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Added some literature: - Entry to the encyclopedia of philosophy that brings the whole context historical and logical together. - 2 papers on RDF and institution theory. Given that RDF is so simple, and yet so widely understood, it will be an interesting way for many to get to grips with this.
Henry Story (@bblfish)
Thanks!
In general, nLab entries are committed to truth (and beauty) only in the long run in order to allow for a wide range of useful contributions starting with fixing typos. There is no need to stand in awe or else be shy when it comes to editing.
My interest in institutions stems from linguistics where there is a similar proliferation of grammar frameworks and comparison of grammars across signatures is a problem. Unfortunately, this was all way back then and the theory isn’t that present to me right now hence I am regretfully not well prepared to take a more active part.
Since institutions (or even classical model theory - although this has improved lately!) are somewhat peripheral to what most people here have an urgent interest in it would probably more promising to rise issues of a more general categorical nature arising in the context of institutions in order to make the nLab community responsive.
I have been looking at applying IT to RDF (see cstheory StackExchange Question). After discussing the way I modeled things with my maths tutor (Corina Cirstea) she insisted that the model M contains a function for interpretation too. And indeed we checked in “Semantic web languages–towards an institutional perspective” and they define the range of M for the Bare RDF Institution BRDF as the tuple I = (R, P, S, ext), which can rearranged for more clarity as (S, (R,P,ext)) or even more simply (S,M):
So the functor you called M, others call Mod, sends a signature to a category of interpretations, not just to one of models it seems. Hence the use of M or Mod seems very misleading. To use the symbol Int for Interpretation would also be problematic because it looks like integer. So I thought that this would perhaps be the place to use the ☿ symbol that represents Mercury the roman version of Hermes, the god of interpretations. So following the footsteps of the US president of making big announcements on social media I tweeted the following suggestion of a definition of an Institution:
“CategoryTheory defines an Institution of meaning as (Sig,☿,Sen, ⊨) where Sig is a category of symbols, ☿ a functor Sig → Cat, selecting a category of interpretations, Sen a functor from |Sig| → Set taking each sig $\Sigma$ to sentences and ⊨ as the satisfaction relation.”
If one had the Mod functor go directly to the Models, then an Institution would look much more like a David Lewisian (mathematical) language. That is the meaning of terms would be fixed for that language. In IT an Institution is open to all interpretations. That’s not immediately evident when reading the highly abstract texts on the subject.
Anyway, if the above is correct, then it seems ☿ would be a good symbol for the interpretation functor. But perhaps people know a better use for it?
[1] Lucanu, Dorel, Yuan Fang Li, and Jin Song Dong. “Semantic web languages–towards an institutional perspective.” Algebra, Meaning, and Computation. Springer, Berlin, Heidelberg, 2006. 99-123.
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