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)
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