ISSUE-119

russell paradox

OWL 2 Full may become inconsistent due to self restrictions

State:

CLOSED

Product:

Raised by:

Michael Schneider

Opened on:

2008-04-20

Description:

If the OWL 2 Full semantics for self restrictions is specified analogue to the semantics of restrictions in OWL 1 Full, then OWL 2 Full will become unsatisfiable.

RDF compatible semantics treat rdf:type as a normal property. The introduction of self restrictions into OWL 2 Full allows to define classes which have the famous Russell set "{x| x notin x}" as their class extension.

  _:c rdf:type owl:Class .
  _:c owl:complementOf _:s .
  _:s rdf:type owl2:SelfRestriction .
  _:s owl:onProperty rdf:type .

For every restriction and every boolean constructor in OWL 1 Full there are (unconstrained) comprehension principles. An analogue comprehension principle for self restrictions would have the form (informally stated):

  "IF 
    we have property p
  THEN 
    there exists a class S 
    which is a self restriction on p"

Since

  rdf:type rdf:type rdf:Property

is true in every RDF ontology, the above comprehension principle would provide the existence of a Russell class in every OWL 2 Full ontology. This would lead to inconsistency of OWL 2 Full, which means that the empty RDF graph would not have any model when interpreted under OWL 2 Full semantics.

There are different possible ways to avoid this problem by weakening the semantics accordingly. It has to be decided, which solution to choose.

Related Actions Items:

• ACTION-139 on Ian Horrocks to Shepherd/coordinate the patching process (per ISSUE 119) - due 2008-05-14, closed
• ACTION-152 on Michael Schneider to OWL Full Semantics - due 2008-08-24, closed

Related emails:

1. Re: My answers to Jie Bao's review of the Full Semantics (from baojie@cs.rpi.edu on 2008-09-17)
2. My answers to Jie Bao's review of the Full Semantics (from schneid@fzi.de on 2008-09-12)
3. RE: Issue-119 OWL 2 Full may become inconsistent due to self restrictions (from schneid@fzi.de on 2008-09-07)
4. Issue-119 OWL 2 Full may become inconsistent due to self restrictions (from ian.horrocks@comlab.ox.ac.uk on 2008-09-06)
5. Re: [FULL] ISSUE-119: the other approach (from jjc@hpl.hp.com on 2008-05-21)
6. RE: [FULL] ISSUE-119: the other approach (from schneid@fzi.de on 2008-05-20)
7. Re: [FULL] ISSUE-119: the other approach (from ian.horrocks@comlab.ox.ac.uk on 2008-05-19)
8. RE: ISSUE-119: What can be done against the Russell paradox? (from schneid@fzi.de on 2008-04-30)
9. [FULL] ISSUE-119: the other approach (from jjc@hpl.hp.com on 2008-04-28)
10. Re: ISSUE-119: What can be done against the Russell paradox? (from pfps@research.bell-labs.com on 2008-04-28)
11. RE: ISSUE-119: What can be done against the Russell paradox? (from schneid@fzi.de on 2008-04-28)
12. Re: ISSUE-119: What can be done against the Russell paradox? (from pfps@research.bell-labs.com on 2008-04-27)
13. RE: ISSUE-119: What can be done against the Russell paradox? (from schneid@fzi.de on 2008-04-27)
14. RE: ISSUE-119: What can be done against the Russell paradox? (from schneid@fzi.de on 2008-04-26)
15. ISSUE-119: What can be done against the Russell paradox? (from schneid@fzi.de on 2008-04-26)
16. Re: ISSUE-119: What can be done against the Russell paradox? (from pfps@research.bell-labs.com on 2008-04-25)
17. Re: ISSUE-119: What can be done against the Russell paradox? (from pfps@research.bell-labs.com on 2008-04-25)
18. Withdrawl ISSUE-117 (from jjc@hpl.hp.com on 2008-04-22)
19. RE: ISSUE-119 (russell paradox): OWL 2 Full may become inconsistent due to self restrictions (from schneid@fzi.de on 2008-04-21)
20. Re: ISSUE-119 (russell paradox): OWL 2 Full may become inconsistent due to self restrictions (from jjc@hpl.hp.com on 2008-04-21)
21. RE: ISSUE-119 (russell paradox): OWL 2 Full may become inconsistent due to self restrictions (from schneid@fzi.de on 2008-04-21)
22. Re: ISSUE-119 (russell paradox): OWL 2 Full may become inconsistent due to self restrictions (from jjc@hpl.hp.com on 2008-04-21)
23. ISSUE-119 (russell paradox): OWL 2 Full may become inconsistent due to self restrictions (from sysbot+tracker@w3.org on 2008-04-20)

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