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

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?

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
>
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Received on Saturday, 18 January 2020 05:39:12 UTC