Re: Rules for converting from FOL->DL(OWL)?

On 31 Jan 2005, at 05:26, Harry Halpin wrote:
> I am working on a converter for some logical facts from my own 
> internal XML format to OWL. I want to get this right as this is about 
> a million facts, so running the XSL and theorem-prover takes hours! 
> This is a long e-mail, but I give the rules for my converter in both 
> logical form and a FOL XML language based on Discourse Representation 
> Theory (a notational variant of FOL, Kamp and Reyle) into OWL. I tried 
> to be somewhat formal here, but provide concrete syntax as well in my 
> own XML format and OWL. Note that I *know* DL (OWL) is less expressive 
> and has a different model than FOL :)
> However, I am trying to find a subset of FOL that can be converted 
> into DL in a rational manner, so that it can be converted back into 
> FOL and have the same model. This may be very small fragment indeed, 
> or this may be impossible. Still, here's my shot at it.

First of all, I warmly suggest you the read first the chapter in the DL 
handbook on NLP:
Enrico Franconi. Description Logics for Natural Language Processing. 
Chapter in the Description Logics Handbook, edited by F. Baader, D. 
Calvanese, D. L. McGuinness, D. Nardi and P. F. Patel-Schneider, 
Cambridge University Press, December 2002. 
<http://www.inf.unibz.it/~franconi/papers/dlhb-nlp.ps.gz>.

There you can find answers to many of your problems, including the 
davidsonian approach in DL, DRT with DL,  reification, and generalised 
quantifiers (and their limits in DL).
In particular, given the particular nature of your FOL sentences, your 
basic translation problem is easier than you may think.

The main observation is that the logical form is basically an 
existential conjunctive formula. If we assume that its co-reference 
graph is acyclic (a co-reference graph includes literals and variables 
as nodes, and labelled edges indicate the positional presence of a 
variable in a literal), that is mainly true in absence of anaphoric 
expressions, then you can easily encode the logical form correctly and 
completely in OWL-DL by means of a rolling up procedure; see:
Ian Horrocks and Sergio Tessaris. Querying the semantic web: a formal 
approach. In Proc. of the 2002 International Semantic Web Conference 
(ISWC 2002), Springer-Verlag, 2002. 
<http://www.inf.unibz.it/~tessaris/papers/iswc2002.pdf>.

If the co-reference graph is cyclic, then you can resort to a reasoner 
handling DLs and conjunctive queries (see the handbook paper).
Note that the presence of universals (or similar general quantifiers) 
makes the problem much tougher; see, e.g., :
Enrico Franconi (1993). A treatment of plurals and plural 
quantifications based on a theory of collections. Minds and Machines 
(3)4:453-474, Kluwer Academic Publishers, November 1993. 
<http://www.inf.unibz.it/%7Efranconi/papers/mm-93.ps.gz>.

Have fun!
cheers
--e.

Enrico Franconi                  - franconi@inf.unibz.it
Free University of Bozen-Bolzano - http://www.inf.unibz.it/~franconi/
Faculty of Computer Science      - Phone: (+39) 0471-016-120
I-39100 Bozen-Bolzano BZ, Italy  - Fax:   (+39) 0471-016-129

Received on Tuesday, 1 February 2005 07:21:45 UTC