attempt to add some summaries.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 17th 2018

    The selection of category theory contained in the nLab is purely down to the taste of the active authors. There are many things that aren’t included or covered in detail and that is because the nLab is not an encyclopedia. :-) If there were more active category-theorist authors with broader tastes then more areas would be represented.

  1. Re #4: Your suggestions sound good to me, please go ahead! Thanks for your interest and for asking your question here!

    • CommentRowNumber7.
    • CommentAuthorbblfish
    • CommentTimeSep 18th 2018
    • (edited Sep 18th 2018)

    Just to tie things together here is a pointer to the other question I asked a few years ago here on the Category of RDF described by Benjamin Braatz - in his thesis. He came to Category theory via Graph Theory, and was the one who pointed me to Institution Theory, which he mentioned in his thesis. (I was too frightened to read up about it until a month ago, and it actually is not that frightening when one has some good examples of use, as listed in initial post above).

    • CommentRowNumber8.
    • CommentAuthorbblfish
    • CommentTimeSep 18th 2018
    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2018

    as you may have seen, Thomas Holder kindly made a start with beginning an entry institution (see also the nForum thread here)

    • CommentRowNumber10.
    • CommentAuthorbblfish
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)

    Oh Wow! I already feel more confident now. I think I could have written what Thomas Holder wrote myself (not quite as well). Indeed I wrote something similar summary on the Stack Exchange question. (which I duplicated on cstheory as someone in the maths community suggested that may be better. I thought HoTT showed that we’re all doing the same thing…) :-)

    Yesterday I wrote up a summary of the long discussion with Pat Hayes on the subject of Category Theory, Modal Logic, and RDF, with as many of the links to papers that I noticed.

    I added some of the relevant links to that wiki page.