- From: Henry Story <henry.story@bblfish.net>
- Date: Sun, 19 Jan 2020 11:19:48 +0100
- To: Mike Bergman <mike@mkbergman.com>
- Cc: semantic-web@w3.org
> On 18 Jan 2020, at 06:39, Mike Bergman <mike@mkbergman.com> 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 >> > -- > >
Received on Sunday, 19 January 2020 10:19:54 UTC