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FOL interpretation possible for 'A subclassOf r some B' ? #159

Open GoogleCodeExporter opened 9 years ago

GoogleCodeExporter commented 9 years ago 
Given the independent continuants A and B, I still think that one can 
axiomatically define that the following two expressions should have the same 
interpretation: 

1. OWL-DL
A subclassOf r² some B 

2. FOL
(forall (?a ?t)
    (implies (instance-of ?a A ?t))
             (exists (?b)
                 (and (instance-of ?b B ?t) (r³ ?a ?b ?t))))

Note the difference between r² (OWL object property) and r³ (ternary 
relation), which are NOT the same.

r² would have no straightforward interpretation in an OWL ABox

See also formula (9) - (11) in the Grewe paper

Original issue reported on code.google.com by steschu@gmail.com on 12 Mar 2013 at 10:41

GoogleCodeExporter commented 9 years ago 
Can you provide a profile of OWL2-DL that it is possible to translate in this 
way?

Something similar to what Fabian did:
http://common-logic.1085828.n5.nabble.com/OWL-gt-CL-td2151.html

But with additional translations for ternary relations for some class axioms.

Example:
(r2 some A) DisjointWith (r2 some B) 

yields:

(forall (?a ?b ?x ?y ?t)
    (if (and (instance-of ?a A ?t)
             (instance-of ?b B ?t)
             (r3 ?x ?a ?t)
             (r3 ?y ?b ?t)
        (not (= ?x ?y)))))

[not checked]

via some intermediate translations.

If we can find a profile (preferably closely corresponding to profiles commonly 
used) then I think we have made progress. Perhaps then we could simply weaken 
principles #1 from "A clear reading of the OWL version in terms of BFO 
reference" to "A clear reading of the Foo subset of the OWL version in terms of 
BFO reference".

Original comment by cmung...@gmail.com on 12 Mar 2013 at 11:19

GoogleCodeExporter commented 9 years ago 
Hey Chris, 
Went to the referenced thread (thanks). But Fabian's translation is cited to be 
at http://userpages.umbc.edu/~fneuhaus/OWLToCL and that's 404 now. Do you have 
a copy?

Original comment by alanruttenberg@gmail.com on 13 Mar 2013 at 12:25

GoogleCodeExporter commented 9 years ago 
No, I asked him though

Original comment by cmung...@gmail.com on 13 Mar 2013 at 12:49