Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorThomas Holder
    • CommentTimeSep 18th 2018

    Provided a bare minimum so as to ungrey the link. Feel free to expand/correct.

    v1, current

  1. 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)

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorThomas Holder
    • CommentTimeSep 20th 2018
    • (edited Sep 20th 2018)


    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.

  2. fixed typo

    Henry Story (@bblfish)

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorbblfish
    • CommentTimeOct 1st 2018
    • (edited Oct 1st 2018)

    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):

    • M being the model without interpretations, what David Lewis would use for possible world for example. Talk about structures make me think of something like this too.
    • S (semantics?) is the function that assigns to each symbols in the signature a resource in the model.

    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 Σ\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.

  3. Fix typo


    diff, v4, current