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

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

Received on Friday, 17 January 2020 23:51:49 UTC