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

- Lucanu, D., Li, Y. F., & Dong, J. S. (2006). Semantic web languages–towards an institutional perspective. In Algebra, Meaning, and Computation (pp. 99-123). Springer, Berlin, Heidelberg.
- Bao, J., Tao, J., McGuinness, D. L., & Smart, P. (2010). Context representation for the semantic web.

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.

- Berners-Lee, T., Connolly, D., Kagal, L., Scharf, Y., & Hendler, J. (2008). N3logic: A logical framework for the world wide web. Theory and Practice of Logic Programming, 8(3), 249-269.

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)

- Guha, R. V. (1991). Contexts: a formalization and some applications (Vol. 101). Stanford, CA: Stanford University.
- Hayes, P. (1997, November). Contexts in context. In Context in knowledge representation and natural language, AAAI Fall Symposium.
- Bizer, C., Carroll, J. J., Hayes, P., & Stickler, P. (2005). Named Graphs, Provenance and Trust. In Proceedings of the 14th international conference on World Wide Web.
- Hayes, P. (2007). Context Mereology. In AAAI Spring Symposium: Logical Formalizations of Commonsense Reasoning (pp. 59-64). This is I thought a really neat paper.
- Bao, J., Tao, J., McGuinness, D. L., & Smart, P. (2010). Context representation for the semantic web.
- Klarman, S. (2013). Reasoning with contexts in description logics.

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)

]]>The Semantic Web project started at the World Wide Web Consortium (W3C) is a widely deployed project explained officially with a Set theoretical semantics, which is designed to allow one to turn the web into a distributed database, useful for things like distributed social networks. It comes with various logic stacks, etc (RDFS, OWL,…) At the core of it is the RDF Resource Description Framework which comes with RDF semantics

This group may find the thesis Formal Modelling and Application of Graph Transformations in the Resource Description Framework very interesting as it puts the various RDF semantics directly in terms of category theory. For people coming from RDF that is a great way to learn category theory, for those from category theory this is a great way to learn RDF - and to contribute. It would be useful then to tie this in to other concepts from category theory, so that those coming from the RDF world can explore from this basis the space of category theory. Here is the abstract:

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In this thesis, a connection between two areas of research is developed. On the one hand, the Resource Desription Framework (RDF) is the basis of the Semantic Web. On the other hand, algebraic graph transformation has a long history of providing formally well-founded modification concepts for various graph and graph-like structures.
By designing an algebraic transformation approach for RDF, the rich theoretical res- ults of algebraic graph transformation are made available to the RDF world. To achieve this goal, the formal abstract syntax and semantics of RDF is first reformulated in the language of category theory which is used heavily in graph transformation. Then, an abstract, categorical transformation framework is developed which is suitable for being afterwards instantiated by RDF structures. This is necessary since the existing frame- works are not applicable in an unmodified form.
The main theoretical results are a sequential composition operation for transformation rules and theorems showing the possibility to analyse and synthesise transformations for these sequentially composed rules. Moreover, these results are also available for transformation rules with negative application conditions.
The applicability of the resulting concept of RDF graph transformations is shown by two application scenarios. One is a classical Semantic Web application managing bibliographical metadata, while the other uses RDF as an abstract syntax for domain- specific modelling languages.
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RDF has very practical uses. For example to see how RDF can be used to build Distributed Secure Social Networks see for example the ReadWriteWeb project. That project is written in Scala, which has libraries such as scalaz that use a lot of Category Theory, which is why I am here :-)

Does it make sense to add this category to the wiki?

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