Re: Coherent Logic (a.k.a Geometric Logic) and RDF?

> On 18 Jan 2020, at 06:39, Mike Bergman <[email protected]> wrote:
> 
> Hi Henry,
> 
> The Patterson paper is an excellent intro to DL as well. A hearty thanks for this reference. I would be interested to see how extensions to OWL 2 might accomplish the 'typing' objectives noted by Patterson. Do you know of any efforts in that direction?

I don’t know the answer to that, but I have a question open for it
on the web-cats repo
"Is OWL/RDF typed or untyped? Should it be?"
https://gitlab.com/web-cats/CG/issues/9

Henry

> 
> Thanks!
> 
> Best, Mike
> 
> On 1/17/2020 5:51 PM, Henry Story wrote:
>> Hi,
>> 
>>    I came across Coherent Logic recently. Apparently it is
>> as expressive as First Order Logic. And I found that it was used
>> by Jos De Roo’s EYE implementation of an N3 reasoner. [1]
>> I was wondering what the feedback of its use was in the field, and
>> return on experience on how it fit into the Semantic Web stack.
>> 
>> I came across it by reading an excellent  2017 paper by
>> Evan Patterson [2]
>> "Knowledge Representation in Bicategories of Relations”
>> 
>> Where David Spivak (MIT) has put together some very elegant
>> work showing how Category Theory could be applied to Databases,
>> and in a number of articles tying these to RDF and SPARQL, the
>> problem has been that his Database instances are functors from
>> a small Category playing the role of a Schema into the Category Set,
>> where objects are Sets and morphisms are functions. This does
>> not fit well with RDF as many relations such as foaf:knows
>> are not functional.
>> 
>> By adapting this functorial semantics and instead of using
>> normal Categories for Schemas, Patterson uses Bicategories of relations
>> which can have morphisms between morphisms (giving us
>> inference). Then when representing DB instances as functors
>> into the Category Rel, where objects are Sets and morphisms
>> are relations, we get much closer to RDF.
>> Indeed Patterson starts off his discussion with Description Logics.
>> 
>> (Note by the way that both Spivak and Patterson, point to a
>> fundamental concept in Category Theory known as the Grothendieck
>> construction that takes a tabular database and turns it into
>> the flattened structure of RDF, this itself being essential in
>> analyses of SQL or SPARQL Queries)
>> 
>> Now the first part of the paper shows that ”regular logic is the
>> internal language of bicategories of relations”. The final
>> section shows that ”distributive relational ontology logics (ologs)”
>> correspond to Coherent Logic.
>>  This way of putting things gives a special place to ”regular
>> logic” and ”coherent logic”. So I searched around and found
>> the latter used by Jos de Roo’s N3 reasoner EYE, which seems
>> to somewhat confirm Patterson’s modeling of RDF.
>> 
>> 
>> Henry Story
>> 
>> [1] See Twitter thread https://twitter.com/bblfish/status/1215024256985247745
>> [2] https://www.epatters.org/assets/papers/2017-relational-ologs.pdf
>> 
> -- 
> 
>