Re: same-syntax extensions to RDF

> On Thu, 2004-12-16 at 00:11 -0500, Sandro Hawke wrote:
> [...]
> > So most of the LX ontology is just a straightforward transcription of
> > a textbook description of FOL syntax into the slightly odd world of
> > RDF triples, where rather than the BNF
> > 
> >     <conjunction> ::= <formula> '&' <formula>
> > 
> > we have Conjunction as a class, and two properties conjLeft and
> > conjRight with domain Formula and range Conjunction.
> 
> But you also mean to say that "any fin[it]e number of applications
> of these rules yeilds an element of the class Formula" and such,
> right? That's a case of "generalization to infinitely many cases".
>  http://www.w3.org/DesignIssues/Logic#L736

Isn't that roughly:

   all Conj (
      rdf(Conj, rdf_type, lx_Conjunction)
      <->
      (  exists Left Right (
            rdf(Conj, lx_conjLeft, Left),
            rdf(Conj, lx_conjRight, Right),
	    rdf(Left, rdf_type, lx_Formula),
	    rdf(Right, rdf_type, lx_Formula)
         )
      )
   ).

?   The "any number of applications" notion gets expressed via forall.


> i.e. it's not a first-order system.

I'm not sure the clearest way to talk about the levels, or what
constitutes "the system".

My application scenario is that someone wants to transmit FOL
assertions through an RDF channel.  The RDF channel is subject to the
usual merging, erasure, open-world, etc, issues.  The end queries will
be about the presense (entailment) of RDF triples.   

    Alice wants to say "All greek:man are greek:mortal".

    She writes that down in FOL, she describes and asserts that FOL
    in RDF using LX.

    She sends the RDF triples to Bob.

    Bob stuffs them into his triples store that implements LX
    inference.  He also adds "Socrates rdf:type greek:man".  Now he
    queries whether "Socrates rdf:type greek:mortal" and is told Yes
    (with provenance pointing to his addition about Socrates and the
    triples from Alice, and maybe the LX inference machinery).

Or something like that.  Lots of variations.   

     -- sandro

Received on Thursday, 16 December 2004 15:44:58 UTC