Re: RDF Surfaces

Hi Henry (& All),

Long time no chat.  Thanks for the link, I knew I'd written
a smattering of initial thoughts about all this somewhere
on Mathstodon but lost track of where.  I don't know if
the work I've been doing will fit in here, but I'll make
what account I can make of it and we'll see.

Nice seeing everyone on the conference call.  It had to be mostly
a listening session on my part as I tend to be a bit too plodding
in my thought process to work well in those sorts of live media.

As I explained on Mathstodon, I began my study of Peirce — especially
his mathematical logic, theory of signs (semiotics), theory of inquiry
(logic of science), and logical graphs — from my earliest undergrad years
(late 60s).  I naturally turned each new programming language I learned to
work building theorem provers for his alpha graphs (propositional calculus).

The reason I'm telling you all this is to explain how I early on found myself
on a somewhat divergent path from a lot of the literature you'll read in any
one of several mainstream approaches to Peirce.

Okay, enough, I'm thinking I'll start a separate thread to fill out the story.

Regards,

Jon
https://mathstodon.xyz/@Inquiry
https://inquiryintoinquiry.com/
https://oeis.org/wiki/User:Jon_Awbrey
https://www.facebook.com/JonnyCache
https://independent.academia.edu/JonAwbrey


On 2/14/2023 12:29 PM, Henry Story wrote:
> A lot of the material I mentioned came up in the Toots starting here:
> https://mathstodon.xyz/@bblfish/109759820667709486
> 
> The most important and accessible paper that links RDF and Category theory is
> ”Knowledge Representation in Bicategories of Relations”
> https://arxiv.org/abs/1706.00526
> 
> That takes work by David Spivak, who argued around 2008 that databases can
> be modelled as functors from a small category (the schema) with equations
> between paths, to the Category of Set and functions between sets.
> https://www.youtube.com/watch?v=bk36__qkhrk
> 
> This actually a great way to learn category theory for computer scientists,
> as we all know what a DB is.
> 
> One can take any such database instances and map them to something that is
> has the very graph structure of RDF through the Grothendieck construction.
> 
> But the model works much better for RDF when one uses a
> mapping from small bicategories to the bicategory of relations. The great thing
> here is that one finds out that rdf is best located in the space of bicategories:
> where there are arrows between arrows. The arrow is rdfs:subPropertyOf and
> all inferences go through that.
> 
> One can then with the dual and also get negation.
> 
> There are then a number of papers that take Peirce to bicategories of relations too
> and so to first-order logic.
> https://mathstodon.xyz/@bblfish/109757608462711374
> 
> My feeling is that surfaces allow one to go somewhat further, perhaps even
> to the work Peirce did that goes beyond first-order logic (which I don’t know about).
> 
> Bicategories of relations have some very interesting properties relating
> it to the open world concepts and to biology
> https://www.youtube.com/watch?v=DAGJw7YBy8E
> 
> see:
> https://twitter.com/bblfish/status/1397962748429062145
> 
> The idea of a structural continuity between
> categories and RDF triples and quads, and as you will see with the picture at the
> end it does look like we end up with surfaces that way.
> 
> 
> 
> 
> That is not a peer-reviewed paper, and it has no proofs that go with it.
> But if useful, it may be something I could work on more carefully, perhaps with the help
> of a proof assistance such as Agda.
> 
> Henry
> 
> 
>> On 6. Feb 2023, at 11:25, Patrick Hochstenbach <Patrick.Hochstenbach@UGent.be> wrote:
>>
>> Dear all
>>   With the doodle we tried to pick a date for the RDF Surfaces call with the maximum number of participants. The date will be on Tuesday February 14th16:00-17:00 (CET). To check your local time use this website: http://www.timebie.com/std/centraleuropean.php?q=16
>>   We will meet using Jitsi (no software required to use this video platform)
>>   https://meet.jit.si/EasternGallonsIntendBlindly
>>
>> The agenda of the meeting will be a short introduction followed by a short rationale why we are investigating RDF Surfaces (or ‘BLOGIC’ as proposed by Pat Hayes) for semantic web use cases. Based on this we open the discussion and would like to hear about your interest in RDF Surfaces and discuss ways to move forward.
>>
>> BR
>> Patrick
> 
> Henry Story
> 
> https://co-operating.systems
> WhatsApp, Signal, Tel: +33 6 38 32 69 84‬
> Twitter: @bblfish
>

Received on Tuesday, 14 February 2023 22:45:25 UTC