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

Hi Henri,

Here's my feedback in a nutshell.

Coherent logic formulae were expressed in N3 and used an ugly way to
express disjunction in the conclusion of log:implies. It would have
been nice to use use a '|' to separate the conclusions but that would
have required an extension of N3 which was not feasable. For an example
see the Pappus Desargues Hessenberg [1] test case at [2], [3], [4] and [5].

In EYE we impemented a so called "branch engine" on top of the original
"trunk engine". The former engine is like a Skolem Machine [6] whereas
the latter is a forward backward chainer (backward chaining for rules
using <= in N3 and forward chaining for rules using => in N3).

Althoug we came up with challenging use cases in the building construction
domain and in the healtcare and life science domain we were not seeing
that is was used. It is not good to maintain an engine that is not used
hence we removed the branch engine some years ago.

Kind regards,
Jos

[1] https://en.wikipedia.org/wiki/Desargues%27s_theorem#Relation_to_Pappus's_theorem
[2] https://github.com/w3c/N3/blob/master/grammar/tests/N3Tests/07test/pd_hes_theory.n3
[3] https://github.com/w3c/N3/blob/master/grammar/tests/N3Tests/07test/pd_hes_tactic.n3
[4] https://github.com/w3c/N3/blob/master/grammar/tests/N3Tests/07test/pd_hes_query.n3
[5] https://github.com/w3c/N3/blob/master/grammar/tests/N3Tests/07test/pd_hes_result.n3
[6] https://skolemmachines.org/



Jos De Roo     | Agfa HealthCare
Data Scientist | HE/Clinical Analytics
http://josd.github.io/

Agfa HealthCare NV, Moutstraat 100, B-9000 Gent, Belgium
http://www.agfa.com/healthcare

________________________________
From: Henry Story <henry.story@bblfish.net>
Sent: 18 January 2020 00:51
To: semantic-web <semantic-web@w3.org>
Subject: 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