DL Riddle

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Yesterday we stumbled upon quite a hard description logics problem. At least I think it is hard. The question was, why is this ontology unsatisfiable? Just six axioms. The ontology is availbe in OWL RDF/XML, in PDF (created with the owl tools), and here in Abstract Syntax.

Class(Rigid complete restriction(subclassof allValuesFrom(complementOf(AntiRigid))))
Class(NonRigid partial)
DisjointClasses(NonRigid Rigid)
ObjectProperty(subclassof Transitive)
Individual(publishedMaterial type(NonRigid))
Individual(issue type(Rigid) value(subclassof publishedMaterial))

So, the question is, why is this ontology unsatisfiable? It is even a minimally unsatisfiable subset, actually, that means, remove any of the axioms and you get a satisfiable ontology. Maybe you like to use it to test your students. Or yourself. The debugger in SWOOP actually gave me the right hint, but it didn't offer the full explanation. I figured it out, after a few minutes of hard thinking (so, now you know how bad I am at DL).

Do you know? (I'll post the answer in the comments if no one else does in a few days)

(Just in case you wonder, this ontology is based on a the OntOWLClean ontology from Chris Welty, see his paper at FOIS2006 if you like more info)

Originally published on Semantic Nodix

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