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FOL interpretation possible for 'A subclassOf r some B' ? #158

Open zhengj2007 opened 9 years ago

zhengj2007 commented 9 years ago

From steschu@gmail.com on March 12, 2013 18:41:05

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: http://code.google.com/p/bfo/issues/detail?id=159

zhengj2007 commented 9 years ago

From cmung...@gmail.com on March 12, 2013 16:19:21

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".