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• CommentRowNumber1.
• CommentAuthorbblfish
• CommentTimeAug 24th 2014
• (edited Aug 24th 2014)

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:

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.

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?

• CommentRowNumber2.
• CommentAuthorspitters
• CommentTimeAug 29th 2014

Your project looks interesting. Are you aware of the recent work by Mike Stay on Splicious ?

I don’t think RDF per se fits the description of the nlab, we are not using it yet. If we did, it would be a meta topic, I think.

You are welcome to elaborate on functional programming and its categorical background. I am not sure whether algebraic graph transformations fit, if they do you could mention RDF as an example.

• CommentRowNumber3.
• CommentAuthorbblfish
• CommentTimeMay 1st 2016
• (edited May 1st 2016)

Hi here is an another earlier paper “Semantic Web Languages – Towards an Institutional Perspective” by Dorel Lucanu, Yuan Fang Li, and Jin Song Dong. (It still uses the awkward RDF/XML notation, which was the fashion at the time. The fashion now is JSON-LD. But actually the best notation is N3 (or its easy subset Turtle) )

The abstract:

Abstract. The Semantic Web (SW) is viewed as the next generation of the Web that enables intelligent software agents to process and aggregate data autonomously. Ontology languages provide basic vocabularies to semantically markup data on the SW. We have witnessed an increase of numbers of SW languages in the last years. These languages, such as RDF, RDF Schema (RDFS), the OWL suite of languages, the OWL− suite, SWRL, are based on different semantics, such as the RDFS-based, description logic-based, Datalog-based semantics. The relationship among the various semantics poses a challenge for the SW community for making the languages interoperable. Institutions provide a means of reasoning about software specifications regardless of the logical system. This makes it an ideal candidate to represent and reason about the various languages in the Semantic Web. In this paper, we construct institutions for the SW languages and use institution morphisms to relate them. We show that RDF framework together with the RDF serializations of SW languages form an indexed institution. This allows the use of Grothendieck institutions to combine Web ontologies described in various languages.

I am putting these forward as nForum seems like the right place to have links for the set of work being developed here. It is too advanced for me, but with time I may start understanding this.